Considers the question of whether there may be infinitely many models equivalent to a hypothesized one, presenting an example of a set of infinitely many models equivalent to an a priori hypothesized covariance structure model. (SLD)

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)

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 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)

Discusses a method, based on bootstrap methodology, for obtaining an approximate confidence interval for the difference in root mean square error of approximation of two structural equation models. Illustrates the method using a numerical example. (SLD)

Illustrates how commonly available structural equation modeling programs can be used to conduct some basic matrix manipulations and generate multivariate normal data with given means and positive definite covariance matrix. Demonstrates the outlined procedure. (SLD)

Outlines a covariance structure analysis approach to the study of parameter trends. Uses the program RAMONA to illustrate the method by fitting a corresponding confirmatory factor analysis model to correlational data from a study involving several psychometric tests and fluid intelligence tasks. (SLD)

Discusses the difference in noncentrality parameters of nested structural equation models and their utility in evaluating statistical power associated with the pertinent restriction test. Asymptotic confidence intervals for that difference are presented. These intervals represent a useful adjunct to goodness-of-fit indexes in assessing constraints…

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)

Structural equation modeling is used in the simultaneous study of individual and group latent change patterns on several longitudinally assessed variables. The approach, which is based on a special case of the comprehensive latent curve analysis of W. Meredith and J. Tisak (1990), is illustrated with a two-group study. (SLD)

A widely and readily applicable covariance structure modeling approach is outlined that allows point and interval estimation of scale reliability with fixed components. The procedure employs only linear constraints introduced in a congeneric model, which after reparameterization permit expression of composite reliability as a function of…

In applications of structural equation modeling, it is often desirable to obtain measures of uncertainty for special functions of model parameters. This article provides a didactic discussion of how a method widely used in applied statistics can be employed for approximate standard error and confidence interval evaluation of such functions. The…

Studied modeling individual latent growth curves of older adults on measures of fluid intelligence by fitting second-order polynomial curves reflecting initial test performance improvement followed by relative stability/drop to the recorded scores of each of 248 subjects. Results suggest substantial plasticity in fluid intelligence of older…