Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses

Tyler Strachan; Uk Hyun Cho; Terry Ackerman; Shyh-Huei Chen; Jimmy de la Torre; Edward H Ip

doi:10.1177/01466216221084218

Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses

Appl Psychol Meas. 2022 Jul;46(5):347-360. doi: 10.1177/01466216221084218. Epub 2022 Jun 15.

Authors

Tyler Strachan¹, Uk Hyun Cho¹, Terry Ackerman², Shyh-Huei Chen³, Jimmy de la Torre⁴, Edward H Ip³

Affiliations

¹ Educational Research Methodology, University of North Carolina at Greensboro, Greensboro, NC, USA.
² University of Iowa, Iowa City, IA, USA.
³ Department on Biostatistical Sciences, Wake Forest School of Medicine, Winston-Salem, NC, USA.
⁴ Department of Education, The University of Hong Kong, Pokfulam, Hong Kong.

Abstract

The linear composite direction represents, theoretically, where the unidimensional scale would lie within a multidimensional latent space. Using compensatory multidimensional IRT, the linear composite can be derived from the structure of the items and the latent distribution. The purpose of this study was to evaluate the validity of the linear composite conjecture and examine how well a fitted unidimensional IRT model approximates the linear composite direction in a multidimensional latent space. Simulation experiment results overall show that the fitted unidimensional IRT model sufficiently approximates linear composite direction when correlation between bivariate latent variables is positive. When the correlation between bivariate latent variables is negative, instability occurs when the fitted unidimensional IRT model is used to approximate linear composite direction. A real data experiment was also conducted using 20 items from a multiple-choice mathematics test from American College Testing.

Keywords: item response theory; linear composite; multidimensional item response theory; unidimensional scale.