The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure is correctly specified, the four procedures are asymptotically equivalent. However, this equivalence is often used when models are not correctly specified. This short paper clarifies conditions under which these procedures are not asymptotically equivalent. Analytical results indicate that, when a model is not correct, two factors contribute to the nonequivalence of the different procedures. One is that the estimated covariance matrices by different procedures are different, the other is that they use different scales to measure the distance between the sample covariance matrix and the estimated covariance matrix. The results are illustrated using real as well as simulated data. Implication of the results to model fit indices is also discussed using the comparative fit index as an example.

The collection of repeated measures in psychological research is one of the most common data collection formats employed in survey and experimental research. The behavioral decision theory literature documents the existence of the dynamic evolution of preferences that occur over time and experience due to learning, exposure to additional information, fatigue, cognitive storage limitations, etc. We introduce a Bayesian dynamic linear methodology employing an empirical Bayes estimation framework that permits the detection and modeling of such potential changes to the underlying preference utility structure of the respondent. An illustration of revealed stated preference analysis (i.e., conjoint analysis) is given involving students’ preferences for apartments and their underlying attributes and features. We also present the results of several simulations demonstrating the ability of the proposed procedure to recover a variety of different sources of dynamics that may surface with preference elicitation over repeated sequential measurement. Finally, directions for future research are discussed.

The asymptotic standard deviation (SD) of the alpha coefficient with standardized variables is derived under normality.The research shows that the SD of the standardized alpha coefficient becomes smaller as the number of examinees and/or items increase. Furthermore, this research shows that the degree of the dependence of the SD on the number of items is a function of the average correlation coefficients. When the average correlation approaches 1, the SD of the alpha coefficient decreases rapidly as the number of items increase, with the order of p. On the other hand, when the items are only weakly correlated, increasing the number of items decreases the SD of the alpha coefficient at a much slower rate.

In the signal detection paradigm, the non-parametric index of sensitivity A′, as first introduced by Pollack and Norman (1964), is a popular alternative to the more traditional d′ measure of sensitivity. Smith (1995) clarified a confusion about the interpretation of A′ in relation to the area beneath proper receiver operating characteristic (ROC) curves, and provided a formula (which he called A′′) for this commonly held interpretation. However, he made an error in his calculations. Here, we rectify this error by providing the correct formula (which we call A) and compare the discrepancy that would have resulted. The corresponding measure for bias b is also provided. Since all such calculations apply to “proper” ROC curves with non-decreasing slopes, we also prove, as a separate result, the slope-monotonicity of ROC curves generated by likelihood-ratio criterion.

The purpose of this note is twofold: (a) to present the formula for the item information function (IIF) in any direction for the Multidimensional 3-Parameter Logistic (M3-PL) model and (b) to give the equation for the location of maximum item information (θmax) in the direction of the item discrimination vector. Several corollaries are given. Implications for future research are discussed.