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…

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…

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…

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,…

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…

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…

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…

Visual processes in Grade 1 were examined for their predictive influences in nonalphanumeric and alphanumeric rapid naming (RAN) in 51 poor early and 69 typical readers. In a lagged design, children were followed longitudinally from Grade 1 to Grade 3 over 5 testing occasions. RAN outcomes in early Grade 2 were predicted by speeded and nonspeeded…

This study examines the validity of a statewide teacher evaluation system in the Commonwealth of Virginia. Three hundred and thirty-eight teachers from 16 at-risk schools located in eight school districts participated in an evaluation system pilot during the 2011-2012 academic year. Teachers received ratings on six teacher effectiveness process…