The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

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…

This article is concerned with the large-sample parameter estimator behavior in applications of Bayesian confirmatory factor analysis in behavioral measurement. The property of strong convergence of the popular Bayesian posterior median estimator is discussed, which states numerical convergence with probability 1 of the resulting estimates to the…

A class of effect size indices are discussed that evaluate the degree to which two nested confirmatory factor analysis models differ from each other in terms of fit to a set of observed variables. These descriptive effect measures can be used to quantify the impact of parameter restrictions imposed in an initially considered model and are free…

This note is concerned with evaluation of location parameters for polytomous items in multiple-component measuring instruments. A point and interval estimation procedure for these parameters is outlined that is developed within the framework of latent variable modeling. The method permits educational, behavioral, biomedical, and marketing…

Utilizing the perspective of finite mixture modeling, this note considers whether a finding of a plausible one-parameter logistic model could be spurious for a population with substantial unobserved heterogeneity. A theoretically and empirically important setting is discussed involving the mixture of two latent classes, with the less restrictive…

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…

This article outlines a procedure for examining the degree to which a common factor may be dominating additional factors in a multicomponent measuring instrument consisting of binary items. The procedure rests on an application of the latent variable modeling methodology and accounts for the discrete nature of the manifest indicators. The method…

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.…

A latent variable modeling approach for scale reliability evaluation in heterogeneous populations is discussed. The method can be used for point and interval estimation of reliability of multicomponent measuring instruments in populations representing mixtures of an unknown number of latent classes or subpopulations. The procedure is helpful also…

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 approach is outlined that can be used for meta-analysis of reliability coefficients of multicomponent measuring instruments. Important limitations of efforts to combine composite reliability findings across multiple studies are initially pointed out. A reliability synthesis procedure is discussed that is based on…

A latent variable modeling approach that can be used to examine whether several psychometric tests are parallel is discussed. The method consists of sequentially testing the properties of parallel measures via a corresponding relaxation of parameter constraints in a saturated model or an appropriately constructed latent variable model. The…

A readily implemented procedure is discussed for interval estimation of indexes of interrelationship between items from multiple-component measuring instruments as well as between items and total composite scores. The method is applicable with categorical (ordinal) observed variables, and can be widely used in the process of scale construction,…

A method for estimating criterion validity of scales with homogeneous components is outlined. It accomplishes point and interval estimation of interrelationship indices between composite scores and criterion variables and is useful for testing hypotheses about criterion validity of measurement instruments. The method can also be used with missing…