Pearson's correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman's [rho] is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or…

Most methods for structural equation modeling (SEM) focused on the analysis of covariance matrices. However, "Historically, interesting psychological theories have been phrased in terms of correlation coefficients." This might be because data in social and behavioral sciences typically do not have predefined metrics. While proper methods…

Causal asymmetry is a situation where the causal factors under study are more suitable for explaining the outcome than its absence (or vice versa); they do not explain both equally well. In such a situation, presence of a cause leads to presence of the effect, but absence of the cause may not lead to absence of the effect. A conceptual discussion…

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…

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of post-treatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due…

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading…

To measure "treatment" effects, social science researchers typically rely on nonexperimental data. In education, school and teacher effects on students are often measured through value-added models (VAMs) that are not fully understood. We propose a framework that relates to the education production function in its most flexible form and…

Accelerated longitudinal designs (ALDs) provide an opportunity to capture long developmental periods in a shorter time framework using a relatively small number of assessments. Prior literature has investigated whether univariate developmental processes can be characterized with data obtained from ALDs. However, many important questions in…

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing…

Causal analyses typically focus on average treatment effects. Yet for substantive research on topics like inequality, interest extends to treatments' distributional consequences. When individuals differ in their responses to treatment, three types of inequality may result. Treatment may shape inequalities between subgroups defined by pretreatment…

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…

While states are no longer required to set up teacher evaluation systems based in significant part on student test scores, quite a few continue to use value-added (VAMs) or student growth percentile (SGP) models for that purpose. In this study, we analyzed three years of teacher data to illustrate the performance of teachers' median growth…

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological…

Recently, quantitative researchers have shown increased interest in two-step factor score regression (FSR) approaches to structural model estimation. A particularly promising approach proposed by Croon involves first extracting factor scores for each latent factor in a larger model, then correcting the variance-covariance matrix of the factor…