How Item Response Theory can solve problems of ipsative data

.......................................................................................................... 3 Introduction ..................................................................................................... 4 Single-stimulus response format ................................................................... 4 Response biases affecting single-stimulus items ............................................ 5 Forced-choice format .................................................................................... 7 Problems of ipsative data ............................................................................. 8 Relative nature of scores .............................................................................. 9 Distorted construct validity ......................................................................... 10 Distorted reliability estimates ...................................................................... 11 Inadequacy of the classical methods of scoring forced-choice items ............. 13 IRT approaches to scoring forced-choice items............................................ 14 The need to model forced-choice dominance items ...................................... 16 Thurstone’s framework for comparative judgment ...................................... 17 Method ........................................................................................................... 20 Binary coding of forced-choice response data .............................................. 20 Thurstonian factor models for forced-choice items ...................................... 22 Response model for ranking......................................................................... 22 Items as indicators of latent traits ............................................................... 24 Thurstonian Models for forced-choice items as IRT models ........................ 27 Reparameterized model (first-order Thurstonian IRT factor model) ................ 27 Identification of Thurstonian IRT models for forced-choice questionnaires ...... 31 Item characteristic function ........................................................................ 32 Estimation of Thurstonian IRT models for forced-choice questionnaires .......... 34 Latent trait estimation ................................................................................ 36 Information functions and reliability estimation ............................................ 37 Response biases and forced-choice format ..................................................... 42 Simulation studies ........................................................................................... 45 Simulation study 1. A forced-choice questionnaire measuring 2 traits ........ 46