Gollob & Reichardt, 1987). As an alternative we can estimate the difference factors, or differences in the factor scores, and we can use these either as out comes or predictors. By far the most popular structural equation model for longitudinal data is the "antoregressive" or "time forward" prediction model (as in Fig. 10.1). With just two points of measurement this is inseparable from the difference score model (Fig. 10.1). In a model more expanded along the variables and occasions axes, we might be able to make a more formal and rigorous distinction between "traits" and "states" (see Hertzog & Nesselroade, 1987). For example, a state might have some relation over time and a mean but, in contrast to a trait, these covariance and mean changes would average out to zero over many occasions. With more than two occasions of measurement we can begin to compare the value of these models as explanations of our data.
It is a truism that putting more information into a data base allows one to get more information out. Developmentalists must heed this truism, nevertheless, and aim for better representation of persons, variables, and occasions of measurement in building their data bases. Given more extensive data, more general multivariate models can be developed and applied to the task of understanding development.
The analytic approach used here demonstrated some parallels and some differences between traditional multivariate models and newer structural equation models. The applications studied here showed the same substantive results in most all cases, but also illustrated why the newer methods are "more precise and clear in their testing implications'' (after Cattell, 1966; Nesselroade & Cattell, 1988). From a developmental perspective we were able to show how these models deal directly with "interindividual differences in intra-individual change" (see Baltes, Reese, & Nesselroade, 1977/ 1988). These formal models provide a structural vehicle for the examination of changes in groups and changes in individuals as well.
We think these multivariate structural approaches can be useful to developmental research in psychology. At all stages of any research study we will need to make both qualitative and quantitative evaluations. The qualitative features of any study come in the data selection and in the model selection. As we have demonstrated here, the quantitative indexes simply provide us with an objective organization for substantively motivated but inherently qualitative judgments. We have tried to show how these quantitative models do not blindly spit out a maximum likely answer to our questions. Instead, structural equation models provide a set of visual aids to help us focus on the often ambiguous and fuzzy phenomena of development.