Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-24T12:57:13.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploring the Dynamics of Latent Variable Models

Published online by Cambridge University Press:  11 April 2019

Kevin Reuning Open the ORCID record for Kevin Reuning [Opens in a new window] ,
Michael R. Kenwick Open the ORCID record for Michael R. Kenwick [Opens in a new window]  and
Christopher J. Fariss Open the ORCID record for Christopher J. Fariss [Opens in a new window]
Kevin Reuning*
Affiliation:
Department of Political Science, Miami University, Oxford, OH 45056, USA. Email: [email protected]
Michael R. Kenwick
Affiliation:
Department of Political Science, Rutgers University, New Brunswick, NJ 08901USA. Email: [email protected]
Christopher J. Fariss
Affiliation:
Department of Political Science, University of Michigan, Ann Arbor, MI 48104, USA. Email: [email protected]
*
*Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

latent variablesdynamic modelingBayesian analysis
Type
Articles
Information
Political Analysis , Volume 27 , Issue 4 , October 2019 , pp. 503 - 517
Copyright
Copyright © The Author(s) 2019. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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: https://doi.org/10.7910/DVN/SSLCFF (Reuning, Kenwick, and Fariss 2018).

Contributing Editor: R. Michael Alvarez

References

Arat, Z. F. 1991. Democracy and Human Rights in Developing Countries . Boulder, CO: Lynne Rienner Publishers.Google Scholar
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.Google Scholar
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):197–213.Google Scholar
Barbera, P. 2015. “Birds of the Same Feather Tweet Together. Bayesian Ideal Point Estimation Using Twitter Data.” Political Analysis 23(1):76–91.Google Scholar
Blaydes, L., and Linzer, D. A.. 2008. “The Political Economy of Women’s Support for Fundamentalist Islam.” World Politics 60(July):576–609.Google Scholar
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.Google Scholar
Bowman, K., Lehoucq, F., and Mahoney, J.. 2005. “Measuring Political Democracy: Case Expertise, Data Adequacy, and Central America.” Comparative Political Studies 38:939–970.Google Scholar
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 20:1–32.Google Scholar
Caughey, D., and Warshaw, C.. 2015. “Dynamic Estimation of Latent Opinion Using a Hierarchical Group-Level IRT Model.” Political Analysis 23:197–211.Google Scholar
Coppedge, M., and Reinicke, W. H.. 1991. “Measuring Polyarchy.” In On Measuring Democracy: Its Consequences and Concomitants , edited by Inkeles, Alex, 47–68. New Brunswick, NJ: Transaction Publishers.Google Scholar
Duncan, T. E., and Duncan, S. C.. 2004. “An Introduction to Latent Growth Curve Modeling.” Behavior Therapy 35(2):333–363.Google Scholar
Epstein, L., and Knight, J.. 2013. “Reconsidering Judicial Preferences.” Annual Review of Political Science 16:11–31.Google Scholar
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.Google Scholar
Fariss, C. J. 2014. “Respect for Human Rights has Improved Over Time: Modeling the Changing Standard of Accountability.” American Political Science Review 108(2):297–318.Google Scholar
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):239–272.Google Scholar
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):325–333.Google Scholar
Freedom House. 2007. “Freedom in the World.” http://www.freedomhouse.org.Google Scholar
Furr, D. C.2017. “Bayesian and Frequentist Cross-Validation Methods for Explanatory Item Response Models.” PhD thesis, University of California, Berkeley.Google Scholar
Gasiorowski, M. J. 1996. “An Overview of the Political Regime Change Data Set.” Comparative Political Studies 29:469–483.Google Scholar
Gelman, A., and Hill, J.. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models . Cambridge University Press.Google Scholar
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.Google Scholar
Geweke, J. 1993. “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 8(S1):S19–S40.Google Scholar
Grief, A., and Laitin, D. D.. 2004. “A Theory of Endogenous Institutional Change.” American Political Science Review 98(4):633–650.Google Scholar
Hamilton, J. D. 2010. “Regime Switching Models.” In Macroeconometrics and Time Series Analysis , 202–209. New York: Springer.Google Scholar
Hollyer, J. R., Rosendorff, B. P., and Vreeland, J. R.. 2014. “Measuring Transparency.” Political Analysis 22:413–434.Google Scholar
Imai, K., Lo, J., and Olmsted, J.. 2016. “Fast Estimation of Ideal Points with Massive Data.” American Political Science Review 110(4):631–656.Google Scholar
