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…

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 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 procedure for examining essential unidimensionality in multicomponent measuring instruments is discussed. The method is based on an application of latent variable modeling and is concerned with the extent to which a common factor for all components of a given scale accounts for their correlations. The approach provides point and interval…

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…

Interval estimation of intraclass correlation coefficients in hierarchical designs is discussed within a latent variable modeling framework. A method accomplishing this aim is outlined, which is applicable in two-level studies where participants (or generally lower-order units) are clustered within higher-order units. The procedure can also be…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

In international achievement studies, questionnaires typically ask about the presence of particular household assets in students' homes. Responses to the assets questions are used to compute a total score, which is intended to represent household wealth in models of test performance. This study uses item analysis and confirmatory factor analysis…

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 correlation structure modeling method for comparison of mediated effects is outlined. The procedure permits point and interval estimation of differences in mediator effects, and is useful with models postulating 1 or more predictor, intervening, or response variables that may also be latent constructs. The approach allows scale-free evaluation…

Outlines a correlation structures modeling approach to the study of stability in reliability of multiple, repeatedly administered measures and illustrates the method on data from a fluid intelligence study (P. Bates and others, 1986). The method is also applicable when examining relationships between model parameters across all variables.…

Studied the population discrepancy of coefficient alpha from the composite reliability coefficient for fixed congeneric measures with correlated errors and expressed it in terms of parameters of the measures. Recommends structural equation modeling for identifying cases in which the discrepancy can be large. (SLD)

Outlines a method for comparing completely standardized solutions in multiple groups. The method is based on a correlation structure analysis of equal-size samples and uses the correlation distribution theory implemented in the structural equation modeling program RAMONA. (SLD)