Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based…

Multiple imputation (MI) is a popular method for handling missing data. In education research, it can be challenging to use MI because the data often have a clustered structure that need to be accommodated during MI. Although much research has considered applications of MI in hierarchical data, little is known about its use in cross-classified…

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual…

Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and…

The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM…

Cluster analysis is a set of statistical methods for discovering new group/class structure when exploring data sets. This article reviews the following popular libraries/commands in the R software language for applying different types of cluster analysis: from the stats library, the kmeans, and hclust functions; the mclust library; the poLCA…

Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with…

Researchers designing multisite and cluster randomized trials of educational interventions will usually conduct a power analysis in the planning stage of the study. To conduct the power analysis, researchers often use estimates of intracluster correlation coefficients and effect sizes derived from an analysis of survey data. When there is…

We present types of constructs, individual- and cluster-level, and their confirmatory factor analytic validation models when data are from individuals nested within clusters. When a construct is theoretically individual level, spurious construct-irrelevant dependency in the data may appear to signal cluster-level dependency; in such cases,…

Questionnaires that include items eliciting count responses are becoming increasingly common in psychology. This study proposes methodological techniques to overcome some of the challenges associated with analyzing multivariate item response data that exhibit zero inflation, maximum inflation, and heaping at preferred digits. The modeling…

Meta-analysis is a statistical technique that allows an analyst to synthesize effect sizes from multiple primary studies. To estimate meta-analysis models, the open-source statistical environment R is quickly becoming a popular choice. The meta-analytic community has contributed to this growth by developing numerous packages specific to…

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

Meta-analyses often include studies that report multiple effect sizes based on a common pool of subjects or that report effect sizes from several samples that were treated with very similar research protocols. The inclusion of such studies introduces dependence among the effect size estimates. When the number of studies is large, robust variance…

In a traditional regression-discontinuity design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous assignment variable. The treatment effect is measured at a single cutoff location along the assignment variable. This article introduces the multivariate regression-discontinuity design (MRDD), where multiple…

The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context, the analysis of student performance and capabilities plays a fundamental role. In this work, the authors propose a multivariate latent growth model for studying the performances of a…