This note highlights and illustrates the links between item response theory and classical test theory in the context of polytomous items. An item response modeling procedure is discussed that can be used for point and interval estimation of the individual true score on any item in a measuring instrument or item set following the popular and widely…

This note discusses the merits of coefficient alpha and their conditions in light of recent critical publications that miss out on significant research findings over the past several decades. That earlier research has demonstrated the empirical relevance and utility of coefficient alpha under certain empirical circumstances. The article highlights…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

This note is concerned with examining the relationship between within-group and between-group variances in two-level nested designs. A latent variable modeling approach is outlined that permits point and interval estimation of their ratio and allows their comparison in a multilevel study. The procedure can also be used to test various hypotheses…

A latent variable modeling procedure is discussed that can be used to test if two or more homogeneous multicomponent instruments with distinct components are measuring the same underlying construct. The method is widely applicable in scale construction and development research and can also be of special interest in construct validation studies.…

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

A latent variable modeling procedure that can be used to evaluate intraclass correlation coefficients in two-level settings with discrete response variables is discussed. The approach is readily applied when the purpose is to furnish confidence intervals at prespecified confidence levels for these coefficients in setups with binary or ordinal…

A critical discussion of the assumption of uncorrelated errors in classical psychometric theory and its applications is provided. It is pointed out that this assumption is essential for a number of fundamental results and underlies the concept of parallel tests, the Spearman-Brown's prophecy and the correction for attenuation formulas as well as…

Certain diversity among team members is beneficial to the growth of an organization. Multiple measures have been proposed to quantify diversity, although little is known about their psychometric properties. This article proposes several methods to evaluate the unidimensionality and reliability of three measures of diversity. To approximate the…

The relationship between saturated path-analysis models and their fit to data is revisited. It is demonstrated that a saturated model need not fit perfectly or even well a given data set when fit to the raw data is examined, a criterion currently frequently overlooked by researchers utilizing path analysis modeling techniques. The potential of…

A procedure is presented to transform an n-dimensional scatter diagram into a two-dimensional scatter diagram while preserving proximity relationships between points. This procedure can help in the presentation and interpretation of multivariate results. (Author/SLD)