Tag Archives: Computational models

If you want to be cited, calibrate your agent-based model: A Reply to Chattoe-Brown

By Marijn A. Keijzer

This is a reply to a previous comment, (Chattoe-Brown 2022).

The social simulation literature has called on its proponents to enhance the quality and realism of their contributions through systematic validation and calibration (Flache et al., 2017). Model validation typically refers to assessments of how well the predictions of their agent-based models (ABMs) map onto empirically observed patterns or relationships. Calibration, on the other hand, is the process of enhancing the realism of the model by parametrizing it based on empirical data (Boero & Squazzoni, 2005). We would expect that presenting a validated or calibrated model serves as a signal of model quality, and would thus be a desirable characteristic of a paper describing an ABM.

In a recent contribution to RofASSS, Edmund Chattoe-Brown provocatively argued that model validation does not bear fruit for researchers interested in boosting their citations. In a sample of articles from JASSS published on opinion dynamics he observed that “the sample clearly divides into non-validated research with more citations and validated research with fewer” (Chattoe-Brown, 2022). Well-aware of the bias and limitations of the sample at hand, Chattoe-Brown calls on refutation of his hypothesis. An analysis of the corpus of articles in Web of Science, presented here, could serve that goal.

To test whether there exists an effect of model calibration and/or validation on the citation counts of papers, I compare citation counts of a larger number of original research articles on agent-based models published in the literature. I extracted 11,807 entries from Web of Science by searching for items that contained the phrases “agent-based model”, “agent-based simulation” or “agent-based computational model” in its abstract.[1] I then labeled all items that mention “validate” in its abstract as validated ABMs and those that mention “calibrate” as calibrated ABMs. This measure if rather crude, of course, as descriptions containing phrases like “we calibrated our model” or “others should calibrate our model” are both labeled as calibrated models. However, if mentioning that future research should calibrate or validate the model is not related to citations counts (which I would argue it indeed is not), then this inaccuracy does not introduce bias.

The shares of entries that mention calibration or validation are somewhat small. Overall, just 5.62% of entries mention validation, 3.21% report a calibrated model and 0.65% fall in both categories. The large sample size, however, will still enable the execution of proper statistical analysis and hypothesis testing.

How are mentions of calibration and validation in the abstract related to citation counts at face value? Bivariate analyses show only minor differences, as revealed in Figure 1. In fact, the distribution of citations for validated and non-validated ABMs (panel A) is remarkably similar. Wilcoxon tests with continuity correction—the nonparametric version of the simple t test—corroborate their similarity (W = 3,749,512, p = 0.555). The differences in citations between calibrated and non-calibrated models appear, albeit still small, more pronounced. Calibrated ABMs are cited slightly more often (panel B), as also supported by a bivariate test (W = 1,910,772, p < 0.001).

Picture 1

Figure 1. Distributions of number of citations of all the entries in the dataset for validated (panel A) and calibrated (panel B) ABMs and their averages with standard errors over years (panels C and D)

Age of the paper might be a more important determinant of citation counts, as panels C and D of Figure 1 suggest. Clearly, the age of a paper should be important here, because older papers have had much more opportunity to get cited. In particular, papers younger than 10 years seem to not have matured enough for its citation rates to catch up to older articles. When comparing the citation counts of purely theoretical models with calibrated and validated versions, this covariate should not be missed, because the latter two are typically much younger. In other words, the positive relationship between model calibration/validation and citation counts could be hidden in the bivariate analysis, as model calibration and validation are recent trends in ABM research.

I run a Poisson regression on the number of citations as explained by whether they are validated and calibrated (simultaneously) and whether they are both. The age of the paper is taken into account, as well as the number of references that the paper uses itself (controlling for reciprocity and literature embeddedness, one might say). Finally, the fields in which the papers have been published, as registered by Web of Science, have been added to account for potential differences between fields that explains both citation counts and conventions about model calibration and validation.

Table 1 presents the results from the four models with just the main effects of validation and calibration (model 1), the interaction of validation and calibration (model 2) and the full model with control variables (model 3).

Table 1. Poisson regression on the number of citations

# Citations
(1) (2) (3)
Validated -0.217*** -0.298*** -0.094***
(0.012) (0.014) (0.014)
Calibrated 0.171*** 0.064*** 0.076***
(0.014) (0.016) (0.016)
Validated x Calibrated 0.575*** 0.244***
(0.034) (0.034)
Age 0.154***
(0.0005)
Cited references 0.013***
(0.0001)
Field included No No Yes
Constant 2.553*** 2.556*** 0.337**
(0.003) (0.003) (0.164)
Observations 11,807 11,807 11,807
AIC 451,560 451,291 301,639
Note: *p<0.1; **p<0.05; ***p<0.01

The results from the analyses clearly suggest a negative effect of model validation and a positive effect of model calibration on the likelihood of being cited. The hypothesis that was so “badly in need of refutation” (Chattoe-Brown, 2022) will remain unrefuted for now. The effect does turn positive, however, when the abstract makes mention of calibration as well. In both the controlled (model 3) and uncontrolled (model 2) analyses, combining the effects of validation and calibration yields a positive coefficient overall.[2]

The controls in model 3 substantially affect the estimates from the three main factors of interest, while remaining in expected directions themselves. The age of a paper indeed helps its citation count, and so does the number of papers the item cites itself. The fields, furthermore, take away from the main effects somewhat, too, but not to a problematic degree. In an additional analysis, I have looked at the relationship between the fields and whether they are more likely to publish calibrated or validated models and found no substantial relationships. Citation counts will differ between fields, however. The papers in our sample are more often cited in, for example, hematology, emergency medicine and thermodynamics. The ABMs in the sample coming from toxicology, dermatology and religion are on the unlucky side of the equation, receiving less citations on average. Finally, I have also looked at papers published in JASSS specifically, due to the interest of Chattoe-Brown and the nature of this outlet. Surprisingly, the same analyses run on the subsample of these papers (N=376) showed a negative relationship between citation counts and model calibration/validation. Does the JASSS readership reveal its taste for artificial societies?

In sum, I find support for the hypothesis of Chattoe-Brown (2022) on the negative relationship between model validation and citations counts for papers presenting ABMs. If you want to be cited, you should not validate your ABM. Calibrated ABMs, on the other hand, are more likely to receive citations. What is more, ABMs that were both calibrated and validated are most the most successful papers in the sample. All conclusions were drawn considering (i.e. controlling for) the effects of age of the paper, the number of papers the paper cited itself, and (citation conventions in) the field in which it was published.

While the patterns explored in this and Chattoe-Brown’s recent contribution are interesting, or even puzzling, they should not distract from the goal of moving towards realistic agent-based simulations of social systems. In my opinion, models that combine rigorous theory with strong empirical foundations are instrumental to the creation of meaningful and purposeful agent-based models. Perhaps the results presented here should just be taken as another sign that citation counts are a weak signal of academic merit at best.

Data, code and supplementary analyses

All data and code used for this analysis, as well as the results from the supplementary analyses described in the text, are available here: https://osf.io/x9r7j/

Notes

[1] Note that the hyphen between “agent” and “based” does not affect the retrieved corpus. Both contributions that mention “agent based” and “agent-based” were retrieved.

[2] A small caveat to the analysis of the interaction effect is that the marginal improvement of model 2 upon model 1 is rather small (AIC difference of 269). This is likely (partially) due to the small number of papers that mention both calibration and validation (N=77).

Acknowledgements

Marijn Keijzer acknowledges IAST funding from the French National Research Agency (ANR) under the Investments for the Future (Investissements d’Avenir) program, grant ANR-17-EURE-0010.

References

Boero, R., & Squazzoni, F. (2005). Does empirical embeddedness matter? Methodological issues on agent-based models for analytical social science. Journal of Artificial Societies and Social Simulation, 8(4), 1–31. https://www.jasss.org/8/4/6.html

Chattoe-Brown, E. (2022) If You Want To Be Cited, Don’t Validate Your Agent-Based Model: A Tentative Hypothesis Badly In Need of Refutation. Review of Artificial Societies and Social Simulation, 1st Feb 2022. https://rofasss.org/2022/02/01/citing-od-models

Flache, A., Mäs, M., Feliciani, T., Chattoe-Brown, E., Deffuant, G., Huet, S., & Lorenz, J. (2017). Models of social influence: towards the next frontiers. Journal of Artificial Societies and Social Simulation, 20(4). https://doi.org/10.18564/jasss.3521


Keijzer, M. (2022) If you want to be cited, calibrate your agent-based model: Reply to Chattoe-Brown. Review of Artificial Societies and Social Simulation, 9th Mar 2022. https://rofasss.org/2022/03/09/Keijzer-reply-to-Chattoe-Brown


 

If You Want To Be Cited, Don’t Validate Your Agent-Based Model: A Tentative Hypothesis Badly In Need of Refutation

By Edmund Chattoe-Brown

As part of a previous research project, I collected a sample of the Opinion Dynamics (hereafter OD) models published in JASSS that were most highly cited in JASSS. The idea here was to understand what styles of OD research were most influential in the journal. In the top 50 on 19.10.21 there were eight such articles. Five were self-contained modelling exercises (Hegselmann and Krause 2002, 58 citations, Deffuant et al. 2002, 35 citations, Salzarulo 2006, 13 citations, Deffuant 2006, 13 citations and Urbig et al. 2008, 9 citations), two were overviews of OD modelling (Flache et al. 2017, 13 citations and Sobkowicz 2009, 10 citations) and one included an OD example in an article mainly discussing the merits of cellular automata modelling (Hegselmann and Flache 1998, 12 citations). In order to get in to the top 50 on that date you had to achieve at least 7 citations. In parallel, I have been trying to identify Agent-Based Models that are validated (undergo direct comparison of real and equivalent simulated data). Based on an earlier bibliography (Chattoe-Brown 2020) which I extended to the end of 2021 for JASSS and articles which were described as validated in the highly cited articles listed above, I managed to construct a small and unsystematic sample of validated OD models. (Part of the problem with a systematic sample is that validated models are not readily searchable as a distinct category and there are too many OD models overall to make reading them all feasible. Also, I suspect, validated models just remain rare in line with the larger scale findings of Dutton and Starbuck (1971, p. 130, table 1) and discouragingly, much more recently, Angus and Hassani-Mahmooei (2015, section 4.5, figure 9). Obviously, since part of the sample was selected by total number of citations, one cannot make a comparison on that basis, so instead I have used the best possible alternative (given the limitations of the sample) and compared articles on citations per year. The problem here is that attempting validated modelling is relatively new while older articles inevitably accumulate citations however slowly. But what I was trying to discover was whether new validated models could be cited at a much higher annual rate without reaching the top 50 (or whether, conversely, older articles could have a high enough total citations to get into the top 50 without having a particularly impressive annual citation rate.) One would hope that, ultimately, validated models would tend to receive more citations than those that were not validated (but see the rather disconcerting related findings of Serra-Garcia and Gneezy 2021). Table 1 shows the results sorted by citations per year.

