IBM® SPSS® Amos™ 28

Several fit measures encourage you to reflect on the fact that, no matter how badly your model fits, things could always be worse.

Bentler and Bonett (1980) and Tucker and Lewis (1973) suggested fitting the independence model or some other very badly fitting "baseline" model as an exercise to see how large the discrepancy function becomes. The object of the exercise is to put the fit of your own model(s) into some perspective. If none of your models fit very well, it may cheer you up to see a really bad model. For example, as the following output shows, Model A from Example 6 has a rather large discrepancy (71.544) in relation to its degrees of freedom. On the other hand, 71.544 does not look so bad compared to 2131.790 (the discrepancy for the independence model).

This things-could-be-worse philosophy of model evaluation is incorporated into a number of fit measures. All of the measures tend to range between zero and one, with values close to one indicating a good fit. Only NFI (described below) is guaranteed to be between zero and one, with one indicating a perfect fit. (CFI is also guaranteed to be between zero and one, but this is because values bigger than one are reported as one, while values less than zero are reported as zero.)

The independence model is only one example of a model that can be chosen as the baseline model, although it is the one most often used, and the one that Amos uses. Sobel and Bohrnstedt (1985) contend that the choice of the independence model as a baseline model is often inappropriate. They suggest alternatives, as did Bentler and Bonett (1980), and give some examples to demonstrate the sensitivity of NFI to the choice of baseline model.