Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-13T13:43:15.190Z Has data issue: false hasContentIssue false

Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey Datasets*

Published online by Cambridge University Press:  14 October 2013


Increasing numbers of comparative survey datasets span multiple waves. Moving beyond purely cross-sectional analyses, multilevel longitudinal analyses of such datasets should generate substantively important insights into the political, social and economic correlates of many individual-level outcomes of interest (attitudes, behaviors, etc.). This article describes two simple techniques for extracting such insights, which allow change over time in y to be a function of change over time in x and/or of a time-invariant x. The article presents results from simulation studies that assess the techniques in the presence of complications that are likely to arise with real-world data, and concludes with applications to the issues of generalized social trust and postmaterialist values, using data from World/European Values Surveys.

Original Articles
Copyright © The European Political Science Association 2013 

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.)


*Malcolm Fairbrother is Lecturer in Global Policy and Politics, School of Geographical Sciences, University of Bristol, University Road Bristol BS8 1SS, United Kingdom ( For useful comments and suggestions, he thanks Rima Wilkes, Andy Bell, Dmitriy Poznyak, David Manley and Kelvyn Jones; two anonymous PSRM reviewers; fellow members of the University of Bristol's School of Geographical Sciences Spatial Modelling Group; and audiences at ECPR 2011 in Reykjavik, ESRA 2011 in Lausanne, the 2011 ASA Spring Methodology Conference at Tilburg University and a 2012 symposium on The Quality of Measurement at the Technische Universität Dresden. Thanks also to Gethin Williams for help running simulations remotely and in parallel on multiple cores of a Linux server. To view supplementary material for this article, please visit


