It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. The result is a novel analysis with increased…

The year 2022 is the 20th anniversary of Joseph Schafer and John Graham's paper titled "Missing data: Our view of the state of the art," currently the most highly cited paper in the history of "Psychological Methods." Much has changed since 2002, as missing data methodologies have continually evolved and improved; the range of…

Despite the broad appeal of missing data handling approaches that assume a missing at random (MAR) mechanism (e.g., multiple imputation and maximum likelihood estimation), some very common analysis models in the behavioral science literature are known to cause bias-inducing problems for these approaches. Regression models with incomplete…

The Bayesian information criterion (BIC) can be useful for model selection within multilevel modeling studies. However, the formula for BIC requires a value for N, which is unclear in multilevel models, since N is observed in at least two levels. The present study uses simulated data to evaluate the rate of false positives and power when using a…

Statistical mediation allows researchers to investigate potential causal effects of experimental manipulations through intervening variables. It is a powerful tool for assessing the presence and strength of postulated causal mechanisms. Although mediation is used in certain areas of psychology, it is rarely applied in cognitive psychology and…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

Specialized imputation routines for multilevel data are widely available in software packages, but these methods are generally not equipped to handle a wide range of complexities that are typical of behavioral science data. In particular, existing imputation schemes differ in their ability to handle random slopes, categorical variables,…

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

Maori and Pacific students generally do not attain the same levels of tertiary success as New Zealanders of European descent, particularly in science, technology, engineering, and mathematics (STEM) subjects. Te Ropu Awhina (Awhina), an equity initiative at Victoria University of Wellington in New Zealand between 1999 and 2015, aimed to produce…

The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix [sigma] of group-level varying coefficients are often degenerate. One can do better, even…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…