Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has…

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…

There are two schools of thought in statistical analysis, frequentist, and Bayesian. Though the two approaches produce similar estimations and predictions in large-sample studies, their interpretations are different. Bland Altman analysis is a statistical method that is widely used for comparing two methods of measurement. It was originally…

Measurement of latent constructs is one of the most challenging tasks in psychological research. Unlike physical variables, latent constructs are not directly observable but are inferred through individuals' responses to a set of items often referred to as measurement instruments, tests, surveys, or assessments. For decades, exploratory factor…

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a…

This article discusses the basics of the "4 scales of measurement" and how they are applicable to research or everyday tools of life. To do this you will be able to list and describe the four types of scales of measurement used in quantitative research; provide examples of uses of the four scales of measurement; and determine the…

Conventional approaches for selecting a reference indicator (RI) could lead to misleading results in testing for measurement invariance (MI). Several newer quantitative methods have been available for more rigorous RI selection. However, it is still unknown how well these methods perform in terms of correctly identifying a truly invariant item to…

One crucial function of a classroom, and a school more generally, is to prepare students for future learning. Students should have the capacity to learn new information and to acquire new skills. This ability to "learn" is a core competency in our rapidly changing world. But how do we measure ability to learn? And how can we measure how…

This article presents findings on the consequences of matrix sampling of context questionnaires for the generation of plausible values in large-scale assessments. Three studies are conducted. Study 1 uses data from PISA 2012 to examine several different forms of missing data imputation within the chained equations framework: predictive mean…

Much of the science reported in the media depends on correlation coefficients. But the size of correlation coefficients depends, in part, on the reliability with which the correlated variables are measured. Understanding this is a statistical literacy issue.

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon…

In confirmatory factor analysis quite similar models of measurement serve the detection of the difficulty factor and the factor due to the item-position effect. The item-position effect refers to the increasing dependency among the responses to successively presented items of a test whereas the difficulty factor is ascribed to the wide range of…

The primary purpose of this book is to offer a broad-based examination into the role of scientific inquiry in contemporary special education. As with the first two editions, which were published in 2001 and 2011, the goal is to provide a comprehensive overview of the philosophical, ethical, methodological, and analytical fundamentals of social…

Background: Economists are making increasing use of measures of student achievement obtained through large-scale survey assessments such as NAEP, TIMSS, and PISA. The construction of these measures, employing plausible value (PV) methodology, is quite different from that of the more familiar test scores associated with assessments such as the SAT…

Each iteration of high stakes accountability has included requirements to include measures of attendance in their accountability programs, thereby increasing the salience of this measure. Researchers too have turned to attendance and chronic absence as important outcomes in evaluations and policy studies. Often, too little attention is paid to the…