Latent variables should remain as such: Evidence from a Monte Carlo study

Abstract

Use of subject scores as manifest variables to assess the relationship between latent variables produces attenuated estimates. This has been demonstrated for raw scores from classical test theory (CTT) and factor scores derived from factor analysis. Conclusions on scores have not been sufficiently extended to item response theory (IRT) theta estimates, which are still recommended for estimation of relationships between latent variables. This is because IRT estimates appear to have preferable properties compared to CTT, while structural equation modeling (SEM) is often advised as an alternative to scores for estimation of the relationship between latent variables. The present research evaluates the consequences of using subject scores as manifest variables in regression models to test the relationship between latent variables. Raw scores and three methods for obtaining theta estimates were used and compared to latent variable SEM modeling. A Monte Carlo study was designed by manipulating sample size, number of items, type of test, and magnitude of the correlation between latent variables. Results show that, despite the advantage of IRT models in other areas, estimates of the relationship between latent variables are always more accurate when SEM models are used. Recommendations are offered for applied researchers.