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Example 17
The p value is 0.173; therefore, we accept the hypothesis that Model A is correct at the
0.05 level.
As the present example illustrates, in order to test a model with incomplete data, you
have to compare its fit to that of another, alternative model. In this example, we wanted
to test Model A, and it was necessary also to fit Model B as a standard against which
Model A could be compared. The alternative model has to meet two requirements.
First, you have to be satisfied that it is correct. Model B certainly meets this criterion,
since it places no constraints on the implied moments, and cannot be wrong. Second,
it must be more general than the model you wish to test. Any model that can be
obtained by removing some of the constraints on the parameters of the model under
test will meet this second criterion. If you have trouble thinking up an alternative
model, you can always use the saturated model, as was done here.
Performing All Steps with One Program
It is possible to write a single program that fits both models (the factor model and the
saturated model) and then calculates the chi-square statistic and its p value. The
program in Ex17-all.vb shows how this can be done.