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Abstract:
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Parameter estimation in latent variable models for discrete data (common in the social sciences when questionnaires with Likert scales are administered) pose multiple challenges. Firstly, a model needs to be specified that accounts for multiple sources of measurement error. Secondly, the maximum likelihood estimators are often difficult to compute or even computationally intractable. We implement three parameter estimation techniques for models of this type — correlation reconstruction (a method based on polychoric correlation), a stochastic EM algorithm for maximum likelihood estimation, and a pairwise likelihood method. All methods assume that both the latent traits and measurement error components are mutually independent and normally distributed. The purpose of this study is two-fold: methods are compared both in terms of efficiency (measured using root mean square error) and their calculation time (computational burden). The results of a simulation study comparing the three estimation methods under different parameter configurations are presented and discussed.
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