Article Status Number of JASSS Citations[1] Number of Years[2] Citations Per Year
Bernardes et al. 2002 Validated 1 20 0.05
Bernardes et al. 2001 Validated 2 21 0.096
Fortunato and Castellano 2007 Validated 2 15 0.13
Caruso and Castorina 2005 Validated 4 17 0.24
Chattoe-Brown 2014 Validated 2 8 0.25
Brousmiche et al. 2016 Validated 2 6 0.33
Hegselmann and Flache 1998 Non-Validated 12 24 0.5
Urbig et al. 2008 Non-Validated 9 14 0.64
Sobkowicz 2009 Non-Validated 10 13 0.77
Deffuant 2006 Non-Validated 13 16 0.81
Salzarulo 2006 Non-Validated 13 16 0.81
Duggins 2017 Validated 5 5 1
Deffuant et al. 2002 Non-Validated 35 20 1.75
Flache et al. 2017 Non-Validated 13 5 2.6
Hegselmann and Krause 2002 Non-Validated 58 20 2.9

Table 1. Annual Citation Rates for OD Articles Highly Cited in JASSS (Systematic Sample) and Validated OD Articles in or Cited in JASSS (Unsystematic Sample)

With the notable (and potentially encouraging) exception of Duggins (2017), the most recent validated OD model I have been able to discover in JASSS, the sample clearly divides into non-validated research with more citations and validated research with fewer. The position of Duggins (2017) might suggest greater recent interest in validated OD models. Unfortunately, however, qualitative analysis of the citations suggests that these are not cited as validated models per se (and thus as a potential improvement over non-validated models) but merely as part of general classes of OD model (like those involving social networks or repulsion – moving away from highly discrepant opinions). This tendency to cite validated models without acknowledging that they are validated (and what the implications of that might be) is widespread in the articles I looked at.

Obviously, there is plenty wrong with this analysis. Even looking at citations per annum we are arguably still partially sampling on the dependent variable (articles selected for being widely cited prove to be widely cited!) and the sample of validated OD models is unsystematic (though in fairness the challenges of producing a systematic sample are significant.[3]) But the aim here is to make a distinctive use of RoFASSS as a rapid mode of permanent publication and to think differently about science. If I tried to publish this in a peer reviewed journal, the amount of labour required to satisfy reviewers about the research design would probably be prohibitive (even if it were possible). As a result, the case to answer about this apparent (and perhaps undesirable) pattern in data might never see the light of day.

But by publishing quickly in RoFASSS without the filter of peer review I actively want my hypothesis to be rejected or replaced by research based on a better design (and such research may be motivated precisely by my presenting this interesting pattern with all its imperfections). When it comes to scientific progress, the chance to be clearly wrong now could be more useful than the opportunity to be vaguely right at some unknown point in the future.

Acknowledgements

This analysis was funded by the project “Towards Realistic Computational Models Of Social Influence Dynamics” (ES/S015159/1) funded by ESRC via ORA Round 5 (PI: Professor Bruce Edmonds, Centre for Policy Modelling, Manchester Metropolitan University: https://gtr.ukri.org/projects?ref=ES%2FS015159%2F1).

Notes

[1] Note that the validated OD models had their citations counted manually while the high total citation articles had them counted automatically. This may introduce some comparison error but there is no reason to think that either count will be terribly inaccurate.

[2] Including the year of publication and the current year (2021).

[3] Note, however, that there are some checks and balances on sample quality. Highly successful validated OD models would have shown up independently in the top 50. There is thus an upper bound to the impact of the articles I might have missed in manually constructing my “version 1” bibliography. The unsystematic review of 47 articles by Sobkowicz (2009) also checks independently on the absence of validated OD models in JASSS to that date and confirms the rarity of such articles generally. Only four of the articles that he surveys are significantly empirical.

References

Angus, Simon D. and Hassani-Mahmooei, Behrooz (2015) ‘“Anarchy” Reigns: A Quantitative Analysis of Agent-Based Modelling Publication Practices in JASSS, 2001-2012’, Journal of Artificial Societies and Social Simulation, 18(4), October, article 16, <http://jasss.soc.surrey.ac.uk/18/4/16.html>. doi:10.18564/jasss.2952

Bernardes, A. T., Costa, U. M. S., Araujo, A. D. and Stauffer, D. (2001) ‘Damage Spreading, Coarsening Dynamics and Distribution of Political Votes in Sznajd Model on Square Lattice’, International Journal of Modern Physics C: Computational Physics and Physical Computation, 12(2), February, pp. 159-168. doi:10.1140/e10051-002-0013-y

Bernardes, A. T., Stauffer, D. and Kertész, J. (2002) ‘Election Results and the Sznajd Model on Barabasi Network’, The European Physical Journal B: Condensed Matter and Complex Systems, 25(1), January, pp. 123-127. doi:10.1142/S0129183101001584

Brousmiche, Kei-Leo, Kant, Jean-Daniel, Sabouret, Nicolas and Prenot-Guinard, François (2016) ‘From Beliefs to Attitudes: Polias, A Model of Attitude Dynamics Based on Cognitive Modelling and Field Data’, Journal of Artificial Societies and Social Simulation, 19(4), October, article 2, <https://www.jasss.org/19/4/2.html>. doi:10.18564/jasss.3161

Caruso, Filippo and Castorina, Paolo (2005) ‘Opinion Dynamics and Decision of Vote in Bipolar Political Systems’, arXiv > Physics > Physics and Society, 26 March, version 2. doi:10.1142/S0129183105008059

Chattoe-Brown, Edmund (2014) ‘Using Agent Based Modelling to Integrate Data on Attitude Change’, Sociological Research Online, 19(1), February, article 16, <https://www.socresonline.org.uk/19/1/16.html>. doi:0.5153/sro.3315

Chattoe-Brown Edmund (2020) ‘A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation: Version 1’, CPM Report CPM-20-216, 12 June, <http://cfpm.org/discussionpapers/256>

Deffuant, Guillaume (2006) ‘Comparing Extremism Propagation Patterns in Continuous Opinion Models’, Journal of Artificial Societies and Social Simulation, 9(3), June, article 8, <https://www.jasss.org/9/3/8.html>.

Deffuant, Guillaume, Amblard, Frédéric, Weisbuch, Gérard and Faure, Thierry (2002) ‘How Can Extremism Prevail? A Study Based on the Relative Agreement Interaction Model’, Journal of Artificial Societies and Social Simulation, 5(4), October, article 1, <https://www.jasss.org/5/4/1.html>.

Duggins, Peter (2017) ‘A Psychologically-Motivated Model of Opinion Change with Applications to American Politics’, Journal of Artificial Societies and Social Simulation, 20(1), January, article 13, <http://jasss.soc.surrey.ac.uk/20/1/13.html>. doi:10.18564/jasss.3316

Dutton, John M. and Starbuck, William H. (1971) ‘Computer Simulation Models of Human Behavior: A History of an Intellectual Technology’, IEEE Transactions on Systems, Man, and Cybernetics, SMC-1(2), April, pp. 128-171. doi:10.1109/TSMC.1971.4308269

Flache, Andreas, Mäs, Michael, Feliciani, Thomas, Chattoe-Brown, Edmund, Deffuant, Guillaume, Huet, Sylvie and Lorenz, Jan (2017) ‘Models of Social Influence: Towards the Next Frontiers’, Journal of Artificial Societies and Social Simulation, 20(4), October, article 2, <http://jasss.soc.surrey.ac.uk/20/4/2.html>. doi:10.18564/jasss.3521

Fortunato, Santo and Castellano, Claudio (2007) ‘Scaling and Universality in Proportional Elections’, Physical Review Letters, 99(13), 28 September, article 138701. doi:10.1103/PhysRevLett.99.138701

Hegselmann, Rainer and Flache, Andreas (1998) ‘Understanding Complex Social Dynamics: A Plea For Cellular Automata Based Modelling’, Journal of Artificial Societies and Social Simulation, 1(3), June, article 1, <https://www.jasss.org/1/3/1.html>.

Hegselmann, Rainer and Krause, Ulrich (2002) ‘Opinion Dynamics and Bounded Confidence Models, Analysis, and Simulation’, Journal of Artificial Societies and Social Simulation, 5(3), June, article 2, <http://jasss.soc.surrey.ac.uk/5/3/2.html>.

Salzarulo, Laurent (2006) ‘A Continuous Opinion Dynamics Model Based on the Principle of Meta-Contrast’, Journal of Artificial Societies and Social Simulation, 9(1), January, article 13, <http://jasss.soc.surrey.ac.uk/9/1/13.html>.

Serra-Garcia, Marta and Gneezy, Uri (2021) ‘Nonreplicable Publications are Cited More Than Replicable Ones’, Science Advances, 7, 21 May, article eabd1705. doi:10.1126/sciadv.abd1705

Sobkowicz, Pawel (2009) ‘Modelling Opinion Formation with Physics Tools: Call for Closer Link with Reality’, Journal of Artificial Societies and Social Simulation, 12(1), January, article 11, <http://jasss.soc.surrey.ac.uk/12/1/11.html>.

Urbig, Diemo, Lorenz, Jan and Herzberg, Heiko (2008) ‘Opinion Dynamics: The Effect of the Number of Peers Met at Once’, Journal of Artificial Societies and Social Simulation, 11(2), March, article 4, <http://jasss.soc.surrey.ac.uk/11/2/4.html>.


Chattoe-Brown, E. (2022) If You Want To Be Cited, Don’t Validate Your Agent-Based Model: A Tentative Hypothesis Badly In Need of Refutation. Review of Artificial Societies and Social Simulation, 1st Feb 2022. https://rofasss.org/2022/02/01/citing-od-models


 

Reply to Frank Dignum

By Edmund Chattoe-Brown

This is a reply to Frank Dignum’s reply (about Edmund Chattoe-Brown’s review of Frank’s book)

As my academic career continues, I have become more and more interested in the way that people justify their modelling choices, for example, almost every Agent-Based Modeller makes approving noises about validation (in the sense of comparing real and simulated data) but only a handful actually try to do it (Chattoe-Brown 2020). Thus I think two specific statements that Frank makes in his response should be considered carefully:

  1. … we do not claim that we have the best or only way of developing an Agent-Based Model (ABM) for crises.” Firstly, negative claims (“This is not a banana”) are not generally helpful in argument. Secondly, readers want to know (or should want to know) what is being claimed and, importantly, how they would decide if it is true “objectively”. Given how many models sprang up under COVID it is clear that what is described here cannot be the only way to do it but the question is how do we know you did it “better?” This was also my point about institutionalisation. For me, the big lesson from COVID was how much the automatic response of the ABM community seems to be to go in all directions and build yet more models in a tearing hurry rather than synthesise them, challenge them or test them empirically. I foresee a problem both with this response and our possible unwillingness to be self-aware about it. Governments will not want a million “interesting” models to choose from but one where they have externally checkable reasons to trust it and that involves us changing our mindset (to be more like climate modellers for example, Bithell & Edmonds 2020). For example, colleagues and I developed a comparison methodology that allowed for the practical difficulties of direct replication (Chattoe-Brown et al. 2021).
  2. The second quotation which amplifies this point is: “But we do think it is an extensive foundation from which others can start, either picking up some bits and pieces, deviating from it in specific ways or extending it in specific ways.” Again, here one has to ask the right question for progress in modelling. On what scientific grounds should people do this? On what grounds should someone reuse this model rather than start their own? Why isn’t the Dignum et al. model built on another “market leader” to set a good example? (My point about programming languages was purely practical not scientific. Frank is right that the model is no less valid because the programming language was changed but a version that is now unsupported seems less useful as a basis for the kind of further development advocated here.)

I am not totally sure I have understood Frank’s point about data so I don’t want to press it but my concern was that, generally, the book did not seem to “tap into” relevant empirical research (and this is a wider problem that models mostly talk about other models). It is true that parameter values can be adjusted arbitrarily in sensitivity analysis but that does not get us any closer to empirically justified parameter values (which would then allow us to attempt validation by the “generative methodology”). Surely it is better to build a model that says something about the data that exists (however imperfect or approximate) than to rely on future data collection or educated guesses. I don’t really have the space to enumerate the times the book said “we did this for simplicity”, “we assumed that” etc. but the cumulative effect is quite noticeable. Again, we need to be aware of the models which use real data in whatever aspects and “take forward” those inputs so they become modelling standards. This has to be a collective and not an individualistic enterprise.

