A Quasi-Poisson Item Response Theory Model for Heterogeneous Dispersion in Count Data

Abstract

Item-level count data frequently arise in cognitive, educational, and psychological assessments. Correctly handling different dispersion levels in count data is crucial for accurate statistical inference. This research proposes a Quasi-Poisson item response theory model that accommodates overdispersion, underdispersion, and equidispersion in count data, aiming to explicitly model the connection between the mean and variance parameters, providing a method that is both computationally efficient and statistically robust. This semiparametric model specifies the first two conditional moments for the count variables and derives marginal moments to estimate model parameters. Simulation studies demonstrate the Quasi-Poisson model’s efficacy in parameter recovery across different dispersion scenarios and its negligible computation time. Empirical data analysis further underscores the model’s superior fit and computational efficiency in a real-world setting.

Keywords

unbounded count data method of moments least squares multivariate delta method weighted likelihood scoring

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