Theoretical and Empirical Comparisons between Two Models for Continuous Item Response

Multivariate Behavioral Research
Pere J Ferrando

Abstract

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.

References

Jul 1, 1978·British Journal of Clinical Pharmacology·C Maxwell
May 1, 1984·The British Journal of Mathematical and Statistical Psychology·M W Browne
Dec 11, 1999·The British Journal of Clinical Psychology·S M Brumfitt, P Sheeran
Mar 25, 2000·Scandinavian Journal of Psychology·G Andersson, L Yardley
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Jul 1, 2001·Multivariate Behavioral Research·P J Ferrando, U Lorenzo-Seva
Jul 1, 1994·Multivariate Behavioral Research·G J Mellenbergh

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Citations

Jul 1, 2014·Multivariate Behavioral Research·Pere J Ferrando
Jun 27, 2012·Behavior Research Methods·Cengiz Zopluoglu
Aug 18, 2020·Multivariate Behavioral Research·Javier RevueltaMiguel Ángel Alcazar-Córcoles
Mar 12, 2020·Educational and Psychological Measurement·Cengiz Zopluoglu

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