References

Bithell, M. and Edmonds, B. (2020) The Systematic Comparison of Agent-Based Policy Models – It’s time we got our act together!. Review of Artificial Societies and Social Simulation, 11th May 2021. https://rofasss.org/2021/05/11/SystComp/

Chattoe-Brown, E. (2020) A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation. Review of Artificial Societies and Social Simulation, 12th June 2020. https://rofasss.org/2020/06/12/abm-validation-bib/

Chattoe-Brown, E. (2021) A review of “Social Simulation for a Crisis: Results and Lessons from Simulating the COVID-19 Crisis”. Journal of Artificial Society and Social Simulation. 24(4). https://www.jasss.org/24/4/reviews/1.html

Chattoe-Brown, E., Gilbert, N., Robertson, D. A., & Watts, C. J. (2021). Reproduction as a Means of Evaluating Policy Models: A Case Study of a COVID-19 Simulation. medRxiv 2021.01.29.21250743; DOI: https://doi.org/10.1101/2021.01.29.21250743

Dignum, F. (2020) Response to the review of Edmund Chattoe-Brown of the book “Social Simulations for a Crisis”. Review of Artificial Societies and Social Simulation, 4th Nov 2021. https://rofasss.org/2021/11/04/dignum-review-response/

Dignum, F. (Ed.) (2021) Social Simulation for a Crisis: Results and Lessons from Simulating the COVID-19 Crisis. Springer. DOI:10.1007/978-3-030-76397-8


Chattoe-Brown, E. (2021) Reply to Frank Dignum. Review of Artificial Societies and Social Simulation, 10th November 2021. https://rofasss.org/2021/11/10/reply-to-dignum/


 

Response to the review of Edmund Chattoe-Brown of the book “Social Simulations for a Crisis”

By Frank Dignum

This is a reply to a review in JASSS (Chattoe-Brown 2021) of (Dignum 2021).

Before responding to some of the specific concerns of Edmund I would like to thank him for the thorough review. I am especially happy with his conclusion that the book is solid enough to make it a valuable contribution to scientific progress in modelling crises. That was the main aim of the book and it seems that is achieved. I want to reiterate what we already remarked in the book; we do not claim that we have the best or only way of developing an Agent-Based Model (ABM) for crises. Nor do we claim that our simulations were without limitations. But we do think it is an extensive foundation from which others can start, either picking up some bits and pieces, deviating from it in specific ways or extending it in specific ways.

The concerns that are expressed by Edmund are certainly valid. I agree with some of them, but will nuance some others. First of all the concern about the fact that we seem to abandon the NetLogo implementation and move to Repast. This fact does not make the ABM itself any less valid! In itself it is also an important finding. It is not possible to scale such a complex model in NetLogo beyond around two thousand agents. This is not just a limitation of our particular implementation, but a more general limitation of the platform. It leads to the important challenge to get more computer scientists involved to develop platforms for social simulations that both support the modelers adequately and provide efficient and scalable implementations.

That the sheer size of the model and the results make it difficult to trace back the importance and validity of every factor on the results is completely true. We have tried our best to highlight the most important aspects every time. But, this leaves questions as to whether we make the right selection of highlighted aspects. As an illustration to this, we have been busy for two months to justify our results of the simulations of the effectiveness of the track and tracing apps. We basically concluded that we need much better integrated analysis tools in the simulation platform. NetLogo is geared towards creating one simulation scenario, running the simulation and analyzing the results based on a few parameters. This is no longer sufficient when we have a model with which we can create many scenarios and have many parameters that influence a result. We used R now to interpret the flood of data that was produced with every scenario. But, R is not really the most user friendly tool and also not specifically meant for analyzing the data from social simulations.

Let me jump to the third concern of Edmund and link it to the analysis of the results as well. While we tried to justify the results of our simulation on the effectiveness of the track and tracing app we compared our simulation with an epidemiological based model. This is described in chapter 12 of the book. Here we encountered the difference in assumed number of contacts per day a person has with other persons. One can take the results, as quoted by Edmund as well, of 8 or 13 from empirical work and use them in the model. However, the dispute is not about the number of contacts a person has per day, but what counts as a contact! For the COVID-19 simulations standing next to a person in the queue in a supermarket for five minutes can count as a contact, while such a contact is not a meaningful contact in the cited literature. Thus, we see that what we take as empirically validated numbers might not at all be the right ones for our purpose. We have tried to justify all the values of parameters and outcomes in the context for which the simulations were created. We have also done quite some sensitivity analyses, which we did not all report on just to keep the volume of the book to a reasonable size. Although we think we did a proper job in justifying all results, that does not mean that one can have different opinions on the value that some parameters should have. It would be very good to check the influence on the results of changes in these parameters. This would also progress scientific insights in the usefulness of complex models like the one we made!

I really think that an ABM crisis response should be institutional. That does not mean that one institution determines the best ABM, but rather that the ABM that is put forward by that institution is the result of a continuous debate among scientists working on ABM’s for that type of crisis. For us, one of the more important outcomes of the ASSOCC project is that we really need much better tools to support the types of simulations that are needed for a crisis situation. However, it is very difficult to develop these tools as a single group. A lot of the effort needed is not publishable and thus not valued in an academic environment. I really think that the efforts that have been put in platforms such as NetLogo and Repast are laudable. They have been made possible by some generous grants and institutional support. We argue that this continuous support is also needed in order to be well equipped for a next crisis. But we do not argue that an institution would by definition have the last word in which is the best ABM. In an ideal case it would accumulate all academic efforts as is done in the climate models, but even more restricted models would still be better than just having a thousand individuals all claiming to have a useable ABM while governments have to react quickly to a crisis.

The final concern of Edmund is about the empirical scale of our simulations. This is completely true! Given the scale and details of what we can incorporate we can only simulate some phenomena and certainly not everything around the COVID-19 crisis. We tried to be clear about this limitation. We had discussions about the Unity interface concerning this as well. It is in principle not very difficult to show people walking in the street, taking a car or a bus, etc. However, we decided to show a more abstract representation just to make clear that our model is not a complete model of a small town functioning in all aspects. We have very carefully chosen which scenarios we can realistically simulate and give some insights in reality from. Maybe we should also have discussed more explicitly all the scenarios that we did not run with the reasons why they would be difficult or unrealistic in our ABM. One never likes to discuss all the limitations of one’s labor, but it definitely can be very insightful. I have made up for this a little bit by submitting an to a special issue on predictions with ABM in which I explain in more detail, which should be the considerations to use a particular ABM to try to predict some state of affairs. Anyone interested to learn more about this can contact me.

To conclude this response to the review, I again express my gratitude for the good and thorough work done. The concerns that were raised are all very valuable to concern. What I tried to do in this response is to highlight that these concerns should be taken as a call to arms to put effort in social simulation platforms that give better support for creating simulations for a crisis.

References

Dignum, F. (Ed.) (2021) Social Simulation for a Crisis: Results and Lessons from Simulating the COVID-19 Crisis. Springer. DOI:10.1007/978-3-030-76397-8

Chattoe-Brown, E. (2021) A review of “Social Simulation for a Crisis: Results and Lessons from Simulating the COVID-19 Crisis”. Journal of Artificial Society and Social Simulation. 24(4). https://www.jasss.org/24/4/reviews/1.html


Dignum, F. (2020) Response to the review of Edmund Chattoe-Brown of the book “Social Simulations for a Crisis”. Review of Artificial Societies and Social Simulation, 4th Nov 2021. https://rofasss.org/2021/11/04/dignum-review-response/


 

Does It Take Two (And A Creaky Search Engine) To Make An Outstation? Hunting Highly Cited Opinion Dynamics Articles in the Journal of Artificial Societies and Social Simulation (JASSS)

By Edmund Chattoe-Brown

In an important article, Squazzoni and Casnici (2013) raise the issue of how social simulation (as manifested in the Journal of Artificial Societies and Social Simulation – hereafter JASSS – the journal that has probably published the most of this kind of research for longest) cites and is cited in the wider scientific community. They discuss this in terms of social simulation being a potential “outstation” of social science (but better integrated into physical science and computing). This short note considers the same argument in reverse. As an important site of social simulation research, is it the case that JASSS is effectively representing research done more widely across the sciences?

The method used to investigate this was extremely simple (and could thus easily be extended and replicated). On 28.08.21, using the search term “opinion dynamics” in “all fields”, all sources from Web of Science (www.webofknowledge.com, hereafter WOS) that were flagged as “highly cited” were selected as a sample. For each article (only articles turned out to be highly cited), the title was searched in JASSS and the number of hits recorded. Common sense was applied in this search process to maximise the chances of success. So if a title had two sub clauses, these were searched jointly as quotations (to avoid the “hits” being very sensitive to the reproduction of punctuation linking clauses.) In addition, the title of the journal in which the article appeared was searched to give a wider sense of how well the relevant journal is known is JASSS.

However, now we come to the issue of the creaky search engine (as well as other limitations of quick and dirty searches). Obviously searching for the exact title will not find variants of that title with spelling mistakes or attempts to standardise spelling (i. e. changing behavior to behaviour). Further, it turns out that the Google search engine (which JASSS uses) does not promise the consistency that often seems to be assumed for it (http://jdebp.uk/FGA/google-result-counts-are-a-meaningless-metric.html). For example, when I searched for “SIAM Review” I mostly got 77 hits, rather often 37 hits and very rarely 0 or 1 hits. (PDFs are available for three of these outcomes from the author but the fourth could not be reproduced to be recorded in the time available.) This result occurred when another search took place seconds after the first so it is not, for example, a result of substantive changes to the content of JASSS. To deal with this problem I tried to confirm the presence of a particular article by searching jointly for all its co-authors. Mostly this approach gave a similar result (but where it does not it is noted in the table below). In addition, wherever there were a relatively large number of hits for a specific search, some of these were usually not the ones intended. (For example no hit on the term “global challenges” actually turned out to be for the journal Global Challenges.) In addition, JASSS often gives an oddly inconsistent number of hits for a specific article: It may appear as PDF and HTML as well as in multiple indices or may occur just once. (This discouraged attempts to go from hits to the specific number of unique articles citing these WOS sources. As it turns out, this additional detail would have added little to the headline result.)

The term “opinion dynamics” was chosen somewhat arbitrarily (for reasons connected with other research) and it is not claimed that this term is even close to a definitive way of capturing any models connected with opinion/attitude change. Nonetheless, it is clear that the number of hits and the type of articles reported on WOS (which is curated and quality controlled) are sufficient (and sufficiently relevant) for this to be a serviceable search term to identify a solid field of research in JASSS (and elsewhere). I shall return to this issue.

The results, shown in the table below are striking on several counts. (All these sources are fully cited in the references at the end of this article.) Most noticeably, JASSS is barely citing a significant number of articles that are very widely cited elsewhere. Because these are highly cited in WOS this cannot be because they are too new or too inaccessible. The second point is the huge discrepancy in citation for the one article on the WOS list that appears in JASSS itself (Flache et al. 2017). Thirdly, although some of these articles appear in journals that JASSS otherwise does not cite (like Global Challenges and Dynamic Games and Applications) others appear in journals that are known to JASSS and generally cited (like SIAM Review).