Anderson, Christopher J.Tverdova, Yuliya V.. 2003. ‘Corruption, Political Allegiances, and Attitudes Toward Government in Contemporary Democracies’. American Journal of Political Science 47(1):91109.Google Scholar
Azzalini, Adelchi. 2011. R package ‘sn’. Version 0.4–17.Google Scholar
Bafumi, Joseph, Gelman, Andrew. 2006. ‘Fitting Multilevel Models When Predictors and Group Effects Correlate’. Paper prepared for the 2006 Annual Meeting of the Midwest Political Science Association, Chicago, 20–23 April.Google Scholar
Barr, Dale J., Levy, Roger, Scheepers, ChristophTily, Harry J.. 2013. ‘Random Effects Structure for Confirmatory Hypothesis Testing: Keep It Maximal’. Journal of Memory and Language 68:255278.Google Scholar
Bartels, Brandon L. 2008. ‘Beyond “Fixed Versus Random Effects”: A Framework for Improving Substantive and Statistical Analysis of Panel, Time-Series Cross-Sectional, and Multilevel Data’. Unpublished manuscript. Available at, accessed 29 March 2013.Google Scholar
Bates, Douglas, Maechler, Martin, Bolker, Ben. 2012. R package ‘lme4’. Version 0.999999-0.Google Scholar
Beck, Nathaniel. 2007. ‘From Statistical Nuisances to Serious Modeling: Changing How We Think About the Analysis of Time-Series–Cross-Section Data’. Political Analysis 15:97100.Google Scholar
Bell, Andrew, Jones, Kelvyn. 2012. ‘Explaining Fixed Effects: Random Effects Modelling of Time-Series Cross-Sectional and Panel Data’. Unpublished manuscript. Available at, accessed 29 March 2013.Google Scholar
Bjørnskov, Christian. 2008. ‘Social Trust and Fractionalization: A Possible Reinterpretation’. European Sociological Review 24(3):271283.Google Scholar
Brady, David, Fullerton, Andrew S.Cross, Jennifer Moren. 2009. ‘Putting Poverty in Political Context: A Multi-Level Analysis of Adult Poverty across 18 Affluent Democracies’. Social Forces 88(1):271299.Google Scholar
Christensen, Rune Haubo. 2012. ‘Ordinal’ package. Version 5.22.Google Scholar
Clarke, Harold D.Dutt, Nitish. 1991. ‘Measuring Value Change in Western Industrialized Societies: The Impact of Unemployment’. American Political Science Review 85:905920.CrossRefGoogle Scholar
Clarke, Harold D., Dutt, NitishRapkin, Jonathan. 1997. ‘Conversations in Context: The (Mis)Measurement of Value Change in Advanced Industrial Societies’. Political Behavior 19(1):1939.Google Scholar
Collins, Linda M. 2006. ‘Analysis of Longitudinal Data: The Integration of Theoretical Model, Temporal Design, and Statistical Model’. Annual Review of Psychology 57:505528.Google Scholar
Cozzolino, Philip J. 2011. ‘Trust, Cooperation, and Equality: A Psychological Analysis of the Formation of Social Capital’. British Journal of Social Psychology 50:302320.Google Scholar
Davis, Darren W.Davenport, Christian. 1999. ‘Assessing the Validity of the Postmaterialism Index’. American Political Science Review 93(3):649664.Google Scholar
De Boef, SuzannaKeele, Luke. 2008. ‘Taking Time Seriously’. American Journal of Political Science 52(1):184200.Google Scholar
Ebbes, Peter, Böckenholt, UlfWedel, Michel. 2004. ‘Regressor and Random-Effects Dependencies in Multilevel Models’. Statistica Neerlandica 58(2):161178.Google Scholar
Enders, Craig K.Tofighi, Davood. 2007. ‘Centering Predictor Variables in Cross-Sectional Multilevel Models: A New Look at an Old Issue’. Psychological Methods 12(2):121138.Google Scholar
Fairbrother, MalcolmMartin, Isaac W.. 2013. ‘Does Inequality Erode Social Trust? Results from Multilevel Models of US States and Counties’. Social Science Research 42(2):347360.Google Scholar
Freitag, MarkusBühlmann, Marc. 2009. ‘Crafting Trust: The Role of Political Institutions in Comparative Perspective’. Comparative Political Studies 42(12):15371566.Google Scholar
Gelman, Andrew. 2005. ‘Two-Stage Regression and Multilevel Modeling: A Commentary’. Political Analysis 13:459461.Google Scholar
Gelman, AndrewHill, Jennifer. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. New York: Cambridge University Press.Google Scholar
