Penalized structural equation models (PSEM) is a new powerful estimation technique that can be used to tackle a variety of difficult structural estimation problems that can not be handled with previously developed methods. In this paper we describe the PSEM framework and illustrate the quality of the method with simulation studies.…

The purpose of this research note is to introduce a latent growth curve reconstruction approach based on the Tabu search algorithm. The approach algorithmically enables researchers to optimally determine at both the individual and the group levels the order of the polynomial needed to represent the latent growth curve model. The procedure is…

The computational model of school achievement represents a novel approach to theorizing school achievement, conceptualizing educational interventions as modifications to students' learning curves. By modeling the process and products of educational achievement simultaneously, this tool addresses several unresolved questions in educational…

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…

We evaluate the feasibility of estimating test-score growth for schools and districts with a gap year in test data. Our research design uses a simulated gap year in testing when a true test gap did not occur, which facilitates comparisons of district- and school-level growth estimates with and without a gap year. We find that growth estimates…

Longitudinal data analysis has received widespread interest throughout educational, behavioral, and social science research, with latent growth curve modeling currently being one of the most popular methods of analysis. Despite the popularity of latent growth curve modeling, limited attention has been directed toward understanding the issues of…

Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…

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,…

As an alternative to common-item equating when common items do not function as expected, the single-group growth model (SGGM) scaling uses common examinees or repeaters to link test scores on different forms. The SGGM scaling assumes that, for repeaters taking adjacent administrations, the conditional distribution of scale scores in later…

This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of…

Student growth percentiles (SGPs, Betebenner, 2009) are used to locate a student's current score in a conditional distribution based on the student's past scores. Currently, following Betebenner (2009), quantile regression (QR) is most often used operationally to estimate the SGPs. Alternatively, multidimensional item response theory (MIRT) may…

To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor…

This paper reports on a study conducted to investigate the consistency of the results between 2 approaches to estimating school effectiveness through value-added modeling. Estimates of school effects from the layered model employing item response theory (IRT) scaled data are compared to estimates derived from a discrete growth model based on the…