Reference WOS Citations Article Title Hits in JASSS Journal Title Hits in JASSS
Acemoglu and Ozdaglar (2011) 301 0 (1 based on joint authors) 2
Motsch and Tadmor (2014) 214 0 77
Van Der Linden et al. (2017) 191 0 6 (but none for the journal)
Acemoğlu et al. (2013) 186 1 2 (but 1 article)
Proskurnikov et al. (2016) 165 0 9
Dong et al. (2017) 147 0 48 (but rather few for the journal)
Jia et al. (2015) 118 0 77
Dong et al. (2018) 117 0 (1 based on joint authors) 48 (but rather few for the journal)
Flache et al. (2017) 86 58 (17 based on joint authors) N/A
Urena et al. (2019) 72 0 6
Bu et al. (2020) 56 0 5
Zhang et al. (2020) 55 0 33 (but only some of these are for the journal)
Xiong et al. (2020) 28 0 1
Carrillo et al. (2020) 13 0 0

One possible interpretation of this result is simply that none of the most highly cited articles in WOS featuring the term “opinion dynamics” happen to be more than incidentally relevant to the scientific interests of JASSS. On consideration, however, this seems a rather improbable coincidence. Firstly, these articles were chosen exactly because they are highly cited so we would have to explain how they could be perceived as so useful generally but specifically not in JASSS. Secondly, the same term (“opinion dynamics”) consistently generates 254 hits in JASSS, suggesting that the problem isn’t a lack of overlap in terminology or research interests.

This situation, however, creates a problem for more conclusive explanation. The state of affairs here is not that these articles are being cited and then rejected on scientific grounds given the interests of JASSS (thus providing arguments I could examine). It is that they are barely being cited at all. Unfortunately, it is almost impossible to establish why something is not happening. Perhaps JASSS authors are not aware of these articles to begin with. Perhaps they are aware but do not see the wider scientific value of critiquing them or attempting to engage with their irrelevance in print.

But, given that the problem is non citation, my concern can be made more persuasive (perhaps as persuasive as it can be given problems of convincingly explaining an absence) by investigating the articles themselves. (My thanks are due to Bruce Edmonds for encouraging me to strengthen the argument in this way.) There are definitely some recurring patterns in this sample. Firstly, a significant proportion of the articles are highly mathematical and, therefore (as Agent-Based Modelling often criticises) rely on extreme simplifying assumptions and toy examples. Even here, however, it is not self-evident that such articles should not be cited in JASSS merely because they are mathematical. JASSS has itself published relatively mathematical articles and, if an article contains a mathematical model that could be “agentised” (thus relaxing its extreme assumptions) which is no less empirical than similar models in JASSS (or has particularly interesting behaviours) then it is hard to see why this should not be discussed by at least a few JASSS authors. A clear example of this is provided by Acemoğlu et al. (2013) which argues that existing opinion dynamics models fail to produce the ongoing fluctuations of opinion observed in real data (see, for example, Figures 1-3 in Chattoe-Brown 2014 which also raises concerns about the face validity of popular social simulations of opinion dynamics). In fact, the assumptions of this model could easily be questioned (and real data involves turning points and not just fluctuations) but the point is that JASSS articles are not citing it and rejecting it based on argument but simply not citing it. A model capable of generating ongoing opinion fluctuations (however imperfect) is simply too important to the current state of opinion dynamics research in social simulation not to be considered at all. Another (though less conclusive) example is Motsch and Tadmor (2014) which presents a model suggesting (counter intuitively) that interaction based on heterophily can better achieve consensus than interaction based on homophily. Of course one can reject such an assumption on empirical grounds but JASSS is not currently doing that (and in fact the term heterophily is unknown in the journal except for the title of a cited article.)

Secondly, there are also a number of articles which, while not providing important results seem no less plausible or novel than typical OD articles that are published in JASSS. For example, Jia et al. (2015) add self-appraisal and social power to a standard OD model. Between debates, agents amend the efficacy they believe that they and others have in terms of swaying the outcome and take that into account going forward. Proskurnikov et al. (2016) present the results of a model in which agents can have negative ties with each other (as well as the more usual positive ones) and thus consider the coevolution of positive/negative sentiments and influence (describing what they call hostile camps i. e. groups with positive ties to each other and negative ties to other groups). This is distinct from the common repulsive effect in OD models where agents do not like the opinions of others (rather than disliking the others themselves.)

Finally, both Dong et al. (2017) and Zhang et al. (2020) reach for the idea (through modelling) that experts and leaders in OD models may not just be randomly scattered through the population as types but may exist because of formal organisations or accidents of social structure: This particular agent is either deliberately appointed to have more influence or happens to have it because of their network position.

On a completely different tack, two articles (Dong et al. 2018 and Acemoglu and Ozdaglar 2011) are literature reviews or syntheses on relevant topics and it is hard to see how such broad ranging articles could have so little value to OD research in JASSS.

It will be admitted that some of the articles in the sample are hard to evaluate with certainty. Mathematical approaches often seem to be more interested in generating mathematics than in justifying its likely value. This is particularly problematic when combined with a suggestion that the product of the research may be instrumental algorithms (designed to get things done) rather than descriptive ones (designed to understand social behaviour). An example of this is several articles which talk about achieving consensus without really explaining whether this is a technical goal (for example in a neural network) or a social phenomenon and, if the latter, whether this places constraints on what it legitimate: You can reach consensus by debate but not by shooting dissenters!

But as well as specific ideas in specific models, this sample of articles also suggest a different emphasis from those currently found within JASSS OD research. For example, there is much more interest in deliberately achieving consensus (and the corresponding hazards of manipulation or misinformation impeding that.) Reading these articles collectively gives a sense that JASSS OD models are very much liberal democratic: Agents honestly express their views (or at most are somewhat reticent to protect themselves.) They decently expect the will of the people to prevail. They do not lie strategically to sway the influential, spread rumours to discredit the opinions of opponents or flood the debate with bots. Again, this darker vision is no more right a priori than the liberal democratic one but JASSS should at least be engaging with articles modelling (or providing data on – see Van Der Linden et al. 2017) such phenomena in an OD context. (Although misinformation is mentioned in some OD articles in JASSS it does not seem to be modelled. There also seems to be another surprising glitch in the search engine which considers the term “fake news” to be a hit for misinformation!) This also puts a new slant on an ongoing challenge in OD research, identifying a plausible relationship between fact and opinion. Is misinformation a different field of research (on the grounds that opinions can never be factually wrong) or is it possible for the misinformed to develop mis-opinions? (Those that they would change if what they knew changed.) Is it really the case that Brexiteers, for example, are completely indifferent to the economic consequences which will reveal themselves or did they simply have mistaken beliefs about how high those costs might turn out to be which will cause them to regret their decision at some later stage?

Thus to sum up, while some of the articles in the sample can be dismissed as either irrelevant to JASSS or having a potential relevance that is hard to establish, the majority cannot reasonably be regarded in this way (and a few are clearly important to the existing state of OD research.) While we cannot explain why these articles are not in fact cited, we can thus call into question one possible (Panglossian) explanation for the observed pattern (that they are not cited because they have nothing to contribute).

Apart from the striking nature of the result and its obvious implication (if social simulators want to be cited more widely they need to make sure they are also citing the work of others appropriately) this study has two wider (related) implications for practice.

Firstly, systematic literature reviewing (see, for example, Hansen et al. 2019 – not published in JASSS) needs to be better enforced in social simulation: “Systematic literature review” gets just 7 hits in JASSS. It is not enough to cite just what you happen to have read or models that resemble your own, you need to be citing what the community might otherwise not be aware of or what challenges your own model assumptions. (Although, in my judgement, key assumptions of Acemoğlu et al. 2013 are implausible I don’t think that I could justify non subjectively that they are any more implausible than those of those of the Zaller-Deffuant model – Malarz et al. 2011 – given the huge awareness discrepancy which the two models manifest in social simulation.)

Secondly, we need to rethink the nature of literature reviewing as part of progressive research. I have used “opinion dynamics” here not because it is the perfect term to identify all models of opinion and attitude change but because it throws up enough hits to show that this term is widely used in social simulation. Because I have clearly stated my search term, others can critique it and extend my analysis using other relevant terms like “opinion change” or “consensus formation”. A literature review that is just a bunch of arbitrary stuff cannot be critiqued or improved systematically (rather than nit-picked for specific omissions – as reviewers often do – and even then the critique can’t tell what should have been included if there are no clearly stated search criteria.) It should not be possible for JASSS (and the social simulation community it represents) simply to disregard articles as potentially important in their implications for OD as Acemoğlu et al. (2013). Even if this article turned out to be completely wrong-headed, we need to have enough awareness of it to be able to say why before setting it aside. (Interestingly, the one citation it does receive in JASSS can be summarised as “there are some other model broadly like this” with no detailed discussion at all – and thus no clear statement of how the model presented in the citing article adds to previous models – but uninformative citation is a separate problem.)

Acknowledgements

This article as part of “Towards Realistic Computational Models of Social Influence Dynamics” a project funded through ESRC (ES/S015159/1) by ORA Round 5.

References

Acemoğlu, Daron and Ozdaglar, Asuman (2011) ‘Opinion Dynamics and Learning in Social Networks’, Dynamic Games and Applications, 1(1), March, pp. 3-49. doi:10.1007/s13235-010-0004-1

Acemoğlu, Daron, Como, Giacomo, Fagnani, Fabio and Ozdaglar, Asuman (2013) ‘Opinion Fluctuations and Disagreement in Social Networks’, Mathematics of Operations Research, 38(1), February, pp. 1-27. doi:10.1287/moor.1120.0570

Bu, Zhan, Li, Hui-Jia, Zhang, Chengcui, Cao, Jie, Li, Aihua and Shi, Yong (2020) ‘Graph K-Means Based on Leader Identification, Dynamic Game, and Opinion Dynamics’, IEEE Transactions on Knowledge and Data Engineering, 32(7), July, pp. 1348-1361. doi:10.1109/TKDE.2019.2903712

Carrillo, J. A., Gvalani, R. S., Pavliotis, G. A. and Schlichting, A. (2020) ‘Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus’, Archive for Rational Mechanics and Analysis, 235(1), January, pp. 635-690. doi:10.1007/s00205-019-01430-4

Chattoe-Brown, Edmund (2014) ‘Using Agent Based Modelling to Integrate Data on Attitude Change’, Sociological Research Online, 19(1), February, article 16, <http://www.socresonline.org.uk/19/1/16.html&gt;. doi:10.5153/sro.3315

Dong, Yucheng, Ding, Zhaogang, Martínez, Luis and Herrera, Francisco (2017) ‘Managing Consensus Based on Leadership in Opinion Dynamics’, Information Sciences, 397-398, August, pp. 187-205. doi:10.1016/j.ins.2017.02.052

Dong, Yucheng, Zhan, Min, Kou, Gang, Ding, Zhaogang and Liang, Haiming (2018) ‘A Survey on the Fusion Process in Opinion Dynamics’, Information Fusion, 43, September, pp. 57-65. doi:10.1016/j.inffus.2017.11.009

Flache, Andreas, Mäs, Michael, Feliciani, Thomas, Chattoe-Brown, Edmund, Deffuant, Guillaume, Huet, Sylvie and Lorenz, Jan (2017) ‘Models of Social Influence: Towards the Next Frontiers’, Journal of Artificial Societies and Social Simulation, 20(4), October, article 2, <http://jasss.soc.surrey.ac.uk/20/4/2.html&gt;. doi:10.18564/jasss.3521