Gelman, Andrew, Park, David, Shor, Boris, Bafumi, JosephCortina, Jeronimo. 2008. Red State, Blue State, Rich State, Poor State. Princeton: Princeton University Press.Google Scholar
Hadfield, Jarrod D. 2010. ‘MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package’. Journal of Statistical Software 33(2):122.Google Scholar
Haller, Max. 2002. ‘Theory and Method in the Comparative Study of Values: Critique and Alternative to Inglehart’. European Sociological Review 18(2):139158.Google Scholar
Hausman, Jerry A. 1978. ‘Specification Tests in Econometrics’. Econometrica 46:12511271.Google Scholar
Inglehart, RonaldAbramson, Paul R.. 1999. ‘Measuring Postmaterialism’. American Political Science Review 93(3):665677.Google Scholar
Inglehart, RonaldBaker, Wayne E.. 2000. ‘Modernization, Cultural Change, and the Persistence of Traditional Values’. American Sociological Review 65:1951.Google Scholar
Iversen, TorbenRosenbluth, Frances. 2006. ‘The Political Economy of Gender: Explaining Cross-National Variation in the Gender Division of Labor and the Gender Voting Gap’. American Journal of Political Science 50(1):119.Google Scholar
Jamal, AmaneyNooruddin, Irfan. 2010. ‘The Democratic Utility of Trust: A Cross-National Analysis’. The Journal of Politics 72(1):4559.Google Scholar
Jen, Min Hua, Jones, KelvynJohnston, Ron. 2009. ‘Global Variations in Health: Evaluating Wilkinson's Income Inequality Hypothesis using the World Values Survey’. Social Science & Medicine 68:643653.Google Scholar
Johnson, Noel D.Mislin, Alexandra. 2012. ‘How Much Should We Trust the World Values Survey Trust Question?’ Economics Letters 116:210212.Google Scholar
Karakoç, EkremBaşkan, Birol. 2012. ‘Religion in Politics: How Does Inequality Affect Public Secularization?’ Comparative Political Studies 45(12):15101541.Google Scholar
Kennedy, Bruce P., Kawachi, Ichiro, Glass, RobertaProthrow-Stith, Deborah. 1998. ‘Income Distribution, Socioeconomic Status, and Self-Rated Health in the United States: Multilevel Analysis’. British Medical Journal 317:917921.CrossRefGoogle ScholarPubMed
Kittel, BernhardWinner, Hannes. 2005. ‘How Reliable Is Pooled Analysis in Political Economy? The Globalization-Welfare State Nexus Revisited’. European Journal of Political Research 44:269293.Google Scholar
Knack, StephenKeefer, Philip. 1997. ‘Does Social Capital Have an Economic Payoff? A Cross-Country Investigation’. Quarterly Journal of Economics 112(4):12511288.Google Scholar
Martin, Nathan D.Brady, David. 2007. ‘Workers of the Less Developed World Unite? A Multilevel Analysis of Unionization in Less Developed Countries’. American Sociological Review 72:562584.CrossRefGoogle Scholar
Mathieu, John E., Aguinis, Herman, Culpepper, Steven A.Chen, Gilad. 2012. ‘Understanding and Estimating the Power to Detect Cross-Level Interaction Effects in Multilevel Modeling’. Journal of Applied Psychology 97(5):951966.Google Scholar
Mattes, RobertBratton, Michael. 2007. ‘Learning about Democracy in Africa: Awareness, Performance, and Experience’. American Journal of Political Science 51(1):192217.Google Scholar
Moller, Stephanie, Alderson, Arthur S.Nielsen, François. 2009. ‘Changing Patterns of Income Inequality in U.S. Counties, 1970–2000’. American Journal of Sociology 114:10371101.CrossRefGoogle ScholarPubMed
Mundlak, Yair. 1978. ‘On the Pooling of Time Series and Cross Section Data’. Econometrica 46(1):6985.CrossRefGoogle Scholar
Palm, Franz C., Smeekes, StephanUrbain, Jean-Pierre. 2011. ‘Cross-sectional Dependence Robust Block Bootstrap Panel Unit Root Tests’. Journal of Econometrics 163:85104.Google Scholar
Poznyak, Dmitriy, Abts, KoenraadSwyngedouw, Marc. 2011. ‘The Dynamics of the Extreme Right Support: A Growth Curve Model of the Populist Vote in Flanders-Belgium in 1987–2007’. Electoral Studies 30:672688.Google Scholar
Raudenbush, Stephen. 1989. ‘“Centering” Predictors in Multilevel Analysis: Choices and Consequences’. Multilevel Modelling Newsletter 1:1012.Google Scholar
Raudenbush, Stephen W.Bryk, Anthony S.. 2002. Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd ed.London: Sage.Google Scholar
