Abstract

In various fields such as social sciences, health, and education, it is feasible to represent and describe phenomena that cannot be directly measured. Response patterns are examined through the observation of a set of variables, known as indicators, which are influenced by an unobservable variable referred to as a latent variable or construct. In this context, Latent Class Analysis (LCA) stands out as a significant analytical approach, serving as a statistical modeling technique that utilizes categorical indicators and constructs to define mutually exclusive subgroups of individuals with similar characteristics. The integration of Causal Inference methods with LCA enables researchers to make causal claims regarding measured relationships by analyzing the prevalence of latent classes. Additionally, many studies incorporate complex sampling processes, which include cluster sampling and stratification. This work combines different approaches for causal estimation of interventions on a categorical latent variable using propensity scores within the framework of complex sampling designs. These methodologies are illustrated through an analysis of data regarding the mental health of Brazilians, specifically examining their responses to the nine items of the PHQ-9 (Patient Health Questionnaire-9) from the 2013 National Health Survey (PNS-2013). The objective is to estimate the causal effect of lifestyle choices, such as living alone or not, on depression in adults. Simulation studies are conducted to evaluate the proposed methods.