Hansen, Paula, Liu, Xin and Morrison, Gregory M. (2019) ‘Agent-Based Modelling and Socio-Technical Energy Transitions: A Systematic Literature Review’, Energy Research and Social Science, 49, March, pp. 41-52. doi:10.1016/j.erss.2018.10.021

Jia, Peng, MirTabatabaei, Anahita, Friedkin, Noah E. and Bullo, Francesco (2015) ‘Opinion Dynamics and the Evolution of Social Power in Influence Networks’, SIAM Review, 57(3), pp. 367-397. doi:10.1137/130913250

Malarz, Krzysztof, Gronek, Piotr and Kulakowski, Krzysztof (2011) ‘Zaller-Deffuant Model of Mass Opinion’, Journal of Artificial Societies and Social Simulation, 14(1), 2, <https://www.jasss.org/14/1/2.html&gt;. doi:10.18564/jasss.1719

Motsch, Sebastien and Tadmor, Eitan (2014) ‘Heterophilious Dynamics Enhances Consensus’, SIAM Review, 56(4), pp. 577-621. doi:10.1137/120901866

Proskurnikov, Anton V., Matveev, Alexey S. and Cao, Ming (2016) ‘Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization’, IEEE Transactions on Automatic Control, 61(6), June, pp. 1524-1536. doi:10.1109/TAC.2015.2471655

Squazzoni, Flaminio and Casnici, Niccolò (2013) ‘Is Social Simulation a Social Science Outstation? A Bibliometric Analysis of the Impact of JASSS’, Journal of Artificial Societies and Social Simulation, 16(1), 10, <http://jasss.soc.surrey.ac.uk/16/1/10.html&gt;. doi:10.18564/jasss.2192

Ureña, Raquel, Chiclana, Francisco, Melançon, Guy and Herrera-Viedma, Enrique (2019) ‘A Social Network Based Approach for Consensus Achievement in Multiperson Decision Making’, Information Fusion, 47, May, pp. 72-87. doi:10.1016/j.inffus.2018.07.006

Van Der Linden, Sander, Leiserowitz, Anthony, Rosenthal, Seth and Maibach, Edward (2017) ‘Inoculating the Public against Misinformation about Climate Change’, Global Challenges, 1(2), 27 February, article 1600008. doi:10.1002/gch2.201600008

Xiong, Fei, Wang, Ximeng, Pan, Shirui, Yang, Hong, Wang, Haishuai and Zhang, Chengqi (2020) ‘Social Recommendation With Evolutionary Opinion Dynamics’, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(10), October, pp. 3804-3816. doi:10.1109/TSMC.2018.2854000

Zhang, Zhen, Gao, Yuan and Li, Zhuolin (2020) ‘Consensus Reaching for Social Network Group Decision Making by Considering Leadership and Bounded Confidence’, Knowledge-Based Systems, 204, 27 September, article 106240. doi:10.1016/j.knosys.2020.106240


Chattoe-Brown, E. (2021) Does It Take Two (And A Creaky Search Engine) To Make An Outstation? Hunting Highly Cited Opinion Dynamics Articles in the Journal of Artificial Societies and Social Simulation (JASSS). Review of Artificial Societies and Social Simulation, 19th August 2021. https://rofasss.org/2021/08/19/outstation/


 

The Systematic Comparison of Agent-Based Policy Models – It’s time we got our act together!

By Mike Bithell and Bruce Edmonds

Model Intercomparison

The recent Covid crisis has led to a surge of new model development and a renewed interest in the use of models as policy tools. While this is in some senses welcome, the sudden appearance of many new models presents a problem in terms of their assessment, the appropriateness of their application and reconciling any differences in outcome. Even if they appear similar, their underlying assumptions may differ, their initial data might not be the same, policy options may be applied in different ways, stochastic effects explored to a varying extent, and model outputs presented in any number of different forms. As a result, it can be unclear what aspects of variations in output between models are results of mechanistic, parameter or data differences. Any comparison between models is made tricky by differences in experimental design and selection of output measures.

If we wish to do better, we suggest that a more formal approach to making comparisons between models would be helpful. However, it appears that this is not commonly undertaken most fields in a systematic and persistent way, except for the field of climate change, and closely related fields such as pollution transport or economic impact modelling (although efforts are underway to extend such systematic comparison to ecosystem models –  Wei et al., 2014, Tittensor et al., 2018⁠). Examining the way in which this is done for climate models may therefore prove instructive.

Model Intercomparison Projects (MIP) in the Climate Community

Formal intercomparison of atmospheric models goes back at least to 1989 (Gates et al., 1999)⁠ with the first atmospheric model inter-comparison project (AMIP), initiated by the World Climate Research Programme. By 1999 this had contributions from all significant atmospheric modelling groups, providing standardised time-series of over 30 model variables for one particular historical decade of simulation, with a standard experimental setup. Comparisons of model mean values with available data helped to reveal overall model strengths and weaknesses: no single model was best at simulation of all aspects of the atmosphere, with accuracy varying greatly between simulations. The model outputs also formed a reference base for further inter-comparison experiments including targets for model improvement and reduction of systematic errors, as well as a starting point for improved experimental design, software and data management standards and protocols for communication and model intercomparison. This led to AMIPII and, subsequently, to a series of Climate model inter-comparison projects (CMIP) beginning with CMIP I in 1996. The latest iteration (CMIP 6) is a collection of 23 separate model intercomparison experiments covering atmosphere, ocean, land surface, geo-engineering, and the paleoclimate. This collection is aimed at the upcoming 2021 IPCC process (AR6). Participating projects go through an endorsement process for inclusion, (a process agreed with modelling groups), based on 10 criteria designed to ensure some degree of coherence between the various models – a further 18 MIPS are also listed as currently active (https://www.wcrp-climate.org/wgcm-cmip/wgcm-cmip6). Groups contribute to a central set of common experiments covering the period 1850 to the near-present. An overview of the whole process can be found in (Eyring et al., 2016).

The current structure includes a set of three overarching questions covering the dynamics of the earth system, model systematic biases and understanding possible future change under uncertainty. Individual MIPS may build on this to address one or more of a set of 7 “grand science challenges” associated with the climate. Modelling groups agree to provide outputs in a standard form, obtained from a specified set of experiments under the same design, and to provide standardised documentation to go with their models. Originally (up to CMIP 5), outputs were then added to a central public repository for further analysis, however the output grew so large under CMIP6 that now the data is held dispersed over repositories maintained by separate groups.

Other Examples

Two further more recent examples of collective model  development may also be helpful to consider.

Firstly, an informal network collating models across more than 50 research groups has already been generated as a result of the COVID crisis –  the Covid Forecast Hub (https://covid19forecasthub.org). This is run by a small number of research groups collaborating with the US Centre for Disease Control and is strongly focussed on the epidemiology. Participants are encouraged to submit weekly forecasts, and these are integrated into a data repository and can be vizualized on the website – viewers can look at forward projections, along with associated confidence intervals and model evaluation scores, including those for an ensemble of all models. The focus on forecasts in this case arises out of the strong policy drivers for the current crisis, but the main point is that it is possible to immediately view measures of model performance and to compare the different model types: one clear message that rapidly becomes apparent is that many of the forward projections have 95% (and at some times, even 50%) confidence intervals for incident deaths that more than span the full range of the past historic data. The benefit of comparing many different models in this case is apparent, as many of the historic single-model projections diverge strongly from the data (and the models most in error are not consistently the same ones over time), although the ensemble mean tends to be better.

As a second example, one could consider the Psychological Science Accelerator (PSA: Moshontz et al 2018, https://psysciacc.org/). This is a collaborative network set up with the aim of addressing the “replication crisis” in psychology: many previously published results in psychology have proved problematic to replicate as a result of small or non-representative sampling or use of experimental designs that do not generalize well or have not been used consistently either within or across studies. The PSA seeks to ensure accumulation of reliable and generalizable evidence in psychological science, based on principles of inclusion, decentralization, openness, transparency and rigour. The existence of this network has, for example, enabled the reinvestigation of previous  experiments but with much larger and less nationally biased samples (e.g. Jones et al 2021).

The Benefits of the Intercomparison Exercises and Collaborative Model Building

More specifically, long-term intercomparison projects help to do the following.

  • Build on past effort. Rather than modellers re-inventing the wheel (or building a new framework) with each new model project, libraries of well-tested and documented models, with data archives, including code and experimental design, would allow researchers to more efficiently work on new problems, building on previous coding effort
  • Aid replication. Focussed long term intercomparison projects centred on model results with consistent standardised data formats would allow new versions of code to be quickly tested against historical archives to check whether expected results could be recovered and where differences might arise, particularly if different modelling languages were being used
  • Help to formalize. While informal code archives can help to illustrate the methods or theoretical foundations of a model, intercomparison projects help to understand which kinds of formal model might be good for particular applications, and which can be expected to produce helpful results for given desired output measures
  • Build credibility. A continuously updated set of model implementations and assessment of their areas of competence and lack thereof (as compared with available datasets) would help to demonstrate the usefulness (or otherwise) of ABM as a way to represent social systems
  • Influence Policy (where appropriate). Formal international policy organisations such as the IPCC or the more recently formed IPBES are effective partly through an underpinning of well tested and consistently updated models. As yet it is difficult to see whether such a body would be appropriate or effective for social systems, as we lack the background of demonstrable accumulated and well tested model results.

Lessons for ABM?

What might we be able to learn from the above, if we attempted to use a similar process to compare ABM policy models?

In the first place, the projects started small and grew over time: it would not be necessary, for example, to cover all possible ABM applications at the outset. On the other hand, the latest CMIP iterations include a wide range of different types of model covering many different aspects of the earth system, so that the breadth of possible model types need not be seen as a barrier.

Secondly, the climate inter-comparison project has been persistent for some 30 years – over this time many models have come and gone, but the history of inter-comparisons allows for an overview of how well these models have performed over time – data from the original AMIP I models is still available on request, supporting assessments concerning  long-term model improvement.

Thirdly, although climate models are complex – implementing a variety of different mechanisms in different ways – they can still be compared by use of standardised outputs, and at least some (although not necessarily all) have been capable of direct comparison with empirical data.

Finally, an agreed experimental design and public archive for documentation and output that is stable over time is needed; this needs to be done via a collective agreement among the modelling groups involved so as to ensure a long-term buy-in from the community as a whole, so that there is a consistent basis for long-term model development, building on past experience.

The need for aligning or reproducing ABMs has long been recognised within the community (Axtell et al. 1996; Edmonds & Hales 2003), but on a one-one basis for verifying the specification of models against their implementation, although (Hales et al. 2003) discusses a range of possibilities. However, this is far from a situation where many different models of basically the same phenomena are systematically compared – this would be a larger scale collaboration lasting over a longer time span.

The community has already established a standardised form of documentation in the ODD protocol. Sharing of model code is also becoming routine, and can be easily achieved through COMSES, Github or similar. The sharing of data in a long-term archive may require more investigation. As a starting project COVID-19 provides an ideal opportunity for setting up such a model inter-comparison project – multiple groups already have running examples, and a shared set of outputs and experiments should be straightforward to agree on. This would potentially form a basis for forward looking experiments designed to assist with possible future pandemic problems, and a basis on which to build further features into the existing disease-focussed modelling, such as the effects of economic, social and psychological issues.

