The random intercept cross-lagged panel model (RICLPM) decomposes longitudinal associations between two processes X and Y into stable between-person associations and temporal within-person changes. In a recent study, Bailey et al. demonstrated through a simulation study that the between-person variance components in the RICLPM can occur only due…

This study examined the impact of omitting covariates interaction effect on parameter estimates in multilevel multiple-indicator multiple-cause models as well as the sensitivity of fit indices to model misspecification when the between-level, within-level, or cross-level interaction effect was left out in the models. The parameter estimates…

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized…

Many applications of structural equation modeling involve ordinal (e.g., Likert) variables. A popular way of dealing with ordinal variables is to estimate the model with polychoric correlations rather than Pearson correlations. Such an estimation also requires the asymptotic covariance matrix of polychoric correlations. It is computationally…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

In many psychological and educational applications, it is imperative to obtain valid and reliable score estimates of multilevel processes. For example, in order to assess the quality and characteristics of high impact learning processes, one must compute accurate scores representative of student- and classroom-level constructs. Currently, there…

One common score reported from diagnostic classification assessments is the vector of posterior means of the skill mastery indicators. As with any assessment, it is important to derive and report estimates of the reliability of the reported scores. After reviewing a reliability measure suggested by Templin and Bradshaw, this article suggests three…

Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

A case study of regression analysis based on modeling Gilliland's correlation was described for use in a computational methods course. The case study uses a familiar example to train students in nonlinear least squares regression and to use standardized residual plots for model assessment. Previously published equations for Gilliland's correlation…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…