Using longitudinal mean and covariance structures (LMACS) analysis to assess construct stability over two time points: An example with psychological entitlement

The current paper reviewed two widely used approaches to assessing construct stability over two time points (rank-order and mean-level consistency), as well as common misconceptions about what each indicates. In addition, the application of longitudinal mean and covariance structures (LMACS) analysis as a modern approach to assessing construct stability was explained and demonstrated by assessing the stability of psychological entitlement over 1.5 years measured via the Psychological Entitlement Scale (PES). Confirmatory factor analysis supported a one-factor solution for the PES at both time points, and reliability of scores was adequate (ω = .88 and .89). Full configural and metric invariance and partial scalar invariance were established for the PES. Rank-order consistency of factor scores was moderate (r = .61) and the latent mean difference in psychological entitlement across time was not statistically significant. Results provided construct validity evidence for the PES regarding measurement invariance and also indicated that psychological entitlement tended to be stable on average but not at the individual level over 1.5 years. Discussion of the effects of differential item functioning (DIF) of scalar non-invariant items on mean difference testing and use of the PES with observed scores, the change in psychological entitlement at the individual level, and the advantages of LMACS analysis as a unified approach to assessing construct stability is also provided

Examining the performance of the Metropolis-Hastings Robbins-Monro algorithm in the estimation of multilevel multidimensional IRT models

The purpose of this study was to review the challenges that exist in the estimation of complex (multidimensional) models applied to complex (multilevel) data and to examine the performance of the recently developed Metropolis-Hastings Robbins-Monro (MH-RM) algorithm (Cai, 2010a, 2010b), designed to overcome these challenges and implemented in both commercial and open-source software programs. Unlike other methods, which either rely on high-dimensional numerical integration or approximation of the entire multidimensional response surface, MH-RM makes use of Fisher’s Identity to employ stochastic imputation (i.e., data augmentation) via the Metropolis-Hastings sampler and then apply the stochastic approximation method of Robbins and Monro to approximate the observed data likelihood, which decreases estimation time tremendously. Thus, the algorithm shows great promise in the estimation of complex models applied to complex data. To put this promise to the test, the accuracy and efficiency of MH-RM in recovering item parameters, latent variances and covariances, as well as ability estimates within and between groups (e.g., schools) was examined in a simulation study, varying the number of dimensions, the intraclass correlation coefficient, the number of clusters, and cluster size, for a total of 24 conditions. Overall, MH-RM performed well in recovering the item, person, and group-level parameters of the model. More replications are needed to better determine the accuracy of analytical standard errors for some of the parameters. Limitations of the study, implications for educational measurement practice, and directions for future research are offered

Determining Item Screening Criteria Using Cost-Benefit Analysis

Successful testing programs rely on high-quality test items to produce reliable scores and defensible exams. However, determining what statistical screening criteria are most appropriate to support these goals can be daunting. This study describes and demonstrates cost-benefit analysis as an empirical approach to determining appropriate screening criteria for a given testing program and purpose. Using a certification exam’s item pool and simulation we illustrate how to examine a wide range of screening criteria and reach an acceptable balance between the number of items screened out (cost) and pass/fail classification accuracy (benefit). Accessed 699 times on https://pareonline.net from April 09, 2019 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Schrodinger equation solution for the atom of hydrogen with nucleus rotation (spin) considering

The variant of the Schrodinger equation solution for the atom of hydrogen is studied in view of the nucleus rotation. The distributions of potential for a rotating pointed particle with an electric charge outside the particle are first derived. By quasi-classical way, the result allows to take into account additional splitting of the atom energy levels because of the atomic nucleus rotation