Item Response Theory Models for Forced-Choice Questionnaires

Résumé

Multidimensional forced-choice questionnaires are regarded as a means of controlling response bias. The application of these instruments has been held back historically by the ipsativity of their scores, which precludes inter-individual comparisons. Item response theory has only been applied recently, enabling them for normative scaling. The present dissertation introduces the Multi-Unidimensional Pairwise Preference-2 Parameter Logistic model, an item response model for pairwise forced-choice questionnaires. It consists of three manuscripts, each with different aims. The first manuscript introduces the model and proposes a Bayesian estimation procedure for the joint estimation of structural and incidental parameters. It tests the model estimation under different conditions on a Monte Carlo study, and on empirical data, and compares the results with a procedure based on frequentist structural equation modelling. The second manuscript considers the design of multidimensional forced-choice instruments for controlling response bias. It delves into the underpinnings of multidimensional item response theory to demonstrate how this design may lead to an empirical underidentification under certain conditions, implying a dimensional restriction. The manuscript proposes indices for assessing the dimensionality, and tests them and the consequences of the underidentification on simulated data. The third manuscript tests the invariance assumption of the model, which implies that the item parameters remain unchanged when paired in forced-choice blocks. It proposes a methodology for testing the hypotheses, based on the Likelihood ratio of nested models. The method is then applied to empirical data from forced-choice and graded-scale responses, showing that the assumption largely holds. The manuscript also explores the conditions that are likely to induce violations of the invariance assumption, and proposes hypotheses and methods for testing them.