Additional Challenges for ABMs of Social Phenomena

Nobody supposes that modelling social phenomena is going to have the same set of challenges that climate change models face. Some of the differences include:

  • The availability of good data. Social science is bedevilled by a paucity of the right kind of data. Although an increasing amount of relevant data is being produced, there are commercial, ethical and data protection barriers to accessing it and the data rarely concerns the same set of actors or events.
  • The understanding of micro-level behaviour. Whilst the micro-level understanding of our atmosphere is very well established, those of the behaviour of the most important actors (humans) is not. However, it may be that better data might partially substitute for a generic behavioural model of decision-making.
  • Agreement upon the goals of modelling. Although there will always be considerable variation in terms of what is wanted from a model of any particular social phenomena, a common core of agreed objectives will help focus any comparison and give confidence via ensembles of projections. Although the MIPs and Covid Forecast Hub are focussed on prediction, it may be that empirical explanation may be more important in other areas.
  • The available resources. ABM projects tend to be add-ons to larger endeavours and based around short-term grant funding. The funding for big ABM projects is yet to be established, not having the equivalent of weather forecasting to piggy-back on.
  • Persistence of modelling teams/projects. ABM tends to be quite short-term with each project developing a new model for a new project. This has made it hard to keep good modelling teams together.
  • Deep uncertainty. Whilst the set of possible factors and processes involved in a climate change model are well established, which social mechanisms need to be involved in any model of any particular social phenomena is unknown. For this reason, there is deep disagreement about the assumptions to be made in such models, as well as sharp divergence in outcome due to changes brought about by a particular mechanism but not included in a model. Whilst uncertainty in known mechanisms can be quantified, assessing the impact of those due to such deep uncertainty is much harder.
  • The sensitivity of the political context. Even in the case of Climate Change, where the assumptions made are relatively well understood and done on objective bases, the modelling exercise and its outcomes can be politically contested. In other areas, where the representation of people’s behaviour might be key to model outcomes, this will need even more care (Adoha & Edmonds 2017).

However, some of these problems were solved in the case of Climate Change as a result of the CMIP exercises and the reports they ultimately resulted in. Over time the development of the models also allowed for a broadening and updating of modelling goals, starting from a relatively narrow initial set of experiments. Ensuring the persistence of individual modelling teams is easier in the context of an internationally recognised comparison project, because resources may be easier to obtain, and there is a consistent central focus. The modelling projects became longer-term as individual researchers could establish a career doing just climate change modelling and importance of the work increasingly recognised. An ABM modelling comparison project might help solve some of these problems as the importance of its work is established.

Towards an Initial Proposal

The topic chosen for this project should be something where there: (a) is enough public interest to justify the effort, (b) there are a number of models with a similar purpose in mind being developed.  At the current stage, this suggests dynamic models of COVID spread, but there are other possibilities, including: transport models (where people go and who they meet) or criminological models (where and when crimes happen).

Whichever ensemble of models is focussed upon, these models should be compared on a core of standard, with the same:

  • Start and end dates (but not necessarily the same temporal granularity)
  • Covering the same set of regions or cases
  • Using the same population data (though possibly enhanced with extra data and maybe scaled population sizes)
  • With the same initial conditions in terms of the population
  • Outputting a core of agreed measures (but maybe others as well)
  • Checked against their agreement against a core set of cases, with agreed data sets
  • Reported on in a standard format (though with a discussion section for further/other observations)
  • well documented and with code that is open access
  • Run a minimum of times with different random seeds

Any modeller/team that had a suitable model and was willing to adhere to the rules would be welcome to participate (commercial, government or academic) and these teams would collectively decide the rules, development and write any reports on the comparisons. Other interested stakeholder groups could be involved including professional/academic associations, NGOs and government departments but in a consultative role providing wider critique – it is important that the terms and reports from the exercise be independent or any particular interest or authority.

Conclusion

We call upon those who think ABMs have the potential to usefully inform policy decisions to work together, in order that the transparency and rigour of our modelling matches our ambition. Whilst model comparison exercises of the kind described are important for any simulation work, particular care needs to be taken when the outcomes can affect people’s lives.

References

Aodha, L. & Edmonds, B. (2017) Some pitfalls to beware when applying models to issues of policy relevance. In Edmonds, B. & Meyer, R. (eds.) Simulating Social Complexity – a handbook, 2nd edition. Springer, 801-822. (A version is at http://cfpm.org/discussionpapers/236)

Axtell, R., Axelrod, R., Epstein, J. M., & Cohen, M. D. (1996). Aligning simulation models: A case study and results. Computational & Mathematical Organization Theory, 1(2), 123-141. https://link.springer.com/article/10.1007%2FBF01299065

Edmonds, B., & Hales, D. (2003). Replication, replication and replication: Some hard lessons from model alignment. Journal of Artificial Societies and Social Simulation, 6(4), 11. http://jasss.soc.surrey.ac.uk/6/4/11.html

Eyring, V., Bony, S., Meehl, G. A., Senior, C. A., Stevens, B., Stouffer, R. J., & Taylor, K. E. (2016). Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geoscientific Model Development, 9(5), 1937–1958. https://doi.org/10.5194/gmd-9-1937-2016

Gates, W. L., Boyle, J. S., Covey, C., Dease, C. G., Doutriaux, C. M., Drach, R. S., Fiorino, M., Gleckler, P. J., Hnilo, J. J., Marlais, S. M., Phillips, T. J., Potter, G. L., Santer, B. D., Sperber, K. R., Taylor, K. E., & Williams, D. N. (1999). An Overview of the Results of the Atmospheric Model Intercomparison Project (AMIP I). In Bulletin of the American Meteorological Society (Vol. 80, Issue 1, pp. 29–55). American Meteorological Society. https://doi.org/10.1175/1520-0477(1999)080<0029:AOOTRO>2.0.CO;2

Hales, D., Rouchier, J., & Edmonds, B. (2003). Model-to-model analysis. Journal of Artificial Societies and Social Simulation, 6(4), 5. http://jasss.soc.surrey.ac.uk/6/4/5.html

Jones, B.C., DeBruine, L.M., Flake, J.K. et al. To which world regions does the valence–dominance model of social perception apply?. Nat Hum Behav 5, 159–169 (2021). https://doi.org/10.1038/s41562-020-01007-2

Moshontz, H. + 85 others (2018) The Psychological Science Accelerator: Advancing Psychology Through a Distributed Collaborative Network ,  1(4) 501-515. https://doi.org/10.1177/2515245918797607

Tittensor, D. P., Eddy, T. D., Lotze, H. K., Galbraith, E. D., Cheung, W., Barange, M., Blanchard, J. L., Bopp, L., Bryndum-Buchholz, A., Büchner, M., Bulman, C., Carozza, D. A., Christensen, V., Coll, M., Dunne, J. P., Fernandes, J. A., Fulton, E. A., Hobday, A. J., Huber, V., … Walker, N. D. (2018). A protocol for the intercomparison of marine fishery and ecosystem models: Fish-MIP v1.0. Geoscientific Model Development, 11(4), 1421–1442. https://doi.org/10.5194/gmd-11-1421-2018

Wei, Y., Liu, S., Huntzinger, D. N., Michalak, A. M., Viovy, N., Post, W. M., Schwalm, C. R., Schaefer, K., Jacobson, A. R., Lu, C., Tian, H., Ricciuto, D. M., Cook, R. B., Mao, J., & Shi, X. (2014). The north american carbon program multi-scale synthesis and terrestrial model intercomparison project – Part 2: Environmental driver data. Geoscientific Model Development, 7(6), 2875–2893. https://doi.org/10.5194/gmd-7-2875-2014


Bithell, M. and Edmonds, B. (2020) The Systematic Comparison of Agent-Based Policy Models - It’s time we got our act together!. Review of Artificial Societies and Social Simulation, 11th May 2021. https://rofasss.org/2021/05/11/SystComp/


 

Should the family size be used in COVID-19 vaccine prioritization strategy to prevent variants diffusion? A first investigation using a basic ABM

By Gianfranco Giulioni

Department of Philosophical, Pedagogical and Economic-Quantitative Sciences, University of Chieti-Pescara, Italy

(A contribution to the: JASSS-Covid19-Thread)

When writing this document, few countries have made significant progress in vaccinating their population while many others still move first steps.

Despite the importance of COVID-19 adverse effects on society, there seems to be too little debate on the best option for progressing the vaccination process after the front-line healthcare personnel has been immunized.

The overall adopted strategies in the front-runner countries prioritize people using their health fragility, and age. For example, this strategy’s effectiveness is supported by Bubar et al. (2021), who provide results based on a detailed age-stratified Susceptible, Exposed, Infectious, Recovered (SEIR) model.

During the Covid infection outbreak, the importance of families in COVID diffusion was stressed by experts and media. This observation motivates the present effort, which investigates if considering family size among the vaccine prioritization strategy can have a role.

This document describes an ABM model developed with the intent of analyzing the question. The model is basic and has the essentials features to investigate the issue.

As highlighted by Squazzoni et al. (2020) a careful investigation of pandemics requires the cooperation of many scientists from different disciplines. To ease this cooperation and to the aim of transparency (Barton et al. 2020), the code is made publicly available to allow further developments and accurate parameters calibration to those who might be interested. (https://github.com/gfgprojects/abseir_family)

The following part of the document will sketch the model functioning and provide some considerations on families’ effects on vaccination strategy.

Brief Model Description

The ABSEIR-family model code is written in Java, taking advantage of the Repast Simphony modeling system (https://repast.github.io/).

Figure 1 gives an overview of the current development state of the model core classes.

Briefly, the code handles the relevant events of a pandemic:

  • the appearance of the first case,
  • the infection diffusion by contacts,
  • the introduction of measures for diffusion limitation such as quarantine,
  • the activation and implementation of the immunization process.

The distinguishing feature of the model is that individuals are grouped in families. This grouping allows considering two different diffusion speeds: fast among family members and slower when contacts involve two individuals from different families.

Figure 1: relationships between the core classes of the ABSEIR-family model and their variables and methods.

It is perhaps worth describing the evolution of an individual state to sketch the functioning of the model.

An individual’s dynamic is guided by a variable named infectionAge. In the beginning, all the individuals have this variable at zero. The program increases the infectionAge of all the individuals having a non zero value of this variable at each time step.

When an individual has contact with an infectious, s/he can get the infection or not. If infected, the individual enters the latency period, i.e. her/his infectionAge is set to 1 and the variable starts moving ahead with time, but s/he is not infectious. Individuals whose infectionAge is greater than the latency period length (ll ) become infectious.

At each time step, an infectious meets all her/his family members and mof randomly chosen non-family members. S/he passes on the infection with probability pif to family members and pof to non-family members. The infection can be passed on only if the contacted individual’s infectionAge equals zero and if s/he is not in quarantine.

The infectious phase ends when the infection is discovered (quarantine) or when the individual recovers i.e., the infectionAge is greater than the latency period length plus the infection length parameter (li).

At the present stage of development, the code does not handle the virus adverse post-infection evolution. All the infected individuals in this model recover. The infectionAge is set at a negative value at recovery because recovereds stay immune for a while (lr). Similarly, vaccination set the individual’s  infectionAge to a (high) negative value (lv).

At the present state of the pandemic evolution it is perhaps useful to use the model to get insights into how the family size could affect the vaccination process’s effectiveness. This will be attempted hereafter.

Highlighting the relevance of families size by an ad-hoc example

The relevance of family size in vaccination strategy can be shown using the following ad-hoc example.

Suppose there are two covid-free villages (say village A and B) whose health authorities are about to start vaccinations to avoid the disease spreading.

