Higher-order factor analysis is a widely used approach for analyzing the structure of a multidimensional test. Whenever first-order factors are correlated researchers are tempted to apply a higher-order factor model. But is this reasonable? What do the higher-order factors measure? What is their meaning? Willoughby, Holochwost, Blanton, and Blair…

The Vanishing Tetrad Test (VTT) (Bollen, Lennox, & Dahly, 2009; Bollen & Ting, 2000; Hipp, Bauer, & Bollen, 2005) is an extension of the Confirmatory Tetrad Analysis (CTA) proposed by Bollen and Ting (Bollen & Ting, 1993). VTT is a powerful tool for detecting model misspecification and can be particularly useful in cases in which…

In measurement theory, causal indicators are controversial and little understood. Methodological disagreement concerning causal indicators has centered on the question of whether causal indicators are inherently sensitive to interpretational confounding, which occurs when the empirical meaning of a latent construct departs from the meaning…

Research into executive functioning (EF) has indeed grown exponentially across the past few decades, but as the Willoughby et al. critique makes clear, there remain fundamental questions to be resolved. The crux of their argument is built upon an examination of the confirmatory factor analysis (CFA) approach to understanding executive processes.…

The authors of the focus article in this issue have emphasized the continuing confusion among some researchers regarding various indicators used in structural equation models (SEMs). Their major claim is that causal indicators are not inherently unstable, and even if they are unstable they are at least not more unstable than other types of…

Building on the work of Bollen (2007) and Bollen & Bauldry (2011), Bainter and Bollen (this issue) clarifies several points of confusion in the literature regarding causal indicator models. This author would certainly agree that the effect indicator (reflective) measurement model is inappropriate for some indicators (such as the social…

These authors agree with Bainter and Bollen that causal effects represents a useful measurement structure in some applications. The structure of the science of the measurement problem should determine the model; the measurement model should not determine the science. They also applaud Bainter and Bollen's important reminder that the full…

In a series of articles and comments, Kenneth Bollen and his collaborators have incrementally refined an account of structural equation models that (a) model a latent variable as the effect of several observed variables and (b) carry an interpretation of the observed variables as, in some sense, measures of the latent variable that they cause.…

In this commentary, Betsy McCoach and David Kenny state they are in general agreement with Bainter and Bollen (this issue) that causal indicators are not inherently unstable. Herein, they outline several similarities and differences between latent variables with reflective and causal indicators. In their examination of the two models, they find…

The construct map is a particularly good way to approach instrument development, and this author states that he was delighted to read Adam Wyse's thoughts about how to use construct maps for standard setting. For a number of popular standard-setting methods, Wyse shows how typical feedback to panelists fits within a construct map framework.…

In this commentary, Englehard and Perkins remark that Maydeu-Olivares has presented a framework for evaluating the goodness of model-data fit for item response theory (IRT) models and correctly points out that overall goodness-of-fit evaluations of IRT models and data are not generally explored within most applications in educational and…

At the outset of his thoughtful and thought-provoking article, Haertel (this issue) clearly identifies the issue with which he will be dealing: The disjunct, or gap, in current approaches to evaluating the merits of a given test, between the intended uses of that test and the validity of its score-based interpretations. The author thinks that…

Measurement is a semantic frame, a constellation of relationships and concepts that correspond to recurring patterns in human activity, highlighting typical roles, processes, and viewpoints (e.g., the "commercial event") but not others. One uses semantic frames to reason about unique and complex situations--sometimes intuitively, sometimes…

This paper presents the author's critique to Paul E. Newton's article titled "Clarifying the consensus definition of validity." In his article, Newton not only clarifies but also redefines the consensus definition of validity. In this redefinition he omits the term "construct" and introduces the term "measurement." Both omission and introduction…

Paul E. Newton's article is valuable in many ways, especially for clarifying confusions and inconsistencies in the assessment business. Most importantly, he points out confusions that persist and where open discussion will help us understand what we say and what we mean to say. But I will focus here on the only faults I find in the article: three…