Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

Across all sciences, the quality of measurements is important. Survey measurements are only appropriate for use when researchers have validity evidence within their particular context. Yet, this step is frequently skipped or is not reported in educational research. This article briefly reviews the aspects of validity that researchers should…

We present factor extension procedures for confirmatory factor analysis that provide estimates of the relations of common and unique factors with external variables that do not undergo factor analysis. We present identification strategies that build upon restrictions of the pattern of correlations between unique factors and external variables. The…

Efforts to improve instructional task design often make reference to the mental structures, such as "schemas" (e.g., Gick & Holyoak, 1983) or "identical elements" (Thorndike & Woodworth, 1901), that are common to both the instructional and target tasks. This component based (e.g., Singley & Anderson, 1989) approach…

Multiple-group confirmatory factor analysis (MG-CFA) is among the most productive extensions of structural equation modeling. Many researchers conducting cross-cultural or longitudinal studies are interested in testing for measurement and structural invariance. The aim of the present paper is to provide a tutorial in MG-CFA using the freely…

A fundamental reason for doing evaluation capacity building (ECB) is to improve program outcomes. Developing common measures of outcomes and the activities, processes, and factors that lead to these outcomes is an important step in moving the science and the practice of ECB forward. This article identifies a number of existing ECB measurement…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Mroch, Suh, Kane, & Ripkey (2009); Suh, Mroch, Kane, & Ripkey (2009); and Kane, Mroch, Suh, & Ripkey (2009) provided elucidating discussions on critical properties of linear equating methods under the nonequivalent groups with anchor test (NEAT) design. In this popular equating design, two test forms are administered to different…

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

This article describes the logic and procedures behind testing for factorial invariance across groups in the context of construct validation. The procedures include testing for configural, measurement, and structural invariance in the framework of multiple-group confirmatory factor analysis (CFA). The "forward" (sequential constraint imposition)…

Mental chronometry (MC) studies cognitive processes measured by time. It provides an absolute, ratio scale. The limitations of instrumentation and statistical analysis caused the early studies in MC to be eclipsed by the "paper-and-pencil" psychometric tests started by Binet. However, they use an age-normed, rather than a ratio scale, which…

Nowadays, there is a wide debate about what rural means. An operational definition of rural concept is essential in order to measure health problems, optimize resource allocation and facilitate decision making aimed at closing the gap on inequity between areas. In 2005, the rurality index for Small Areas in Spain (IRAP) was developed using the…

A large literature emphasizes the importance of testing for measurement equivalence in scales that may be used as observed variables in structural equation modeling applications. When the same construct is measured across more than one developmental period, as in a longitudinal study, it can be especially critical to establish measurement…

The factorial and construct equivalence of subscales assessing parents' and children's perceptions of the quality of their neighborhood was examined in Mexican American and European American families. All subscales (dangerous people in the neighborhood, sense of safety in the neighborhood, quality of the physical environment) demonstrated adequate…

The five papers in this special issue of the "Journal of Applied Testing Technology" address fundamental issues of validity when tests are modified or accommodations are provided to English Language Learners (ELL) or students with disabilities. Three papers employed differential item functioning (DIF) and factor analysis and found the…