A procedure for evaluating the average R-squared index for a given set of observed variables in an exploratory factor analysis model is discussed. The method can be used as an effective aid in the process of model choice with respect to the number of factors underlying the interrelationships among studied measures. The approach is developed within…

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 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 method is outlined, which accomplishes estimation of criterion validity and reliability for a multicomponent measuring instrument with hierarchical structure. The approach provides point and interval estimates for the scale criterion validity and reliability coefficients, and can also be used for testing composite or…

An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R[squared] indexes associated with repeatedly followed measures in longitudinal…

This article is concerned with the question of whether the missing data mechanism routinely referred to as missing completely at random (MCAR) is statistically examinable via a test for lack of distributional differences between groups with observed and missing data, and related consequences. A discussion is initially provided, from a formal logic…

A latent variable analysis procedure for evaluation of reliability coefficients for 2-level models is outlined. The method provides point and interval estimates of group means' reliability, overall reliability of means, and conditional reliability. In addition, the approach can be used to test simple hypotheses about these parameters. The…

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…

Relevant aspects of the example provided by Raykov and Marcoulides (2001) are emphasized, specifically the distinctiveness of infinitely many members of its sequence of equivalent structural equation models. This emphasis appears to be needed in light of recent statements by Markus (2002), whose intended counterexamples do not present a…

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,…

This article presents a didactic discussion of a multilevel covariance structure modeling approach to estimation of lowest level mediation effect indexes in two-level studies. The procedure is useful when addressing questions about relations among total and indirect effects between variables of interest while accounting for the hierarchical…

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term…

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…

A covariance structure modeling perspective on reliability estimation can be used to construct a formal approach to estimation of reliability in multilevel models. This article presents a didactic discussion of the relation between a structural modeling procedure for scale reliability estimation and the notion of reliability of observed means in…

Provides counterexamples where the covariance matrix provides crucial information about consequential model misspecifications and cautions researchers about overinterpreting the conclusion of D. Rogosa and J. Willett (1985) that the covariance matrix is a severe summary of longitudinal data that may discard crucial information about growth. (SLD)