Skip to main content Accessibility help

Exploring the Dynamics of Latent Variable Models

  • Kevin Reuning (a1), Michael R. Kenwick (a2) and Christopher J. Fariss (a3)


Researchers face a tradeoff when applying latent variable models to time-series, cross-sectional data. Static models minimize bias but assume data are temporally independent, resulting in a loss of efficiency. Dynamic models explicitly model temporal data structures, but smooth estimates of the latent trait across time, resulting in bias when the latent trait changes rapidly. We address this tradeoff by investigating a new approach for modeling and evaluating latent variable estimates: a robust dynamic model. The robust model is capable of minimizing bias and accommodating volatile changes in the latent trait. Simulations demonstrate that the robust model outperforms other models when the underlying latent trait is subject to rapid change, and is equivalent to the dynamic model in the absence of volatility. We reproduce latent estimates from studies of judicial ideology and democracy. For judicial ideology, the robust model uncovers shocks in judicial voting patterns that were not previously identified in the dynamic model. For democracy, the robust model provides more precise estimates of sudden institutional changes such as the imposition of martial law in the Philippines (1972–1981) and the short-lived Saur Revolution in Afghanistan (1978). Overall, the robust model is a useful alternative to the standard dynamic model for modeling latent traits that change rapidly over time.


Corresponding author


Hide All

Authors’ note: An earlier version of this paper was presented at the annual meeting of the American Political Science Association in Philadelphia, PA (2016) and the Latent Variable Mini-Conference at the Varieties of Democracy Institute at the University of Gothenburg, Sweden (2016). We would like to thank the participants at these conferences and also James Lo, Suzie Linn, Kyle Marquardt, Ryan McMahon, Dan Pemstein, Kevin Quinn, Brigitte Seim, Jeff Staton, Jane Sumner, Alex Tahk, and Anne Whitesell for helpful comments and suggestions. The estimates from this paper along with the code necessary to implement the models in STAN and R are publicly available at a dataverse repository here: (Reuning, Kenwick, and Fariss 2018).

