Embedding IRT in Structural Equation Models: A Comparison With Regression Based on IRT Scores

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Abstract
This article reviews the problems associated with using item response theory (IRT)-based latent variable scores for analytical modeling, discusses the connection between IRT and structural equation modeling (SEM)-based latent regression modeling for discrete data, and compares regression parameter estimates obtained using predicted IRT scores and standardized number-right scores in Ordinary Least Squares (OLS) regression with regression estimates obtained using the combined IRT-SEM approach. The Monte Carlo results show the expected a posteriori (EA approach is insensitive to sample size as expected but leads to appreciable attenuation in regression parameter estimates. Standardized number-right estimates and EAP regression estimates were found to be highly comparable. On the other hand, the IRT-SEM method produced smaller finite sample bias, and as expected, generated consistent regression estimates for suitably large sample sizes.