Bayesian latent pattern mixture models for handling attrition in panel studies with refreshment samples

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Many panel studies collect refreshment samples—new, randomly sampled respondents who complete the questionnaire at the same time as a subsequent wave of the panel. With appropriate modeling, these samples can be leveraged to correct inferences for biases caused by nonignorable attrition. We present such a model when the panel includes many categorical survey variables. The model relies on a Bayesian latent pattern mixture model, in which an indicator for attrition and the survey variables are modeled jointly via a latent class model.We allow the multinomial probabilities within classes to depend on the attrition indicator, which offers additional flexibility over standard applications of latent class models. We present results of simulation studies that illustrate the benefits of this flexibility. We apply the model to correct attrition bias in an analysis of data from the 2007–2008 Associated Press/Yahoo News election panel study.






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Si, Y, JP Reiter and DS Hillygus (2016). Bayesian latent pattern mixture models for handling attrition in panel studies with refreshment samples. Annals of Applied Statistics, 10(1). pp. 118–143. 10.1214/15-AOAS876 Retrieved from

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Jerome P. Reiter

Professor of Statistical Science

My primary areas of research include methods for preserving data confidentiality, for handling missing values, for integrating information across multiple sources, and for the analysis of surveys and causal studies. I enjoy collaborating on data analyses with researchers who are not statisticians, particularly in the social sciences and public policy.


D. Sunshine Hillygus

Professor of Political Science

Professor Hillygus has published widely on the topics of American political behavior, campaigns and elections, survey methods, public opinion, and information technology and politics.  She is co-author of Making Young Voters:  Converting Civic Attitudes into Civic Action (Cambridge University Press, 2020), The Persuadable Voter: Wedge Issues in Political Campaigns (Princeton University Press, 2008) and The Hard Count: The Social and Political Challenges of the 2000 Census (Russell Sage Foundation, 2006). She is director of the Duke Initiative on Survey Methodology ( and co-director of the Polarization Lab (

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