ABSTRACT
Chapter 2: Fitting Path Models In this chapter we consider the processes used in actually fitting path models to data on a realistic scale, and evaluating their goodness of fit. This implies computer-oriented methods. This chapter is somewhat more technical than Chapter 1. Some readers on a first pass through the book might prefer to read carefully only the section on hierarchical ffl2 tests, glance at the section on the RMSEA, and then go on to Chapters 3 and 4, coming back to Chapter 2 afterwards. (You will need additional Chapter 2 material to do the exercises in Chapters 3 and 4.)
In simple path diagrams like those we have considered so far, direct algebraic solution of the set of implied equations is often quite practicable. But as the number of observed variables goes up, the number of correlations among them, and hence the number of equations to be solved, increases rapidly. There are n(n − 1)=2 equations, where n is the number of observed variables, or n(n + 1)=2 equations, if variances are solved for as well. Furthermore, path equations by their nature involve product terms, because a compound path is the product of its component arrows. Product terms make the equations recalcitrant to straightforward matrix procedures that can be used to solve sets of linear simultaneous equations. As a result of this, large sets of path equations are in practice usually solved by iterative (i.e., repetitive) trial-and-error procedures, carried out by computers.
