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…

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…

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…

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)

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…

Discusses issues in structural-equation-model selection that pertain to the general utility of the principle of parsimony. Provides an example using data generated by the relatively nonparsimonious simplex model and fitted rather well by a parsimonious growth-curve model belonging to a different class of models. (Author/SLD)

Presents a necessary and sufficient condition for the equivalence of structural-equation models that is applicable to models with parameter restrictions and models that may or may not fulfill assumptions of the rules. Illustrates the application of the approach for studying model equivalence. (SLD)

Presents a didactic collection of covariance and mean structure hypotheses that can be tested using a widely applicable and easy to use structural equation modeling approach. The method is useful when the goal is to examine the observed multivariable structure or test hypotheses regarding interrelationships in measures and when large samples are…

Discusses a method for obtaining point and interval estimates of reliability for composites of measures with a general structure. The approach is based on fitting a correspondingly constrained structural equation model and generalizes earlier covariance structure analysis methods for scale reliability estimation with congeneric tests. (SLD)