There is a longstanding debate on whether the analysis of covariance (ANCOVA) or the change score approach is more appropriate when analyzing non-experimental longitudinal data. In this article, we use a structural modeling perspective to clarify that the ANCOVA approach is based on the assumption that all relevant covariates are measured (i.e.,…

We present a bias-adjusted three-step estimation approach for multilevel latent class models (LC) with covariates. The proposed approach involves (1) fitting a single-level measurement model while ignoring the multilevel structure, (2) assigning units to latent classes, and (3) fitting the multilevel model with the covariates while controlling for…

While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…

Background: Education scientists are increasingly interested in constructing interventions that are adaptive over time to suit the evolving needs of students, classrooms, or schools. Such "adaptive interventions" (also referred to as dynamic treatment regimens or dynamic instructional regimes) determine which treatment should be offered…

When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with certain characteristics in order to improve trial economy or support inferences about subgroups of clusters, may preclude…

This study compared three approaches for handling a fourth level of nesting when analyzing cluster-randomized trial (CRT) data. Although CRT data analyses may include repeated measures, individual, and cluster levels, there may be an additional fourth level that is typically ignored. This study examined the impact of ignoring this fourth level,…

Fixed effects (FE) panel models have been used extensively in the past, as those models control for all stable heterogeneity between units. Still, the conventional FE estimator relies on the assumption of parallel trends between treated and untreated groups. It returns biased results in the presence of heterogeneous slopes or growth curves that…

Cluster memberships associated with the mediation effect are often changed due to the temporal distance between the cause-and-effect variables in longitudinal data. Nevertheless, current practices in multilevel mediation analysis mostly assume a purely hierarchical data structure. A Monte Carlo simulation study is conducted to examine the…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

Many methods are used to measure interrater reliability for studies where each target receives ratings by a different set of judges. The purpose of this study is to explore the use of hierarchical modeling for estimating interrater reliability using the intraclass correlation coefficient. This study provides a description of how the ICC can be…

When analyzing large-scale assessments (LSAs) that use complex sampling designs, it is important to account for probability sampling using weights. However, the use of these weights in multilevel models has been widely debated, particularly regarding their application at different levels of the model. Yet, no consensus has been reached on the best…

Researchers face many choices when conducting large-scale multisite individually randomized control trials. One of the most common quantities of interest in multisite RCTs is the overall average effect. Even this quantity is non-trivial to define and estimate. The researcher can target the average effect across individuals or sites. Furthermore,…

Previous studies have detailed the consequence of ignoring a level of clustering in multilevel models with straightly hierarchical structures and have proposed methods to adjust for the fixed effect standard errors (SEs). However, in behavioral and social science research, there are usually two or more crossed clustering levels, such as when…

Multilevel modeling has been utilized for combining single-case experimental design (SCED) data assuming simple level-1 error structures. The purpose of this study is to compare various multilevel analysis approaches for handling potential complexity in the level-1 error structure within SCED data, including approaches assuming simple and complex…

The focus of the current study is on handling the dependence among multiple regression coefficients representing the treatment effects when meta-analyzing data from single-case experimental studies. We compare the results when applying three different multilevel meta-analytic models (i.e., a univariate multilevel model avoiding the dependence, a…