ABSTRACT
This chapter discusses a hierarchy of univariate and multivariate time series models. The term hierarchy was selected to suggest an ordering of complexity and generality among the models. Although the models differ on these two dimensions, they share two very important characteristics. As time series models, the models attempt to describe the behavior of a process across multiple occasions; in this chapter, the process is the emotional response patterns underlying daughter-father and stepdaughter-stepfather relationships. Yet, time series models of psychological processes are litde employed despite their obvious appropriateness for describing developmental phenomena. Among the reasons given for this neglect include the perceived difficulty of the models, the necessity of collecting data across a large number of occasions, and a reflexive reliance on the repeated measures analysis of variance (MANOVA) paradigm (Glass, Willson, & Gottman, 1975). These conceptions concerning time series analyses underline the importance of the second characteristic the models share: All are relatively simple to analyze and do not require an extraordinary number of observations for their resolution, at least relative to the uniqueness of the information extractable from them. In this chapter, we are concerned with describing how some common, not-so-common, and original time series models may be resolved through a structural equation modeling (SEM) approach. We hope having another tractable analytic tool will encourage the broader use of time series methodology. For each model, we provide a basic description of the model, how the model may be analyzed through SEM, and the results of fitting the model to a specific data set. Throughout, the emphasis is on a confirmatory approach to modeling (i.e., specific factor structure is proposed), as well as a group comparison approach (i.e., stepdaughters are compared with daughters). LISREL-8 (Jöreskog & Sörbom, 1993) was selected as the SEM program, although any one of several others (e.g., EQS, Bentler, 1992) would have done equally as well. Of special note, all of the models discussed in this chapter describe phenomena in the time domain. Although frequency domain time series models have merit for behavioral and social science research, their implementation within current SEM programs is far more complex than in the time domain.
