Analysis of multivariate longitudinal categorical data subject to nonrandom missingness : a latent variable approach

• Main Author: Hafez, Mai
• Published: London School of Economics and Political Science (University of London) 2015
• Subjects: 519.5; HA Statistics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.666782

Longitudinal data are collected for studying changes across time. In social sciences, interest is often in theoretical constructs, such as attitudes, behaviour or abilities, which cannot be directly measured. In that case, multiple related manifest (observed) variables, for example survey questions or items in an ability test, are used as indicators for the constructs, which are themselves treated as latent (unobserved) variables. In this thesis, multivariate longitudinal data is considered where multiple observed variables, measured at each time point, are used as indicators for theoretical constructs (latent variables) of interest. The observed items and the latent variables are linked together via statistical latent variable models. A common problem in longitudinal studies is missing data, where missingness can be classiffed into one of two forms. Dropout occurs when subjects exit the study prematurely, while intermittent missingness takes place when subjects miss one or more occasions but show up on a subsequent wave of the study. Ignoring the missingness mechanism can lead to biased estimates, especially when the missingness is nonrandom. The approach proposed in this thesis uses latent variable models to capture the evolution of a latent phenomenon over time, while incorporating a missingness mechanism to account for possibly nonrandom forms of missingness. Two model specifications are presented, the first of which incorporates dropout only in the missingness mechanism, while the other accounts for both dropout and intermittent missingness allowing them to be informative by being modelled as functions of the latent variables and possibly observed covariates. Models developed in this thesis consider ordinal and binary observed items, because such variables are often met in social surveys, while the underlying latent variables are assumed to be continuous. The proposed models are illustrated by analysing people's perceptions on women's work using three questions from five waves of the British Household Panel Survey.