Contributing Editor: R. Michael Alvarez



Hide All
Arat, Z. F. 1991. Democracy and Human Rights in Developing Countries . Boulder, CO: Lynne Rienner Publishers.
Armstrong II, D. A., Bakker, R., Carroll, R., Hare, C., Poole, K. T., and Rosenthal, H.. 2014. Analyzing Spatial Models of Choice and Judgement with R . New York: Chapman and Hall/CRC.
Baker, A., Sokhey, A. E., Ames, B., and Renno, L. R.. 2016. “The Dynamics of Partisan Identification when Party Brands Change: the Case of the Workers Party in Brazil.” The Journal of Politics 78(1):197213.
Barbera, P. 2015. “Birds of the Same Feather Tweet Together. Bayesian Ideal Point Estimation Using Twitter Data.” Political Analysis 23(1):7691.
Blaydes, L., and Linzer, D. A.. 2008. “The Political Economy of Women’s Support for Fundamentalist Islam.” World Politics 60(July):576609.
Bollen, K. A. 2001. Cross-National Indicators of Liberal Democracy, 1950–1990 . 2nd ICPSR version edn. Ann Arbor, MI: Inter-university Consortium for Political and Social Research.
Bowman, K., Lehoucq, F., and Mahoney, J.. 2005. “Measuring Political Democracy: Case Expertise, Data Adequacy, and Central America.” Comparative Political Studies 38:939970.
Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M. A., Guo, J., Li, P., and Riddell, A.. 2016. “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 20:132.
Caughey, D., and Warshaw, C.. 2015. “Dynamic Estimation of Latent Opinion Using a Hierarchical Group-Level IRT Model.” Political Analysis 23:197211.
Coppedge, M., and Reinicke, W. H.. 1991. “Measuring Polyarchy.” In On Measuring Democracy: Its Consequences and Concomitants , edited by Inkeles, Alex, 4768. New Brunswick, NJ: Transaction Publishers.
Duncan, T. E., and Duncan, S. C.. 2004. “An Introduction to Latent Growth Curve Modeling.” Behavior Therapy 35(2):333363.
Epstein, L., and Knight, J.. 2013. “Reconsidering Judicial Preferences.” Annual Review of Political Science 16:1131.
Epstein, L., Segal, J. A., Spaeth, H. J., and Walker, T. G.. 1996. The Supreme Court Compendium: Data, Decisions, and Developments . 2nd edn. Thousand Oaks, CA: Congressional Quarterly Inc.
Fariss, C. J. 2014. “Respect for Human Rights has Improved Over Time: Modeling the Changing Standard of Accountability.” American Political Science Review 108(2):297318.
Fariss, C. J. 2018. “The Changing Standard of Accountability and the Positive Relationship Between Human Rights Treaty Ratification and Compliance.” British Journal of Political Science 48(1):239272.
Fonseca, T. C. O., Ferreira, M. A. R., and Migon, H. S.. 2008. “Objective Bayesian Analysis for the Student-t Regression Model.” Biometrika 95(2):325333.
Freedom House. 2007. “Freedom in the World.”
Furr, D. C.2017. “Bayesian and Frequentist Cross-Validation Methods for Explanatory Item Response Models.” PhD thesis, University of California, Berkeley.
Gasiorowski, M. J. 1996. “An Overview of the Political Regime Change Data Set.” Comparative Political Studies 29:469483.
Gelman, A., and Hill, J.. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models . Cambridge University Press.
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B.. 2014. Bayesian Data Analysis . 3rd edn. New York: CRC Press.
Geweke, J. 1993. “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 8(S1):S19S40.
Grief, A., and Laitin, D. D.. 2004. “A Theory of Endogenous Institutional Change.” American Political Science Review 98(4):633650.
Hamilton, J. D. 2010. “Regime Switching Models.” In Macroeconometrics and Time Series Analysis , 202209. New York: Springer.
Hollyer, J. R., Rosendorff, B. P., and Vreeland, J. R.. 2014. “Measuring Transparency.” Political Analysis 22:413434.
Imai, K., Lo, J., and Olmsted, J.. 2016. “Fast Estimation of Ideal Points with Massive Data.” American Political Science Review 110(4):631656.
Jackman, S. 2009. Bayesian Analysis for the Social Sciences . Chichester: Wiley.
Jesse, S. A. 2017. “Don’t Know Responses, Personality and the Measurement of Political Knowledge.” Political Science Research and Methods 5(4):711731.
Joseph, L., Wolfson, D. B., Du Berger, R., and Lyle, R. M.. 1997. “Analysis of Panel data With Change-Points.” Statistica Sinica 7:687703.
Kenwick, M.2019. “Is Civilian Control Self-Reinforcing? A Measurement Based Analysis of Civil-Military Relations.” Working Paper.
Kōnig, T., Marbach, M., and Osnabrügge, M.. 2013. “Estimating Party Positions Across Countries and Time—a Dynamic Latent Variable Model for Manifestos Data.” Political Analysis 21(4):468491.
Lange, K., and Sinsheimer, J. S.. 1993. “Normal/Independent Distributions and Their Applications in Robust Regression.” Journal of Computational and Graphical Statistics 2(2):175198.
