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…

The use of large-scale assessments (LSAs) in education has grown in the past decade though analysis of LSAs using multilevel models (MLMs) using R has been limited. A reason for its limited use may be due to the complexity of incorporating both plausible values and weighted analyses in the multilevel analyses of LSA data. We provide additional…

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…

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…

Data are an essential factor in the fourth industrial revolution, demanding engineers and scientists to leverage and analyze their potential for significantly improving the efficiency of industrial processes and their control systems. In classical industrial process control systems, the models are constructed using linear data-driven approaches,…

Given the increased focus of educational research on what works for whom and under what circumstances over the last decade, educational researchers are increasingly turning toward mixture models to identify heterogeneous subgroups among students. Such data are inherently nested, as students are nested within classrooms and schools. Yet there has…

We note two possibilities for how our science might capitalize on advances in computing that harness and weave "big data" into the rich tapestry of how human development unfolds. First, we propose that the classic theoretical models that have guided developmental research since the 1970s and the hierarchical analytical models used to…

Multilevel models are often used to account for the hierarchical structure of social data and the inherent dependencies to produce estimates of regression coefficients, variance components associated with each level, and accurate standard errors. Social network analysis is another important approach to analysing complex data that incorporate the…

Recruiting participants for studies of early-life longitudinal development is challenging, often resulting in practical upper bounds in sample size and missing data due to attrition. These factors pose risks for the statistical power of such studies depending on the intended analytic model. One mitigation strategy is to increase measurement…

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald X[superscript 2] test-based…

We have entered an era in which scientific evidence increasingly informs research practice and policy. As there is an exponential increase in the use of single-case experimental designs (SCEDs) to evaluate intervention effectiveness, there is accumulating evidence available for quantitative synthesis. Consequently, there is a growing interest in…

Simulations were conducted to establish best practice in hyperparameter optimization and accounting for clustering in Generalized Linear Mixed-Effects Model Trees (GLMM trees). Using data-driven best practices, the relationship between a 9th Grade On-Track to Graduate (9G-OTG) indicator and observed high school graduation within four years was…

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity…

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…

A recent review found that 11% of published factor models are hierarchical models with second-order factors. However, dedicated recommendations for evaluating hierarchical model fit have yet to emerge. Traditional benchmarks like RMSEA <0.06 or CFI >0.95 are often consulted, but they were never intended to generalize to hierarchical models.…