| The relationship between nonlinear factor analysis (FA) models and Item Response Theory (IRT) models has been well established. Furthermore, in terms of modern measurement theory, the use of nonlinear FA models to describe item-trait relationships is currently becoming more popular and may offer some statistical and/or computational advantages in the analysis of item response data. Both limited-information (LI) and full-information (FI) nonlinear FA models can be used to derive the familiar IRT parameter estimates. In general, the two approaches (LI and FI) are distinguished simply by the extent to which they use information in the data matrix of examinee (subject) responses.;The focus of this study was to compare the accuracy and efficiency of IRT parameter estimates (i.e., item difficulty, item discrimination) using both LI and FI nonlinear FA models. A Monte Carlo study was employed to investigate the precision and stability of parameter estimates in situations where (a) the manifest variables (test items) are binary and there is a single underlying normally distributed latent variable and (b) the manifest variables are binary and there is a single underlying latent variable that is not normally distributed. In addition, parameter recovery was explored under various simulated test lengths (number of items) and sample sizes (number of examinees).;The results of the study suggest that, for conditions involving a normally distributed latent variable, the limited-information approach incorporated in the NOHARM computer program generally provides more accurate and stable parameter estimates than the theoretically preferred FI estimator incorporated in the TESTFACT computer program. For situations involving a nonnormal distribution of the latent trait, or ability, FI estimation provided a marginally better calibration of the 2-parameter logistic response model. Both estimators were, however, prone to producing item values that were outside of feasible ranges, resulting in poor goodness-of-fit of the estimates. Furthermore, based on the conditions modelled in the study, neither the sample size, the test length, nor the sample size/test length ratio were important in terms of explaining between-program differences in the recovery of the item parameters. |
