If standard two-parameter item response functions are employed in the analysis of a test with some newly constructed items, it can be expected that, for some items, the item response function (IRF) will not fit the data well. This lack of fit can also occur when standard IRFs are fitted to personality or psychopathology items. When investigating…

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…

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

Test-based accountability as well as value-added asessments and much experimental and quasi-experimental research in education rely on achievement tests to measure student skills and knowledge. Yet, we know little regarding fundamental properties of these tests, an important example being the extent of measurement error and its implications for…

A new effect size representing the predictive power of an independent variable from a multiple regression model is presented. The index, denoted as r[subscript sp], is the semipartial correlation of the predictor with the outcome of interest. This effect size can be computed when multiple predictor variables are included in the regression model…

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…

There is widespread interest in using various statistical inference tools as a part of the evaluations for individual teachers and schools. Evaluation systems typically involve classifying hundreds or even thousands of teachers or schools according to their estimated performance. Many current evaluations are largely based on individual estimates…

Statistical modeling of school effectiveness data was originally motivated by the dissatisfaction with the analysis of (school-leaving) examination results that took no account of the background of the students or regarded each school as an isolated unit of analysis. The application of multilevel analysis was generally regarded as a breakthrough,…

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…

The impact of uncertainty about item parameters on test information functions is investigated. The information function of a test is one of the most important tools in item response theory (IRT). Inaccuracy in the estimation of test information can have substantial consequences on data analyses based on IRT. In this article, the major part (called…

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure…

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally.…

Research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Many of these designs involve two levels of clustering or nesting (students within classes and classes within schools). Researchers would like to compute effect size indexes based on the standardized mean difference to…

This article proposes a multilevel model for the assessment of school effectiveness where the intake achievement is a predictor and the response variable is the achievement in the subsequent periods. The achievement is a latent variable that can be estimated on the basis of an item response theory model and hence subject to measurement error.…