Villages are identical in the other aspects except for the family size distribution. Each village has 50 inhabitants, but village A has 10 families with five components each, while village B has two five members families and 40 singletons. Five vaccines arrive each day in each village.

Some additional extreme assumptions are made to make differences straightforward.

First, healthy family members are infected for sure by a member who contracted the virus. Second, each individual has the same number of contacts (say n) outside the family and the probability to pass  on the virus in external contacts is lower than 1. Symptoms take several days before showing up.

Now, the health authority are about to start the vaccination process and has to decide how to employ the available vaccines.

Intuition would suggest that Village B’s health authority should immunize large families first. Indeed, if case zero arrives at the end of the second vaccination day, the spread of the disease among the population should be limited because the virus can be passed on by external contacts only; and the probability of transmitting the virus in external contacts is lower than in the family.

But, should this strategy be used even by village A health authority?

To answer this question, we compare the family-based vaccination strategy with a random-based vaccination strategy. In a random-based vaccination strategy, we expect one members to be immunized in each family at the end of the second vaccination day. In the family-based vaccination strategy, two families are immunized at the end of the second vaccination day. Now, suppose one of the not-immunized citizens gets the virus at the end of day two. It is easy to verify there will be an infected more in the family-based strategy (all the five components of the family) than in the random-based strategy (4 components because one of them was immunized before). Furthermore, this implies that there will be n additional dangerous external contacts in the family-based strategy than in the random-based strategy.

These observations make us conclude that a random vaccination strategy will slow down the infection dynamics in village A while it will speed up infections in village B, and the opposite is true for the family-based immunization strategy.

Some simulation exercises

In this part of the document, the model described above will be used to compare further the family-based and random-based vaccination strategy to be used against the appearance of a new case (or variant) in a situation similar to that described in the example but with a more realistic setting.

As one can easily imagine, the family size distribution and COVID transmission risk in families are crucial to our simulation exercises. It is therefore important to gather real-world information for these phenomena. Fortunately, recent scientific contributions can help.

Several authors point out that a Poisson distribution is a good statistical model representing the family size distribution. This distribution is suitable because a single parameter characterizes it, i.e., its average, but it has the drawback of having a positive probability for zero value. Recently, Jarosz (2020) confirms the Poisson distribution’s goodness for modeling family size and shows how shifting it by one unit would be a valid alternative to solve the zero family size problem.

Furthermore, average family sizes data can be easily found using, for example, the OECD family database (http://www.oecd.org/social/family/database.htm).

The current version of the database (updated on 06-12-2016) presents data for 2015 with some exceptions. It shows how the average size of families in OECD countries is 2.46, ranging from Mexico (3.93) to Sweden (1.8).

The result in Metlay et al. (2021) guides the choice of the infection in the family parameter. They  provide evidence of an overall household infection risk of 10.1%

Simulation exercises consist in parameters sensitivity analysis with respect to the benchmark parameter set reported hereafter.

The simulation initialization is done by loading the family size distribution. Two alternative distributions are used and are tuned to obtain a system with a total number of individuals close to 20000. The two distributions are characterized by different average family sizes (afs) and are shown in figure 2.

Figure 2: two family size distributions used to initialize the simulation. Figures by the dots inform on the frequency of the corresponding size. Black square relates to the distribution with an average of 2.5; red circles relate to the distribution with an average of 3.5

The description of the vaccination strategy gives a possibility to list other relevant parameters. The immunization center is endowed with nv doses of vaccine at each time starting from time tv. At time t0, the state of one of the individuals is changed from susceptible to infected. This subject (case zero) is taken from a family having three susceptibles among their components.

Case zero undergoes the same process as all other following infected individuals described above.

The relevant parameters of the simulations are reported in table 1.

var description values reference
ni number of individuals ≅20000
afs average family size 2.5;3.5 OECD
nv number of vaccine doses available at each time 50;100;150
tv vaccination starting time 1
t0 case zero appearance time 10
ll length of latency 3 Buran et al 2021
li length of infectious period 5 Buran et al 2021
pif probability to infect a family member 0.1 Metlay et al 2021
pof probability to infect a non-family individual 0.01;0.02;0.03
mof number of non-family contacts of an infectious 10

Table 1: relevant parameters of the model.

We are now going to discuss the results of our simulation exercises. We focus particularly on the number of people infected up to a given point in time.

Due to the presence of random elements, each run has a different trajectory. We limit these effects as much as possible to allow ceteris paribus comparisons. For example, we keep the family size distribution equal across runs by loading the distributions displayed in figure 2 instead of using the run-time random number generator. Again, we set the number of non-family contacts (mof) equal for all the agents, although the code could set it randomly at each time step. Despite these randomness reductions, significant differences in the dynamics remain within the same parametrization because of randomness in the network of contacts.

To allow comparisons among different parametrizations in the presence of different evolution, we use the cross-section distributions of the total number of infected at the end of the infection process (i.e. time 200).

Figure 3 reports the empirical cumulative distribution function (ecdf) of several parametrizations. To easily read the figure, we put the different charts as in a plane having the average family size (afs) in the abscissa and the number of available vaccines (nv) in the ordinate. From above, we know two values of afs (i.e. 2.5 and 3.5) and three values of nv (i.e. 50, 100 and 150) are considered. Therefore figure 3 is made up of 6 charts.

Each chart reports ecdfs corresponding to the three different pof levels reported in table 1. In particular, circles denote edcfs for pof = 0.01, squares are for  pof = 0.02 and triangles for  pof = 0.03. At the end, choosing a parameters values triplet (afs, nv, pof), two ecdfs are identified. The red one is for the random-based, while the black one is for the family-based vaccination strategy. The family based vaccination strategy prioritizes families with higher number of members not yet infected.

Figure 3 shows mixed results: the random-based vaccination strategy outperforms the family-based one (the red line is above the balck one) for some parameters combinations while the reverse holds for others. In particular, the random-based tends to dominate the family-based strategy in case of larger family (afs = 3.5) and low and high vaccination levels (nv = 50 and 150). The opposite is true with smaller families at the same vaccination levels. The intermediate level of vaccination provides exceptions.

Figure 3: empirical cumulative distribution function of several parametrizations. The ecdfs is build by taking the number of infected people at period 200 of 100 runs with different random seed for each parametrization.

It is perhaps useful to highlight how, in the model, the family-based vaccination strategy stops the diffusion of a new wave or variant with a significant probability for smaller average family size and low and high vaccination levels (bottom-left and top-left charts) and for large average family size and middle level of vaccination (middle-right chart).

A conclusive note

At present, the model is very simple and can be improved in several directions. The most useful would probably be the inclusion of family-specific information. Setting up the model with additional information on each family member’s age or health state would allow overcoming the “universal mixing assumption” (Watts et al., 2020) currently in the model. Furthermore, additional vaccination strategy prioritization based on multiple criteria (such as vaccinating the families of most fragile or elderly) could be compared.

Initializing the model with census data of a local community could give a chance to analyze a more realistic setting in the wake of Pescarmona et al. (2020) and be more useful and understandable to (local) policy makers (Edmonds, 2020).

Developing the model to provide estimations for hospitalization and mortality is another needed step towards more sound vaccination strategies comparison.

Vaccinating by families could balance direct (vaccinating highest risk individuals) and indirect protection, i.e., limiting the probability the virus reaches most fragiles by vaccinating people with many contacts. It could also have positive economic effects relaunching, for example, family tourism. However, it cannot be implemented at risk of worsening the pandemic.

The present text aims only at posing a question. Further assessments following Squazzoni et al.’s (2020) recommendations are needed.

References

Barton, C.M. et al. (2020) Call for transparency of COVID-19 models. Science, 368(6490), 482-483. doi:10.1126/science.abb8637

Bubar, K.M. et al. (2021) Model-informed COVID-19 vaccine prioritization strategies by age and serostatus. Science 371, 916–921. doi:10.1126/science.abe6959

Edmonds, B. (2020) What more is needed for truly democratically accountable modelling? Review of Artificial Societies and Social Simulation, 2nd May 2020. https://rofasss.org/2020/05/02/democratically-accountable-modelling/

Jarosz, B. (2021) Poisson Distribution: A Model for Estimating Households by Household Size. Population Research and Policy Review, 40, 149–162. doi:10.1007/s11113-020-09575-x

Metlay J.P., Haas J.S., Soltoff A.E., Armstrong KA. Household Transmission of SARS-CoV-2. (2021) JAMA Netw Open, 4(2):e210304. doi:10.1001/jamanetworkopen.2021.0304

Pescarmona, G., Terna, P., Acquadro, A., Pescarmona, P., Russo, G., and Terna, S. (2020) How Can ABM Models Become Part of the Policy-Making Process in Times of Emergencies – The S.I.S.A.R. Epidemic Model. Review of Artificial Societies and Social Simulation, 20th Oct 2020. https://rofasss.org/2020/10/20/sisar/

Watts, C.J., Gilbert, N., Robertson, D., Droy, L.T., Ladley, D and Chattoe-Brown, E. (2020) The role of population scale in compartmental models of COVID-19 transmission. Review of Artificial Societies and Social Simulation, 14th August 2020. https://rofasss.org/2020/08/14/role-population-scale/

Squazzoni, F., Polhill, J. G., Edmonds, B., Ahrweiler, P., Antosz, P., Scholz, G., Chappin, É., Borit, M., Verhagen, H., Giardini, F. and Gilbert, N. (2020) Computational Models That Matter During a Global Pandemic Outbreak: A Call to Action. Journal of Artificial Societies and Social Simulation, 23(2):10. <http://jasss.soc.surrey.ac.uk/23/2/10.html>. doi: 10.18564/jasss.4298


Giulioni, G. (2020) Should the family size be used in COVID-19 vaccine prioritization strategy to prevent variants diffusion? A first investigation using a basic ABM. Review of Artificial Societies and Social Simulation, 15th April 2021. https://rofasss.org/2021/04/15/famsize/


 

The role of population scale in compartmental models of COVID-19 transmission

By Christopher J. Watts1,*, Nigel Gilbert2, Duncan Robertson3, 4, Laurence T. Droy5, Daniel Ladley6and Edmund Chattoe-Brown5

*Corresponding author, 12 Manor Farm Cottages, Waresley, Sandy, SG19 3BZ, UK, 2Centre for Research in Social Simulation (CRESS), University of Surrey, Guildford GU2 7XH, UK, 3School of Business and Economics, Loughborough University, Loughborough, UK, 4St Catherine’s College, University of Oxford, Oxford, UK, 5School of Media, Communication and Sociology, University of Leicester, UK, 6University of Leicester School of Business, University of Leicester, Leicester, LE17RH, UK

(A contribution to the: JASSS-Covid19-Thread)

Compartmental models of COVID-19 transmission have been used to inform policy, including the decision to temporarily reduce social contacts among the general population (“lockdown”). One such model is a Susceptible-Exposed-Infectious-Removed (SEIR) model developed by a team at the London School of Hygiene and Tropical Medicine (hereafter, “the LSHTM model”, Davies et al., 2020a). This was used to evaluate the impact of several proposed interventions on the numbers of cases, deaths, and intensive care unit (ICU) hospital beds required in the UK. We wish here to draw attention to behaviour common to this and other compartmental models of diffusion, namely their sensitivity to the size of the population simulated and the number of seed infections within that population. This sensitivity may compromise any policy advice given.

We therefore describe below the essential details of the LSHTM model, our experiments on its sensitivity, and why they matter to its use in policy making.

