Procedures are presented for conducting power analyses of tests of overall fit of covariance structure models when null and alternative levels of model fit are specified in terms of values of the GFI or AGFI fit indexes. Reasons the root mean square error of approximation fit index may be preferable are discussed. (SLD)

Methods for studying relationships between patterns of change on different variables are considered, showing how the multilevel modeling framework, often used to study univariate change, can be extended to the multivariate case to yield estimates of covariances of parameters representing aspects of change for different variables. (SLD)

The effects of several specification search strategies used with Covariance Structure Modeling to obtain more parsimonious models are examined. The initial models vary in their degree of "correctness." Restricting modifications to those justified by prior theoretical knowledge improves the success of a specification search. (TJH)