Jackman, S. 2009. Bayesian Analysis for the Social Sciences . Chichester: Wiley.Google Scholar
Jesse, S. A. 2017. “Don’t Know Responses, Personality and the Measurement of Political Knowledge.” Political Science Research and Methods 5(4):711–731.Google Scholar
Joseph, L., Wolfson, D. B., Du Berger, R., and Lyle, R. M.. 1997. “Analysis of Panel data With Change-Points.” Statistica Sinica 7:687–703.Google Scholar
Kenwick, M.2019. “Is Civilian Control Self-Reinforcing? A Measurement Based Analysis of Civil-Military Relations.” Working Paper. https://sites.psu.edu/mikekenwick/files/2014/10/Kenwick_civctrl-27x6n9z.pdf.Google Scholar
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):468–491.Google Scholar
Lange, K., and Sinsheimer, J. S.. 1993. “Normal/Independent Distributions and Their Applications in Robust Regression.” Journal of Computational and Graphical Statistics 2(2):175–198.Google Scholar
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):881–896.Google Scholar
Leventoğlu, B., and Slantchev, B. L.. 2007. “The Armed Peace: a Punctuated Equilibrium Theory of War.” American Journal of Political Science 51(4):755–771.Google Scholar
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):881–897.Google Scholar
Linzer, D., and Staton, J. K.. 2016. “A Global Measure of Judicial Independence, 1948–2012.” Journal of Law and Courts 3(2):223–256.Google Scholar
Marshall, M. G., Jaggers, K., and Gurr, T. R.. 2006. “Polity IV: Political Regime Characteristics and Transitions, 1800–2004.” http://www.cidcm.umd.edu/polity/.Google Scholar
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):134–153.Google Scholar
Martin, A. D., and Quinn, K. M.. 2007. “Assessing Preference Change of the US Supreme Court.” Journal of Law, Economics and Organization 23(2):365–385.Google Scholar
Pan, J., and Xu, Y.. 2018. “China’s Ideological Spectrum.” Journal of Politics 80(1):254–273.Google Scholar
Pang, X., Friedman, B., Martin, A. D., and Quinn, K. M.. 2012. “Endogenous Jurisprudential Regimes. Political Analysis.” Political Analysis 20(4):417–436.Google Scholar
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):426–449.Google Scholar
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 19:434–454.Google Scholar
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.Google Scholar
Reuning, K., Kenwick, M. R., and Fariss, C. J.. 2018. “Replication Data for: Exploring the Dynamics of Latent Variable Models.” https://doi.org/10.7910/DVN/SSLCFF, Harvard Dataverse, V1.Google Scholar
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):855–873.Google Scholar
Santifort, C., Sandler, T., and Brandt, P. T.. 2013. “Terrorist Attack and Target Diversity: Changepoints and Their Drivers.” Journal of Peace Research 50(1):75–90.Google Scholar
Schnakenberg, K. E., and Fariss, C. J.. 2014. “Dynamic Patterns of Human Rights Practices.” Political Science and Research Methods 2(1):1–31.Google Scholar
Spirling, A. 2007. “Bayesian Approaches for Limited Dependent Variable Change Point Problems.” Political Analysis 15(4):387–405.Google Scholar
Stegmueller, D. 2011. “Apples and Oranges? The Problem of Equivalence in Comparative Research.” Political Analysis 19:471–487.Google Scholar
Stegmueller, D. 2013. “Modeling Dynamic Preferences: A Bayesian Robust Dynamic Latent Ordered Probit Model.” Political Analysis 21:314–333.Google Scholar
Tahk, A. M. 2015. “A Continuous-Time, Latent-Variable Model of Time Series Data.” Political Analysis 23(2):278–298.Google Scholar
Treier, S., and Hillygus, D. S.. 2009. “The Nature of Political Ideology in the Contemporary Electorate.” Public Opinion Quarterly 73(4):679–703.Google Scholar
Treier, S., and Jackman, S.. 2008. “Democracy as a Latent Variable.” American Journal of Political Science 52(1):201–217.Google Scholar
Vanhanen, T. 2003. Democratization: A Comparative Analysis of 170 Countries . New York: Routledge.Google Scholar
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):1–20.Google Scholar
Voeten, E. 2000. “Clashes in the Assembly.” International Organization 54(2):185–215.Google Scholar
Western, B., and Kleykamp, M.. 2004. “A Bayesian Change Point Model for Historical Time Series analysis.” Political Analysis 12(4):354–374.Google Scholar
Woodward, B., and Armstrong, S.. 1979. The Brethren: Inside the Supreme Court . New York: Simon and Schuster.Google Scholar
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):47–78.Google Scholar
Supplementary material: File

Reuning et al. supplementary material

Reuning et al. supplementary material 1

Download Reuning et al. supplementary material(File)
File 989.1 KB
Supplementary material: Link

Reuning et al. Dataset

Dataset

https://doi.org/10.7910/DVN/SSLCFF
Link