Factor loadings and item discrimination parameters play a key role in scale construction. A multitude of heuristics regarding their interpretation are hardwired into practice--for example, neglecting low loadings and assigning items to exactly one scale. We challenge the common sense interpretation of these parameters by providing counterexamples…

Since Cronbach's (1951) elaboration of a from its introduction by Guttman (1945), this coefficient has become ubiquitous in characterizing assessment instruments in education, psychology, and other social sciences. Also ubiquitous are caveats on the calculation and interpretation of this coefficient. This article summarizes a recent contribution…

The practice of individual assessment has been moving toward the empirically derived Cattell-Horn-Carroll (CHC) theory of intellectual ability, which offers a hierarchical taxonomy of cognitive abilities. Current assessment tools provide varying adherence to operationalizing CHC theory, making clinical inference difficult. Expert consensus…

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling "construct-relevant" multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957) and highlight its…

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation,…

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the…

This article examines the methodological foundations of exploratory factor analysis (EFA) and suggests that it is properly construed as a method for generating explanatory theories. In the first half of the article it is argued that EFA should be understood as an abductive method of theory generation that exploits an important precept of…

Examines some positions in various arguments related to the proper number of factors and proper number of steps when using structural equation models. Defines the issue in estimating structural equation models as a problem of specifying a model appropriately based on theoretical concerns and then diagnosing ills in the model as well as possible.…

The extent to which a scale score generalizes to a latent variable common to all of the scale's indicators is indexed by the scale's general factor saturation. Seven techniques for estimating this parameter--omega[hierarchical] (omega[subscript h])--are compared in a series of simulated data sets. Primary comparisons were based on 160 artificial…

This paper discusses the theoretical scope and practical applicability of generalizability (G) theory through the principle of symmetry. Major ideas are summarized and factors hindering applications of G theory in research conducted in French-speaking Europe are presented. The principle of symmetry affirms that any factor of a design can be…