Theoretical and Empirical Comparisons between Two Models for Continuous Item Response

This article analyzes the relations between two continuous response models intended for typical response items: the linear congeneric model and Samejima's continuous response model (CRM). Using a factor analytical (FA) approach based on the assumption of underlying response variables, I describe how a particular case of the CRM can be considered as a nonlinear counterpart of Spearman's FA model. The mathematical relations between the: item-trait regressions, item parameter values, and conditional and marginal distributions of both models are obtained. The results allow (a) the item parameter values of the linear model to be obtained from CRM item parameter values, and (b) the conditions in which the congeneric model will be a good approximation to the CRM to be predicted. The relations described are illustrated using an empirical example and assessed by means of a simulation study.