Restricted Latent Class Models for Nominal Response Data: Identifiability and Estimation

Restricted latent class models (RLCMs) provide an important framework for diagnosing and classifying respondents on a collection of multivariate binary responses. Recent research made significant advances in theory for establishing identifiability conditions for RLCMs with binary and polytomous response data. Multiclass data, which are unordered nominal response data, are also widely collected in the social sciences and psychometrics via forced-choice inventories and multiple choice tests. We establish new identifiability conditions for parameters of RLCMs for multiclass data and discuss the implications for substantive applications. The new identifiability conditions are applicable to a wealth of RLCMs for polytomous and nominal response data. We propose a Bayesian framework for inferring model parameters, assess parameter recovery in a Monte Carlo simulation study, and present an application of the model to a real dataset.

Automated summary

This study proposes new identifiability conditions for the parameters of Restricted Latent Class Models (RLCMs) for multiclass data and discusses their implications for substantive applications. A Bayesian framework is proposed to infer model parameters, and parameter recovery is assessed through a Monte Carlo simulation study. The model is also applied to a real dataset.