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Abstract:
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Latent structure models (LSMs) are widely applied to binary response data in education and psychology; however, binary response models are not applicable to the wealth of ordinal data collected by educational, psychological, and behavioral researchers. We propose a new LSM for ordinal response data and discuss new identifiability conditions for structured multinomial mixture models with binary attributes. We develop a new Bayesian algorithm for approximating the posterior distribution and provide evidence of accurate parameter recovery in a Monte Carlo simulation study across moderate to large sample sizes. We report results from applications to demonstrate the utility of the method for social and behavioral researchers.
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