This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual…

Growth mixture models (GMMs) are a popular method to identify latent classes of growth trajectories. One shortcoming of GMMs is nonconvergence, which often leads researchers to apply covariance equality constraints to simplify estimation, though this may be a dubious assumption. Alternative model specifications have been proposed to reduce…

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…

The piecewise latent growth models (PWLGMs) can be used to study changes in the growth trajectory of an outcome due to an event or condition, such as exposure to an intervention. When there are multiple outcomes of interest, a researcher may choose to fit a series of PWLGMs or a single parallel-process PWLGM. A comparison of these models is…

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,…

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological…

While states are no longer required to set up teacher evaluation systems based in significant part on student test scores, quite a few continue to use value-added (VAMs) or student growth percentile (SGP) models for that purpose. In this study, we analyzed three years of teacher data to illustrate the performance of teachers' median growth…

This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting…

The purpose of this study is extend previous methods by Raudenbush and Liu (2001) and Spybrook et al. (2011), and provide methods for power analysis of tests of treatment effects in studies of polynomial change with two levels of nesting (e.g., students and schools) where the treatment is either at the third level (e.g., school intervention) or at…

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This…

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…

Although letter naming fluency (LNF) and letter sound fluency (LSF) measures are widely available to educators for assessing early literacy skills of kindergarten children, better understanding of the contributions of these skills to reading development can help improve the interpretation of LNF and LSF data for instructional decisions. This study…

Executive leadership of the U.S. Department of Education (USDOE) initiated a flexibility offering from No Child Left Behind. Our work explores specific design decisions made in these state-specific accountability systems as associated with state political environments, resources, and demographic characteristics. Our analysis, focused on 42 states…

Research Findings: This study reports outcomes from a randomized, controlled trial of an emergent literacy intervention for prekindergarten children at-risk for reading failure. Children (N = 2219) in 114 preschools and childcare centers were screened for eligibility in fall. Children who scored at-risk (n = 476) were randomized to fall or spring…

This paper examines the graduation rates between 2000 and 2015 of United States colleges and universities at the national, state, and institutional levels. This research focuses on two-year and four-year programs. Rates are investigated longitudinally along with variables that distinguish between public/private institutions, percentages of…