Lange, K. L., Little, R. J. A., and Taylor, J. M. G.. 1989. “Robust Statistical Modeling Using the $t$ Distribution.” Journal of the American Statistical Association 408(84):881896.
Leventoğlu, B., and Slantchev, B. L.. 2007. “The Armed Peace: a Punctuated Equilibrium Theory of War.” American Journal of Political Science 51(4):755771.
Li, L., Qiu, S., Zhang, B., and Feng, C. X.. 2016. “Approximating Cross-Validatory Predictive Evaluation in Bayesian Latent Variable Models with Integrated IS and WAIC.” Statistics and Computing 26(4):881897.
Linzer, D., and Staton, J. K.. 2016. “A Global Measure of Judicial Independence, 1948–2012.” Journal of Law and Courts 3(2):223256.
Marshall, M. G., Jaggers, K., and Gurr, T. R.. 2006. “Polity IV: Political Regime Characteristics and Transitions, 1800–2004.”
Martin, A. D., and Quinn, K. M.. 2002. “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the US Supreme Court, 1953–1999.” Political Analysis 10(2):134153.
Martin, A. D., and Quinn, K. M.. 2007. “Assessing Preference Change of the US Supreme Court.” Journal of Law, Economics and Organization 23(2):365385.
Pan, J., and Xu, Y.. 2018. “China’s Ideological Spectrum.” Journal of Politics 80(1):254273.
Pang, X., Friedman, B., Martin, A. D., and Quinn, K. M.. 2012. “Endogenous Jurisprudential Regimes. Political Analysis.” Political Analysis 20(4):417436.
Pemstein, D., Meserve, S. A., and Melton, J.. 2010. “Democratic Compromise: A Latent Variable Analysis of Ten Measures of Regime Type.” Political Analysis 18(4):426449.
Pérez, E. O. 2011. “The Origins and Implications of Language Effects in Multilingual Surveys: A MIMIC Approach With Application to Latino Political Attitudes.” Political Analysis 19:434454.
Przeworski, A., Alvarez, M., Cheibub, J., and Limongi, F.. 2000. Democracy and Development: Political Regimes and Economic Well-Being in the World, 1950–1990 . Cambridge: Cambridge University Press.
Reuning, K., Kenwick, M. R., and Fariss, C. J.. 2018. “Replication Data for: Exploring the Dynamics of Latent Variable Models.”, Harvard Dataverse, V1.
Rosa, G. J. M., Gianola, D., and Padovani, C. R.. 2004. “Bayesian Longitudinal Data Analysis with Mixed Models and Thick-Tailed Distributions Using MCMC.” Journal of Applied Statistics 31(7):855873.
Santifort, C., Sandler, T., and Brandt, P. T.. 2013. “Terrorist Attack and Target Diversity: Changepoints and Their Drivers.” Journal of Peace Research 50(1):7590.
Schnakenberg, K. E., and Fariss, C. J.. 2014. “Dynamic Patterns of Human Rights Practices.” Political Science and Research Methods 2(1):131.
Spirling, A. 2007. “Bayesian Approaches for Limited Dependent Variable Change Point Problems.” Political Analysis 15(4):387405.
Stegmueller, D. 2011. “Apples and Oranges? The Problem of Equivalence in Comparative Research.” Political Analysis 19:471487.
Stegmueller, D. 2013. “Modeling Dynamic Preferences: A Bayesian Robust Dynamic Latent Ordered Probit Model.” Political Analysis 21:314333.
Tahk, A. M. 2015. “A Continuous-Time, Latent-Variable Model of Time Series Data.” Political Analysis 23(2):278298.
Treier, S., and Hillygus, D. S.. 2009. “The Nature of Political Ideology in the Contemporary Electorate.” Public Opinion Quarterly 73(4):679703.
Treier, S., and Jackman, S.. 2008. “Democracy as a Latent Variable.” American Journal of Political Science 52(1):201217.
Vanhanen, T. 2003. Democratization: A Comparative Analysis of 170 Countries . New York: Routledge.
Vehtari, A., Gelman, A., and Gabry, J.. 2016. “Practical Bayesian Model Evaluation Using Leave-one-out Cross-Validation and WAIC.” Statistics and Computing 27(5):120.
Voeten, E. 2000. “Clashes in the Assembly.” International Organization 54(2):185215.
Western, B., and Kleykamp, M.. 2004. “A Bayesian Change Point Model for Historical Time Series analysis.” Political Analysis 12(4):354374.
Woodward, B., and Armstrong, S.. 1979. The Brethren: Inside the Supreme Court . New York: Simon and Schuster.
Zhang, Z., Lai, K., Lu, Z., and Tong, X.. 2013. “Bayesian Inference and Application of Robust Growth Curve Models Using Student’s $t$ Distribution.” Structural Equation Modeling: A Multidisciplinary Journal 20(1):4778.
MathJax is a JavaScript display engine for mathematics. For more information see


Related content

Powered by UNSILO
Type Description Title
Supplementary materials

Reuning et al. supplementary material
Reuning et al. supplementary material 1

 Unknown (989 KB)
989 KB
Supplementary materials

Reuning et al. Dataset


Exploring the Dynamics of Latent Variable Models

  • Kevin Reuning (a1), Michael R. Kenwick (a2) and Christopher J. Fariss (a3)


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.