Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

The literature on teachers' unions is relatively silent about the role of union strength in affecting important outcomes, due in large part to the difficulty in measuring union strength. In this article, we illustrate a method for obtaining valid, reliable, and replicable measures of union strength through the use of a Partial Independence Item…

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects…

The concern behind my question, "Can there be validity without reliability?" (Moss, 1994), was about the influence of measurement practices on the quality of education. I argued that conventional operationalizations of reliability in the measurement literature, which I summarized as "consistency, quantitatively defined, among independent…

It is understandable that parents, policy makers, educators, etc. want to know how schools are functioning. Extensive resources are expended on the educational enterprise and it is only reasonable that the impact of those resources be determined. However, determining the amount of change in students' skills and knowledge is not easy. Further,…

Three principal factors supported our decision to participate in the piloting of the Pennsylvania Value-Added Assessment System (PVAAS). First, participants needed to have or secure electronic student assessment data. As a very data-oriented school district, we had over five years of longitudinal student data stored electronically for use in our…

The Tennessee Value-Added Assessment System measures teacher effectiveness on the basis of student gains, implicitly controlling for socioeconomic status and other background factors that influence initial levels of achievement. The absence of explicit controls for student background has been criticized on the grounds that these factors influence…

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Value-added models of student achievement have received widespread attention in light of the current test-based accountability movement. These models use longitudinal growth modeling techniques to identify effective schools or teachers based upon the results of changes in student achievement test scores. Given their increasing popularity, this…

This article presents a psychometric model for estimating ability and item-selection strategies in self-adapted testing. In contrast to computer adaptive testing, in self-adapted testing the examinees are allowed to select the difficulty of the items. The item-selection strategy is defined as the distribution of difficulty conditional on the…

Multilevel linear models (MLMs) provide a powerful framework for analyzing data collected at nested or non-nested levels, such as students within classrooms. The current article draws on recent analytical and software advances to demonstrate that a broad class of MLMs may be estimated as structural equation models (SEMs). Moreover, within the SEM…

In the social sciences, evaluating the effectiveness of a program or intervention often leads researchers to draw causal inferences from observational research designs. Bias in estimated causal effects becomes an obvious problem in such settings. This article presents the Heckman Model as an approach sometimes applied to observational data for the…