Avoiding and Correcting Bias in Score-Based Latent Variable Regression With Discrete Manifest Items

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate parameters in the structural equation. We are concerned with the bias in these OLS estimates; we present two approaches to deal with this bias. Extending the work of Skrondal and Laake (2001) Skrondal, A. and Laake, P. 2001. Regression among factor scores. Psychometrika, 66: 563–576. [Crossref], [Web of Science ®] , [Google Scholar] on continuous items, we derive sufficient conditions under which the use of scores based on item response theory leads to unbiased OLS estimates at the population level; we deem this approach “bias avoiding.” We also consider Croon's (2002) Croon, M. 2002. “Using predicted latent scores in general latent structure models”. In Latent variable and latent structure models, Edited by: Marcoulides, G. A. and Moustaki, I. 195–223. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.  [Google Scholar] bias correction methodology for continuous items and explore its efficacy on discrete items; we deem this approach “bias correcting.” We illustrate the performance of the 2 approaches through numerical examples of large simulated data sets.