The present work focuses on the performance of two types of shrinkage priors--the horseshoe prior and the recently developed regularized horseshoe prior--in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold…

Purpose and Background: Despite the flexibility of multilevel structural equation modeling (MLSEM), a practical limitation many researchers encounter is how to effectively estimate model parameters with typical sample sizes when there are many levels of (potentially disparate) nesting. We develop a method-of-moment corrected maximum likelihood…

A conceptual distinction is drawn between indicators, which serve to define latent variables, and outcomes, which do not. However, commonly used frequentist and Bayesian estimation procedures do not honor this distinction. They allow the outcomes to influence the latent variables and the measurement model parameters for the indicators, rendering…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

To date, in gifted education and related fields various conventional factor analytic and clustering techniques have been used extensively for investigation of the underlying structure of data. Latent profile analysis is a relatively new method in the field. In this article, we provide an introduction to latent profile analysis for gifted education…