The LSHTM model

Compartmental models of disease transmission divide members of a population according to their disease states, including at a minimum people who are “susceptible” to a disease, and those who are “infectious”. Susceptible individuals make social contact with others within the same population at given rates, with no preference for the other’s disease state, spatial location, or social networks (the “universal mixing” assumption). Social contacts result in infections with a chance proportional to the fraction of the population who are currently infectious. Perhaps to reduce the implausibility of the universal mixing assumption, the LSHTM model is run for each of 186 county-level administrative units (“counties”, having an average size of 357,000 people), instead of a single run covering the whole UK population (66.4 million). Each county receives the same seed infection schedule: two new infections per day for 28 days. The 186 county time series are then summed to form a time series for the UK. There are no social contacts between counties, and the 186 county-level runs are independent of each other. Outputs from the model include total and peak cases and deaths, ICU and non-ICU hospital bed occupancy, and the time to peak cases, all reported for the UK as a whole.

Interventions are modelled as 12-week reductions in contact rates, and, in the first experiment, scheduled to commence 6 weeks prior to the peak in UK cases with no intervention. Further experiments shift the start of the intervention, and trigger the intervention upon reaching a given number of ICU beds, rather than a specific time.

Studying sensitivity to population size

The 186 counties vary in their population sizes, from Isles of Scilly (2,242 people) to West Midlands (2.9 million). We investigated whether the variation in population size led to differences in model behaviour. The LSHTM model files were cloned from https://github.com/cmmid/covid-UK , while the data analysis was performed using our own scripts posted at https://github.com/innovative-simulator/PopScaleCompartmentModels .

A graph showing Peak week infections against population size (on a log scale). The peak week looks increasing linear (with the log population scale), but there is a uniform increase in peak week with more seed infections.The figure above shows the results of running the LSHTM model with populations of various sizes, each point being an average of 10 repetitions. The time, in weeks, to the peak in cases forms a linear trend with the base-10 logarithm of population. A linear regression line fitted to these points gives Peak Week = 2.70 log10(Population) – 2.80, with R2 = 0.999.

To help understand this relationship, we then compared the seeding used by the LSHTM team, i.e. 2 infectious persons per day for 28 days, to two forms of reduced seeding, 1 per day for 28 days, and 2 per day for 14 days. Halving the seeding is similar in effect, but not identical to, doubling the population size.

Deterministic versions of other compartmental models of transmission (SIR, SEIR, SI) confirmed the relation between population size and time of occurrence to be a common feature of such models. See the R and Excel files at: https://github.com/innovative-simulator/PopScaleCompartmentModels .

For the simplest, the SI model, the stock of infectious people is described by the logistic function.I(t)=N/(1+exp(-u*C*(t-t*)))Here N is the population size, u susceptibility, and C the contact rate. If I(0)=s, the number of seed infections, then it can be shown that the peak in new infections, I(t*), occurs at timet*=ln(N/s-1)/(u*C)

Hence, for N/s >> 1, the time to peak cases, t*, correlates well with log10N/s.

As well as peak cases, analogous sensitivity was found for the timing of peaks in infections and hospital admissions, and for reaching critical levels, such as the hospital bed capacity as a proportion of the population. In contrast, the heights of peaks, and totals of cases, deaths and beds were constant percentages of population when population size was varied.

Why the unit of population matters

Davies et al. (2020a) make forecasts of both the level of peak cases and the timing of their occurrence. Despite showing that two counties can vary in their results (Davies et al., 2020a, p. 6), and mentioning in the supplementary material some effects of changing the seeding schedule (Davies et al., 2020b, p. 5), they do not mention any sensitivity to population size. But, as we have shown here, given the same number and timing of seed infections, the county with the smallest population will peak in cases earlier than the one with the largest. This sensitivity to population size affects the arguments of Davies et al. in several ways.

Firstly, Davies et al. produce their forecasts for the UK by summing county-level time series. But counties with out-of-sync peaks will sum to produce a shorter, flatter peak for the UK, than would have been achieved by synchronous county peaks. Thus the forecasts of peak cases for the UK are being systematically biased down.

Secondly, timing is important for the effectiveness of the interventions. As Davies et al. note in relation to their experiment on shifting the start time of the intervention, an intervention can be too early or too late. It is too early if, when it ends after 12 weeks, the majority of the population is still susceptible to any remaining infectious cases, and a serious epidemic can still occur. At the other extreme, an intervention can be too late if it starts when most of the epidemic has already occurred.

A timing problem also threatens if the intervention is triggered by the occupancy of ICU beds reaching some critical level. This level will be reached for the UK or average county later than for a small county. Thus the problem extends beyond the timing of peaks to affect other aspects of a policy supported by the model.

Our results imply that an intervention timed optimally for a UK-level, or average county-level, cases peak, as well as an intervention triggered by a UK-level beds occupancy threshold, may be less effective for counties with far-from-average sizes.

There are multiple ways of resolving these issues, including re-scaling seed infections in line with size of population unit, simulating the UK directly rather than as a sum of counties, and rejecting compartmental models in favour of network- or agent-based models. A discussion of the respective pros and cons of these alternatives requires a longer paper. For now, we note that compartmental models remain quick and cheap to design, fit, and study. The issues with Davies et al. (2020a) we have drawn attention to here highlight (1) the importance of adequate sensitivity testing, (2) the need for care when choosing at which scale to model and how to seed an infection, and (3) the problems that can stem from uniform national policy interventions, rather than ones targeted at a more local level.

References

Davies, N. G., Kucharski, A. J., Eggo, R. M., Gimma, A., Edmunds, W. J., Jombart, T., . . . Liu, Y. (2020a). Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study. The Lancet Public Health, 5(7), e375-e385. doi:10.1016/S2468-2667(20)30133-X

Davies, N. G., Kucharski, A. J., Eggo, R. M., Gimma, A., Edmunds, W. J., Jombart, T., . . . Liu, Y. (2020b). Supplement to Davies et al. (2020b). https://www.thelancet.com/cms/10.1016/S2468-2667(20)30133-X/attachment/cee85e76-cffb-42e5-97b6-06a7e1e2379a/mmc1.pdf


Watts, C.J., Gilbert, N., Robertson, D., Droy, L.T., Ladley, D and Chattoe-Brown, E. (2020) The role of population scale in compartmental models of COVID-19 transmission. Review of Artificial Societies and Social Simulation, 14th August 2020. https://rofasss.org/2020/08/14/role-population-scale/


 

A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation

By Edmund Chattoe-Brown

The Motivation

Research that confronts models with data is still sufficiently rare that it is hard to get a representative sense of how it is done and how convincing the results are simply by “background reading”. One way to advance good quality empirical modelling is therefore simply to make it more visible in quantity. With this in mind I have constructed (building on the work of Angus and Hassani-Mahmooei 2015) the first version of a bibliography listing all ABM attempting empirical validation in JASSS between 1998 and 2019 (along with a few other example) – which generates 68 items in all. Each entry gives a full reference and also describes what comparisons are made and where in the article they occur. In addition the document contains a provisional bibliography of articles giving advice or technical support to validation and lists three survey articles that categorise large samples of simulations by their relationships to data (which served as actual or potential sources for the bibliography).

With thanks to Bruce Edmonds, this first version of the bibliography has been made available as a Centre for Policy Modelling Discussion Paper CPM-20-216, which can be downloaded http://cfpm.org/discussionpapers/256.

The Argument

It may seem quite surprising to focus only on validation initially but there is an argument (Chattoe-Brown 2019) which says that this is a more fundamental challenge to the quality of a model than calibration. A model that cannot track real data well, even when its parameters are tuned to do so is clearly a fundamentally inadequate model. Only once some measure of validation has been achieved can we decide how “convincing” it is (comparing independent empirical calibration with parameter tuning for example). Arguably, without validation, we cannot really be sure whether a model tells us anything about the real world at all (no matter how plausible any narrative about its assumptions may appear). This can be seen as a consequence of the arguments about complexity routinely made by ABM practitioners as the plausibility of the assumptions does not map intuitively onto the plausibility of the outputs.

The Uses

Although these are covered in the preface to the bibliography in greater detail, such a sample has a number of scientific uses which I hope will form the basis for further research.

  • To identify (and justify) good and bad practice, thus promoting good practice.
  • To identify (and then perhaps fill) gaps in the set of technical tools needed to support validation (for example involving particular sorts of data).
  • To test the feasibility and value of general advice offered on validation to date and refine it in the face of practical challenges faced by analysis of real cases.
  • To allow new models to demonstrably outperform the levels of validation achieved by existing models (thus creating the possibility for progressive empirical research in ABM).
  • To support agreement about the effective use of the term validation and to distinguish it from related concepts (like verification) and potentially unhelpful (for example ambiguous or rhetorically loaded) uses

The Plan

Because of the labour involved and the diversity of fields in which ABM have now been used over several decades, an effective bibliography on this kind cannot be the work of a single author (or even a team of authors). My plan is thus to solicit (fully credited) contributions and regularly release new versions of the bibliography – with new co-authors as appropriate. (This publishing model is intended to maintain the quality and suitability for citation of the resulting document relative to the anarchy that sometimes arises in genuine communal authorship!) All of the following contributions will be gratefully accepted for the next revision (on which I am already working myself in any event)

  • References to new surveys or literature reviews that categorise significant samples of ABM research by their relationship to data.
  • References for proposed new entries to the bibliography in as much detail as possible.
  • Proposals to delete incorrectly categorised entries. (There are a small number of cases where I have found it very difficult to establish exactly what the authors did in the name of validation, partly as a result of confusing or ambiguous terminology.)
  • Proposed revisions to incorrect or “unfair” descriptions of existing entries (ideally by the authors of those pieces).
  • Offers of collaboration for a proposed companion bibliography on calibration. Ultimately this will lead to a (likely very small) sample of calibrated and validated ABM (which are often surprisingly little cited given their importance to the credibility of the ABM “project” – see, for example, Chattoe-Brown (2018a, 2018b).

Acknowledgements

This article as part of “Towards Realistic Computational Models of Social Influence Dynamics” a project funded through ESRC (ES/S015159/1) by ORA Round 5.

References

Angus, Simon D. and Hassani-Mahmooei, Behrooz (2015) ‘“Anarchy” Reigns: A Quantitative Analysis of Agent-Based Modelling Publication Practices in JASSS, 2001-2012’, Journal of Artificial Societies and Social Simulation, 18(4), October, article 16. <http://jasss.soc.surrey.ac.uk/18/4/16.html> doi:10.18564/jasss.2952

Chattoe-Brown, Edmund (2018a) ‘Query: What is the Earliest Example of a Social Science Simulation (that is Nonetheless Arguably an ABM) and Shows Real and Simulated Data in the Same Figure or Table?’ Review of Artificial Societies and Social Simulation, 11 June. https://rofasss.org/2018/06/11/ecb/

Chattoe-Brown, Edmund (2018b) ‘A Forgotten Contribution: Jean-Paul Grémy’s Empirically Informed Simulation of Emerging Attitude/Career Choice Congruence (1974)’, Review of Artificial Societies and Social Simulation, 1 June. https://rofasss.org/2018/06/01/ecb/

Chattoe-Brown, Edmund (2019) ‘Agent Based Models’, in Atkinson, Paul, Delamont, Sara, Cernat, Alexandru, Sakshaug, Joseph W. and Williams, Richard A. (eds.) SAGE Research Methods Foundations. doi:10.4135/9781526421036836969


Chattoe-Brown, E. (2020) A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation. Review of Artificial Societies and Social Simulation, 12th June 2020. https://rofasss.org/2020/06/12/abm-validation-bib/