Essays on discrete latent variable models

This thesis is formed by three chapters related to discrete latent variable models. The first chapter provides an introduction to latent variable models, focusing on models with discrete unobserved variables. First, the broad class of Finite Mixture Models (FMMs) is presented, along with the description of a mixture of Gaussian components. Then, Latent Class (LC) models are introduced, in their basic formulation, as well as an extension for the inclusion of covariates. Finally, latent class analysis is extended to longitudinal settings, with the definition of Latent Markov (LM) models, and an equivalent variation with covariates is discussed. A causal formulation of an LM model is also introduced, providing a link to the second chapter. In Chapter 2, we propose a causal inference approach that may be applied with longitudinal data and time-varying treatments, to assess the effectiveness of remittances on the poverty level of recipient households. The method relies on the integration of a propensity score based technique, the inverse propensity weighting, with a general LM framework. It is particularly useful when the interest is in an individual characteristic that is not directly observable and the analysis is focused on: (i) clustering individuals in a finite number of classes according to this latent characteristic and (ii) modeling its evolution across time depending on the received treatment. Parameter estimation is based on a two-step procedure. First, individual weights are computed accounting for predetermined covariates. Then, a weighted version of the standard LM model likelihood, based on such weights, is maximized by means of an expectation-maximization algorithm. Finite-sample properties of the estimator are studied by simulation. The application is focused on the effect of remittances on the poverty status of Ugandan households, based on a longitudinal survey spanning the period 2009-2014, and where the manifest variables are indicators of deprivation. In Chapter 3, we propose a novel multivariate approach for the estimation of intergenerational transition matrices. Our methodology is grounded on the assumption that individuals’ social status is unobservable and must be predicted. In this framework, parents and offspring are clustered on the basis of the observed levels of income and occupational categories, thus avoiding any discretionary rule in the definition of class boundaries. The resulting transition matrix is a function of the posterior probabilities of parents and young adults of belonging to each class. Estimation is carried out via maximum likelihood by means of an expectation-maximization algorithm. We illustrate the proposed method using National Longitudinal Survey Data from the United States in the period 1978-2006.