Exponential Family Models for Continuous Responses

Abstract

Two models for continuous responses that allow for separation of item and person parameters are explored. One is a newly developed model which can be seen as a Rasch model for continuous responses, the other is a slight generalization of a model proposed by Müller (1987). For both models it is shown that CML-estimation is possible in principle, but practically unfeasible. Estimation of the parameters using only item pairs, a form of pseudo-likelihood estimation, is proposed and detailed expressions for first and second order partial derivatives are given. A comparison of the information function between models for continuous and for discrete observations is discussed. The relation between these models and the probability measurement developed in the 1960s is addressed as well.