Mixture Models for Repeatedly Measured Survey Data with “Don’t Know” Category and/or Floor Effects

• Activity Number: 517 - New Approaches for Correlated and Clustered Data
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Ralitza Gueorguieva* and Eugenia Buta and Meghan Morean and Patricia Simon and Suchitra Krishnan-Sarin
• Companies: Yale University and Yale University and Yale University and Yale University and Yale University
• Keywords: mixture model; longitudinal data; floor effects; correlated data; random effects models; nominal and ordinal data

Abstract

Survey data items are commonly collected on a Likert scale and may have an additional “don’t know” category. It is also typical to have questions that are not applicable to some individuals or to observe floor or ceiling effects on ordinal or interval responses. These situations necessitate the use of mixture models to properly account for the structure of the data. The model formulation also needs to account for correlations among repeated measures within individual. We present a couple of mixture models with random effects for such situations. In particular, we use logistic sub-models to handle “don’t know”, inapplicable or floor effects and appropriate generalized linear sub-models for the remaining data. Correlated random effects link the sub-models together. For illustration we use data from a survey of tobacco attitudes and behaviors of high school students in Connecticut and from the Populations Assessment of Tobacco and Health (PATH) study. Maximum likelihood estimation methods are used for model fitting and inference. The software implementation is using PROC NLMIXED in SAS. Simulation studies evaluate bias and efficiency of the parameter estimates.