This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…

Multidimensional Item Response Theory (MIRT) has been proposed as a means to model the relation between examinee abilities and test responses. Three recent articles proved that when MIRT is used in ability estimation, an examinee's score could theoretically decrease due to a correct answer or increase due to an incorrect answer. The current…

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…

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function…

Important decisions about students are made by combining multiple measures using complex decision rules. Although methods for characterizing the accuracy of decisions based on a single measure have been suggested by numerous researchers, such methods are not useful for estimating the accuracy of decisions based on multiple measures. This study…

Item factor analysis (IFA), already well established in educational measurement, is increasingly applied to psychological measurement in research settings. However, high-dimensional confirmatory IFA remains a numerical challenge. The current research extends the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm, initially proposed for…

Confucius pointed out that the first step toward wisdom is calling things by the right name. The term "Differential Item Functioning" (DIF) did not arise fully formed from the miasma of psychometrics, it evolved from a variety of less accurate terms. Among its forebears was "item bias" but that term has a pejorative connotation that does not…

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We…

A latent variable modeling method is outlined for constructing a confidence interval (CI) of a popular multivariate effect size measure. The procedure uses the conventional multivariate analysis of variance (MANOVA) setup and is applicable with large samples. The approach provides a population range of plausible values for the proportion of…

Survey items with multiple response categories and multiple-choice test questions are ubiquitous in psychological and educational research. We illustrate the use of log-multiplicative association (LMA) models that are extensions of the well-known multinomial logistic regression model for multiple dependent outcome variables to reanalyze a set of…

The Mantel-Haenszel (MH) procedure (Mantel and Haenszel) is a popular method for estimating and testing a common two-factor association parameter in a 2 x 2 x K table. Holland and Holland and Thayer described how to use the procedure to detect differential item functioning (DIF) for tests with dichotomously scored items. Wang, Bradlow, Wainer, and…

Pretest-posttest experimental designs often are used in randomized control trials (RCTs) in the education field to improve the precision of the estimated treatment effects. For logistic reasons, however, pretest data often are collected after random assignment, so that including them in the analysis could bias the posttest impact estimates. Thus,…

In the case of trials with nested data, the optimal allocation of units depends on the budget, the costs, and the intracluster correlation coefficient. In general, the intracluster correlation coefficient is unknown in advance and an initial guess has to be made based on published values or subject matter knowledge. This initial estimate is likely…

This article introduces a multilevel growth mixture model (MGMM) for classifying both the individuals and the groups they are nested in. Nine variations of the general model are described that differ in terms of categorical and continuous latent variable specification within and between groups. An application in the context of school effectiveness…

Most automated essay scoring programs use a linear regression model to predict an essay score from several essay features. This article applied a cumulative logit model instead of the linear regression model to automated essay scoring. Comparison of the performances of the linear regression model and the cumulative logit model was performed on a…