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Latent variable models are widely used in social sciences for measuring constructs (latent variables) such as ability, attitude, behavior, and wellbeing. Those unobserved constructs are measured through a number of observed items (variables). The observed variables are often subject to item nonresponse, that may be nonignorable. Incorporating a missingness mechanism within the model used to analyze data with nonresponse is crucial to obtain valid estimates for parameters, especially when the missingness is nonignorable.
In this paper, we propose a latent class model (LCM) where a categorical latent variable is used to capture a latent phenomenon, and another categorical latent variable is used to summarize response propensity. The proposed model incorporates a missingness mechanism. Bayesian estimation using Markov Chain Monte Carlo (MCMC) methods are used for fitting this LCM. Real data with binary items from the 2014 Egyptian Demographic and Health Survey (EDHS14) are used. Different levels of missingness are artificially created in order to study results of the model under low, moderate and high levels of missingness.
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