Widespread availability of rich educational databases facilitates the use of conditioning strategies to estimate causal effects with nonexperimental data. With dozens, hundreds, or more potential predictors, variable selection can be useful for practical reasons related to communicating results and for statistical reasons related to improving the…

In psychological and survey research, the prevalence and serious consequences of careless responses from unmotivated participants are well known. In this study, we propose to iteratively detect careless responders and cleanse the data by removing their responses. The careless responders are detected using person-fit statistics. In two simulation…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

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…

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is…

A common strategy for estimating treatment effects in observational studies using individual student-level data is analysis of covariance (ANCOVA) or hierarchical variants of it, in which outcomes (often standardized test scores) are regressed on pretreatment test scores, other student characteristics, and treatment group indicators. Measurement…

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Longitudinal studies are increasingly common in psychological research. Characterized by repeated measurements, longitudinal designs aim to observe phenomena that change over time. One important question involves identification of the exact point in time when the observed phenomena begin to meaningfully change above and beyond baseline…

In longitudinal multilevel studies, especially in educational settings, it is fairly common that participants change their group memberships over time (e.g., students switch to different schools). Participant's mobility changes the multilevel data structure from a purely hierarchical structure with repeated measures nested within individuals and…

In longitudinal education studies, assuming that dropout and missing data occur completely at random is often unrealistic. When the probability of dropout depends on covariates and observed responses (called "missing at random" [MAR]), or on values of responses that are missing (called "informative" or "not missing at random" [NMAR]),…

The nonlinear mixed effects model for continuous repeated measures data has become an increasingly popular and versatile tool for investigating nonlinear longitudinal change in observed variables. In practice, for each individual subject, multiple measurements are obtained on a single response variable over time or condition. This structure can be…

There is an increasing interest in using longitudinal measures of student achievement to estimate individual teacher effects. Current multivariate models assume each teacher has a single effect on student outcomes that persists undiminished to all future test administrations (complete persistence [CP]) or can diminish with time but remains…

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the "significance region," or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA),…

Correlated data are very common in the social sciences. Most common applications include longitudinal and hierarchically organized (or clustered) data. Generalized estimating equations (GEE) are a convenient and general approach to the analysis of several kinds of correlated data. The main advantage of GEE resides in the unbiased estimation of…

Multilevel analysis is a useful technique for analyzing longitudinal data. To describe a person's development across time, the quality of the estimates of the random coefficients, which relate time to individual changes in a relevant dependent variable, is of importance. The present study compares three estimators of the random coefficients: the…