Rothstein, BoUslaner, Eric M.. 2005. ‘All For All: Equality, Corruption, and Social Trust’. World Politics 58:4172.Google Scholar
Ruiter, StijnTubergen, Frank van. 2009. ‘Religious Attendance in Cross-National Perspective: A Multilevel Analysis of 60 Countries’. American Journal of Sociology 115(3):863895.Google Scholar
Shor, Boris, Bafumi, Joseph, Keele, LukePark, David. 2007. ‘A Bayesian Multilevel Modeling Approach to Time-Series Cross-Sectional Data’. Political Analysis 15:165181.Google Scholar
Skrondal, AndersRabe-Hesketh, Sophia. 2008. ‘Multilevel and Related Models for Longitudinal Data’. In J. de Leeuw, E. Meijer (eds.), Handbook of Multilevel Analysis, 275299, New York: Springer.Google Scholar
Skrondal, AndersRabe-Hesketh, Sophia. 2009. ‘Prediction in Multilevel Generalized Linear Models’. Journal of the Royal Statistical Society Series A 172:659687.Google Scholar
Solt, Frederick. 2008. ‘Economic Inequality and Democratic Political Engagement’. American Journal of Political Science 52(1):4860.Google Scholar
Solt, Frederick. 2009. ‘Standardizing the World Income Inequality Database’. Social Science Quarterly 90(2):231242.Google Scholar
Steenbergen, Marco R.Jones, Bradford S.. 2002. ‘Modeling Multilevel Data Structures’. American Journal of Political Science 46(1):218237.Google Scholar
Stegmueller, Daniel. 2013. ‘How Many Countries For Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches’. American Journal of Political Science, forthcoming.Google Scholar
Stevenson, Betsey, Wolfers, Justin. 2008. Economic Growth and Subjective Well-Being: Reassessing the Easterlin Paradox. NBER Working Paper No. 14282.Google Scholar
Subramanian, S.V., Jones, Kelvyn, Kaddour, AfamiaKrieger, Nancy. 2009. ‘Revisiting Robinson: The Perils of Individualistic and Ecologic Fallacy’. International Journal of Epidemiology 38:342360.CrossRefGoogle ScholarPubMed
Uslaner, Eric M.. 2002. The Moral Foundations of Trust. New York: Cambridge University Press.Google Scholar
Uslaner, Eric M.. 2008. ‘Where You Stand Depends on Where Your Grandparents Sat: The Inheritability of Generalized Trust’. Public Opinion Quarterly 72(4):725740.Google Scholar
Uslaner, Eric M.Brown, Mitchell. 2005. ‘Inequality, Trust, and Civic Engagement’. American Politics Research 33(6):868894.Google Scholar
Weldon, Steven A. 2006. ‘The Institutional Context of Tolerance for Ethnic Minorities: A Comparative, Multilevel Analysis of Western Europe’. American Journal of Political Science 50(2):331349.Google Scholar
Western, Bruce. 1998. ‘Causal Heterogeneity in Comparative Research: A Bayesian Hierarchical Modelling Approach’. American Journal of Political Science 42(4):12331259.Google Scholar
Wilkes, Rima, Guppy, NeilFarris, Lily. 2007. ‘Comment on Semyonov, Raijman, and Gorodzeisky, ASR, June 2006: Right-Wing Parties and Anti-Foreigner Sentiment in Europe’. American Sociological Review 72(5):831840.Google Scholar
Wilkinson, Richard G.Pickett, Kate E.. 2006. Income Inequality and Population Health: A Review and Explanation of the Evidence. Social Science & Medicine 62:17681784.Google Scholar
Wilkinson, Richard G.Pickett, Kate E.. 2009. The Spirit Level: Why More Equal Societies Almost Always Do Better. London: Penguin.Google Scholar
Willett, John B., Singer, Judith D.Martin, Nina C.. 1998. ‘The Design and Analysis of Longitudinal Studies of Development and Psychopathology in Context: Statistical Models and Methodological Recommendations’. Development and Psychopathology 10:395426.Google Scholar
Wilson, Sven E.Butler, Daniel M.. 2007. ‘A Lot More to Do: The Sensitivity of Time-Series Cross-Section Analyses to Simple Alternative Specifications’. Political Analysis 15:101123.Google Scholar
Wu, Yow-Wu B.Wooldridge, Powhatan J.. 2005. ‘The Impact of Centering First-Level Predictors on Individual and Contextual Effects in Multilevel Data Analysis’. Nursing Research 54:212216.Google Scholar
Supplementary material: File

Fairbrother Supplementary Material


Download Fairbrother Supplementary Material(File)
File 7.9 KB