We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning (AutoDML). These popular "doubly robust" or "de-biased machine learning estimators" combine outcome modeling with balancing weights -- weights that achieve covariate balance directly in lieu of estimating and…

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…

Small sample sizes contribute to several problems in research and knowledge advancement. This conceptual replication study confirmed and extended the inflation of type II errors and confidence intervals in correlation analyses of small sample sizes common in kinesiology/exercise science. Current population data (N = 18, 230, & 464) on four…

Although parallel analysis has been found to be an accurate method for determining the number of factors in many conditions with complete data, its application under missing data is limited. The existing literature recommends that, after using an appropriate multiple imputation method, researchers either apply parallel analysis to every imputed…

Context: A perennial problem in applied statistics is the inability to justify strong claims about cause-and-effect relationships without full knowledge of the mechanism determining selection into treatment. Few research designs other than the well-implemented random assignment study meet this requirement. Researchers have proposed partial…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…

Background: Over the past decade, research on the development and assessment of tools to improve the generalizability of experimental findings has grown extensively (Tipton & Olsen, 2018). However, many experimental studies in education are based on small samples, which may include 30-70 schools while inference populations to which…

In the complex world of educational policy, causal inferences will be debated. As we review non-experimental designs in educational policy, we focus on how to clarify and focus the terms of debate. We begin by presenting the potential outcomes/counterfactual framework and then describe approximations to the counterfactual generated from the…

This report aims to showcase the value of implementing a Bayesian framework to analyse and report results from international large-scale surveys and provide guidance to users who want to analyse the data using this approach. The motivation for this report stems from the recognition that Bayesian statistical inference is fast becoming a popular…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…