Complex latent variable modeling for multivariate hierarchical data

This thesis extends, in four independent chapters, the stepwise multilevel latent class analysis with covariates methodological framework. In recent decades, the latent class analysis methodological scholarship has developed sophisticated methodologies, including innovative estimation approaches and open-source software implementations, yet many of these methodological advancements have not yet been extended to the multilevel modeling context. With the increasing availability of hierarchical data, such as cross-national surveys, multilevel latent class analysis is becoming increasingly more applicable, and the utility of extending state-of-the-art methods increasingly greater. The first chapter, co-authored by Roberto Di Mari, Zsuzsa Bakk, Jennifer Oser, and Jouni Kuha, makes two contributions. First, it compiles state-of-the-art methodologies for multilevel latent class analysis with covariates, describing benchmark model specifications and estimation approaches, and detailing initialization issues and model selection alternatives. Second, it proposes the novel R package multilevLCA package as the first open-source software implementing the described state-of-the-art methodologies, and the first software overall automatically implementing some stepwise and sequential routines. As such, it contributes both to the methodological statistics literature and to the open-source statistical software literature. This chapter is published as the article Multilevel Latent Class Analysis: State-of-the-Art Methodologies and Their Implementation in the R Package multilevLCA in the journal Multivariate Behavioral Research. The second chapter, co-authored with Zsuzsa Bakk, Jennifer Oser, and Roberto Di Mari, proposes a novel bias-adjusted three-step estimation approach for multilevel latent class analysis models with covariates. This contributes, to the methodological statistics literature, with the first modeling option for multilevel latent class analysis models with covariates involving the practically appealing property of allowing the applied researcher to work with an explicit dependent variable. This chapter is published as the article Bias-Adjusted Three-Step Multilevel Latent Class Modeling with Covariates in the journal Structural Equation Modeling: A Multidisciplinary Journal. The third chapter, co-authored with Jouni Kuha and Jennifer Oser, contributes with a novel two-step estimation approach for multilevel latent class analysis models with covariates and non-equivalence of measurement, to the methodological statistics literature. This approach accounts for violations of a standard modeling assumption and extends benchmark estimation routines to modeling contexts which are common in applied cross-national survey research. This chapter is published as the article Two-Step Multilevel Latent Class Analysis in the Presence of Measurement Non-Equivalence in the journal Structural Equation Modeling: A Multidisciplinary Journal. The fourth chapter, co-authored with Roberto Di Mari and Jouni Kuha, extends benchmark estimation routines for multilevel latent class analysis models with covariates to the Bayesian statistical framework. The novel Bayesian routines contribute to the methodological statistics literature with an alternative methodology with improved performance relative to the standard frequentist approach in common problematic modeling contexts involving small samples. This chapter is work in progress on a more extensive study.