IBM® SPSS® Amos™ 28

Model evaluation is one of the most unsettled and difficult issues connected with structural modeling. Bollen and Long (1993), MacCallum (1990), Mulaik, et al. (1989), and Steiger (1990) present a variety of viewpoints and recommendations on this topic. Dozens of statistics, besides the value of the discrepancy function at its minimum, have been proposed as measures of the merit of a model. Amos calculates most of them.

Fit measures are reported for each model specified by the user and for two additional models called the "saturated" model and the "independence" model. In the saturated model, no constraints are placed on the population moments. The saturated model is the most general model possible. It is a vacuous model in the sense that it is guaranteed to fit any set of data perfectly. Any Amos model is a constrained version of the saturated model. The independence model goes to the opposite extreme. In the independence model, the observed variables are assumed to be uncorrelated with each other. Through version 4.0.1, when means and intercepts were explicit model parameters the means of observed variables were fixed at zero in the independence model. In versions later than 4.0.1, means are unconstrained in the independence model. The independence model is so severely constrained that you would expect it to provide a poor fit to any interesting set of data. It frequently happens that each one of the models that you have specified can be so constrained as to be equivalent to the independence model. If this is the case, the saturated model and the independence model can be viewed as two extremes between which your proposed models lie.

For every estimation method except maximum likelihood, Amos also reports fit measures for a zero model, in which every parameter is fixed at zero.