Classical Item Analysis Using Latent Variable Modeling: A Note on a Direct Evaluation Procedure

Abstract

A directly applicable latent variable modeling procedure for classical item analysis is outlined. The method allows one to point and interval estimate item difficulty, item correlations, and item-total correlations for composites consisting of categorical items. The approach is readily employed in empirical research and as a by-product permits examining the latent structure of tentative versions of multiple-component measuring instruments. The discussed procedure is straightforwardly utilized with the increasingly popular latent variable modeling software Mplus, and is illustrated on a numerical example.

Keywords:

• classical item analysis
• confidence interval
• item difficulty
• inter-item correlation
• item-total (adjusted) correlation
• latent variable modeling

Notes

¹Due to the logit-transformation being a nonlinear function, the CI in Equation 8 is not symmetric. Although one can obtain a symmetric CI using the well-known normal approximation for the relative frequency of correct response (e.g., Agresti & Finlay, 2009), because the corresponding probability is a bounded parameter, such an interval will not be optimal (e.g., Browne, 1982). This is also realized by observing that the sampling distribution of the relative frequency estimator π _i is in general not symmetric (which is easily seen for items with fairly large or small population difficulty parameters).