This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate…

This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

Typical longitudinal growth models assume constant functional growth over time. However, there are often conditions where trajectories may not be constant over time. For example, trajectories of psychological behaviors may vary based on a participant's age, or conversely, participants may experience an intervention that causes trajectories to…

It is demonstrated that the popular three-parameter logistic model can lead to markedly inaccurate individual ability level estimates for mixture populations. A theoretically and empirically important setting is initially considered where (a) in one of two subpopulations (latent classes) the two-parameter logistic model holds for each item in a…

In this article, Roy Howell, and Einar Breivik, congratulate Aguirre-Urreta, M. I., Rönkkö, M., & Marakas, G. M., for their work (2016) "Omission of Causal Indicators: Consequences and Implications for Measurement," Measurement: Interdisciplinary Research and Perspectives, 14(3), 75-97. doi:10.1080/15366367.2016.1205935. They call it…

The authors begin this brief rejoinder by thanking all the authors who took time to provide comments on their work, which appeared in "Measurement: Interdisciplinary Research and Perspectives" v14 n3 2016. All commentaries appear to suggest that causal indicators cannot be used for measurement but differ in how strongly this conclusion…

The Task Model is a description of each task in a workflow. It defines attributes associated with that task. The creation of task models becomes increasingly important as the assessment tasks become more complex. Explicitly delineating the impact of task variables on the ability to collect evidence and make inferences demands thoughtfulness from…

One of the key ideas of evidence-centered assessment design (ECD) is that task features can be deliberately manipulated to change the psychometric properties of items. ECD identifies a number of roles that task-feature variables can play, including determining the focus of evidence, guiding form creation, determining item difficulty and…

Data use is a phenomenon that spans boundaries of disciplines, implicating issues of measurement and assessment, issues of learning and cognition, issues of organizational context and change, and issues of power and politics, among others. Traditionally, scholarship on these different aspects of data use lives in different disciplinary homes. In…

In this rejoinder, Maydeu-Olivares states that, in item response theory (IRT) measurement applications, the application of goodness-of-fit (GOF) methods informs researchers of the discrepancy between the model and the data being fitted (the room for improvement). By routinely reporting the GOF of IRT models, together with the substantive results…

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…

Despite over a century of aligning test and examination scales, the theory of linking has received relatively little attention. Recently, though, frameworks for classifying linking relationships have proliferated, both in England and the United States. Limitations of U.S. frameworks, particularly the idea that linking relationships ought to be…

In this rejoinder, the authors provide their thoughts on each of the commentaries of the seven respondents to their article. They find that the response of Kyngdon differs markedly from the others in questioning some basic elements of the methods of analysis that they propose for the construction of a "road map." The authors emphasize that they…

This article presents the authors' rejoinder to commentaries on linear equating and the NEAT design. The authors appreciate the insightful work of the commentary writers. Each has made a number of interesting points, many of which the authors had not considered at all. Before responding to some of those points, the authors reiterate what they see…

Achilles and the tortoise want to predict peoples' running performance from their age. In determining age the tortoise has cleverly asked his participants for their passports and has noted their date of birth, before letting them run half the distance between Achilles and himself. Achilles, however, has given his participants a questionnaire…