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…

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…

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…

We evaluate the feasibility of estimating test-score growth with a gap year in testing data, informing the scenario when state testing resumes after the 2020 COVID-19-induced test stoppage. Our research design is to simulate a gap year in testing using pre-COVID-19 data--when a true test gap did not occur--which facilitates comparisons of…

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…

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…

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…

Student Growth Percentiles (SGP, 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 is most often used operationally to estimate the SGPs. Alternatively, multidimensional item response theory (MIRT) may also be…

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 technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…