Assessing student achievement over multiple years is complicated by students' annual matriculation through different classrooms. The process of matriculation, or annual classroom change, threatens the validity of statistical inferences because it violates the independence of observations necessary in a regression context. The current study…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Typical longitudinal growth models assume constant functional growth over time. However, there are often conditions where trajectories may not be constant over time. For example, trajectories of psychological behaviors may vary based on a participant's age, or conversely, participants may experience an intervention that causes trajectories to…

Education experiments frequently assign students to treatment or control conditions within schools. Longitudinal components added in these studies (e.g., students followed over time) allow researchers to assess treatment effects in average rates of change (e.g., linear or quadratic). We provide methods for a priori power analysis in three-level…

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist,…

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due…

Curriculum-based measurement (CBM) is a system of assessment used to screen for students at risk for poor learning. CBM benchmark screening assessments are typically administered to all students in the fall, winter, and spring, and these data are frequently used by researchers to model and perhaps explain within-year growth. Modeling growth with…