An Extended Two-Parameter Logistic Item Response Model to Handle Continuous Responses and Sparse Polytomous Responses

The article proposes a novel item response theory model to handle continuous responses and sparse polytomous responses in psychological and educational measurement. The model extends the traditional two-parameter logistic model by incorporating a precision parameter, which, along with a beta distribution, forms an error component that accounts for the response continuity. Furthermore, transforming ordinal responses to a continuous scale enables the fitting of polytomous item responses while consistently applying three parameters per item for model parsimony. The model's accuracy, stability, and computational efficiency in parameter estimation were examined. An empirical application demonstrated the model's effectiveness in representing the characteristics of continuous item responses. Additionally, the model's applicability to sparse polytomous data was supported by cross-validation results from another empirical dataset, which indicates that the model's parsimony can enhance model-data fit compared to existing polytomous models.