Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to…

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized…

Clustered data structures are common in many areas of educational and psychological research (e.g., students clustered in schools, patients clustered by clinician). In the course of conducting research, questions are often administered to obtain scores reflecting latent constructs. Multilevel measurement models (MLMMs) allow for modeling…

Multilevel structural equation models (MSEMs) are well suited for educational research because they accommodate complex systems involving latent variables in multilevel settings. Estimation using Croon's bias-corrected factor score (BCFS) path estimation has recently been extended to MSEMs and demonstrated promise with limited sample sizes. This…

Multivariate analysis of variance (MANOVA) is widely used to test the null hypothesis of equal multivariate means across 2 or more groups. MANOVA rests upon an assumption that error terms are independent of one another, which can be violated if individuals are clustered or nested within groups, such as schools. Ignoring such nesting can result in…

The recently proposed "continuous-time latent curve model with structured residuals" (CT-LCM-SR) addresses several challenges associated with longitudinal data analysis in the behavioral sciences. First, it provides information about process trends and dynamics. Second, using the continuous-time framework, the CT-LCM-SR can handle…

Information and communication technology (ICT) is key to educational development. This study explores the mechanism influencing the use of ICT on students' science literacy. We utilized two-level hierarchical linear models and structural equation models to analyze data collected from the 2015 Program for International Student Assessment (PISA) in…