Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

Mediation analysis in Single Case Experimental Designs (SCEDs) evaluates intervention mechanisms for individuals. Despite recent methodological developments, no clear guidelines exist for maximizing power to detect the indirect effect in SCEDs. This study compares frequentist and Bayesian methods, determining (1) minimum required sample size to…

Cluster-randomized trials have been widely used to evaluate the treatment effects of interventions on student outcomes. When interventions are implemented by teachers, researchers need to account for the nested structure in schools (i.e., students are nested within teachers nested within schools). Schools usually have a very limited number of…

To evaluate multidimensional factor structure, a popular method that combines features of confirmatory and exploratory factor analysis is Bayesian structural equation modeling with small-variance normal priors (BSEM-N). This simulation study evaluated BSEM-N as a variable selection and parameter estimation tool in factor analysis with sparse…

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,…

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a…

Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased…

Within-cluster variance homogeneity is one of the key assumptions of multilevel models; however, assuming a constant (i.e. equal) within-cluster variance may not be realistic. Moreover, existent within-cluster variance heterogeneity should be regarded as a source of additional information rather than a violation of a model assumption. This study…

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the…

The purpose of this study is to demonstrate clustering methods within a functional data analysis (FDA) framework for identifying subgroups of individuals that may be exhibiting categories of misfit. Person response functions (PRFs) estimated within a FDA framework (FDA-PRFs) provide graphical displays that can aid in the identification of persons…

This study investigated the small sample biasness of the ordered logit model parameters under multicollinearity using Monte Carlo simulation. The results showed that the level of biasness associated with the ordered logit model parameters consistently decreases for an increasing sample size while the distribution of the parameters becomes less…

This study explores the performance of classical methods for detecting publication bias--namely, Egger's regression test, Funnel Plot test, Begg's Rank Correlation and Trim and Fill method--in meta-analysis of studies that report multiple effects. Publication bias, outcome reporting bias, and a combination of these were generated. Egger's…

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the…

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL…

Dynamic Measurement Modeling (DMM) is a recently-developed measurement framework for gauging developing constructs (e.g., learning capacity) that conventional single-timepoint tests cannot assess. The current project developed a person-specific DMM Trajectory Deviance Index (TDI) that captures the aberrance of an individual's growth from the…