This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, with optimally chosen but unknown parameter values, to the population covariance matrix. The second is overall error which involves the fit of the model, with parameter values estimated from the sample, to the population covariance matrix. Measures of the two types of error are proposed and point and interval estimates of the measures are suggested. These measures take the number of parameters in the model into account in order to avoid penalizing parsimonious models. Practical difficulties associated with the usual tests of exact fit or a model are discussed and a test of “close fit” of a model is suggested.

This article considers single sample approximations for the cross-validation coefficient in the analysis of covariance structures. An adjustment for predictive validity which may be employed in conjunction with any correctly specified discrepancy function is suggested. In the case of maximum likelihood estimation under normality assumptions the coefficient obtained is a simple linear function of the Akaike Information Criterion. Results of a random sampling experiment are reported.

This paper examines methods for comparing the suitability of alternative models for covariance matrices. A cross-validation procedure is suggested and its properties are examined. To motivate the discussion, a series of examples is presented using longitudinal data.

Thanks to M. W. Browne for several useful discussions that greatly clarified the ideas in this article. An anonymous referee also provided many valuable suggestions.

The total variance in any observed measure of performance can be attributed to 3 sources: (a) the correlation of the measure with the latent variable of interest'(i.e., true score variance), (b) reliable but irrelevant variance due to contamination, and (c) error. A model is proposed that specifies 3, and only 3, determinants of the relevant variance: declarative knowledge, procedural knowledge and skill, and volitional choice (motivation). The 3 determinants are defined, and their implications for performance measurement are discussed. Using data from the U.S. Army Selection and Classification Project (Project A), the authors found that the model fits a simplex pattern to the criterion data matrix. The predictor-determinant correlations are also estimated. Analyses of the data with LISREL provided strong confirmation of the model.

Behavior that develops in phases may exhibit distinctively different rates of change in one time period than in others. In this article, a mixed-effects model for a response that displays identifiable regimes is reviewed. An interesting component of the model is the change point. In substantive terms, the change point is the time when development switches from one phase to another. In a mixed-effects model, the change point can be a random coefficient. This possibility allows individuals to make the transition from one phase to another at different ages or after different lengths of time in treatment. Two examples are reviewed in detail, both of which can be estimated with software that is widely available.

Estimates of standard errors of factor loadings and factor correlations in the unrestricted factor analysis model can be computed for oblique or orthogonal solutions under maximum likelihood. This information can be used to test individual coefficients for significance, to evaluate whether an orthogonal or oblique structure is most consistent with sample data, or to compute confidence intervals for single parameters or confidence regions for arbitrary groups of coefficients. Because the number of parameters estimated in factor analysis is approximately the product of number of variables multiplied by number of factors, a Bonferroni correction for the critical point of the individual test statistics is recommended to control the probability of a Type I error. Several examples are presented.

This article presents first-year cross-sectional findings from a study of the development of eating disorders. Adolescent female (N = 937) 7th through 10th graders completed measures that included information on personality, self-concept, eating patterns, and attitudes. A risk status score was calculated on the basis of comprehensive information regarding DSM-III-R eating disorders criteria and other weight and attitudinal data. All personality measures showed significant differences according to risk, based on subject classification into high, moderate, and mild risk status and comparison groups. Early puberty was not associated with increased risk. The strongest predictor variables for risk were body dissatisfaction, negative emotionality, and lack of interoceptive awareness. The possible diathesis of personality including temperamental factors in the later development of an eating disorder is discussed.