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Example 17
The AllImpliedMoments method in the program displays the following table of
estimates:
These estimates, even the estimated means, are different from the sample values
computed using either pairwise or listwise deletion methods. For example, 53 people
took the visual perception test (visperc). The sample mean of those 53 visperc scores
is 28.245. One might expect the Amos estimate of the mean visual perception score to
be 28.245. In fact it is 28.883.
Amos displays the following fit information for Model B:
Function of log likelihood values can be used to compare the fit of nested models. In
this case, Model A (with a fit statistic of 1375.133 and 19 parameters) is nested within
Model B (with a fit statistic of 1363.586 and 27 parameters). When a stronger model
(Model A) is being compared to a weaker model (Model B), and where the stronger
model is correct, you can say the following: The amount by which the Function of log
likelihood increases when you switch from the weaker model to the stronger model is
an observation on a chi-square random variable with degrees of freedom equal to the
difference in the number of parameters of the two models. In the present example, the
Function of log likelihood for Model A exceeds that for Model B by 11.547
(= 1375.133 – 1363.586). At the same time, Model A requires estimating only 19
parameters while Model B requires estimating 27 parameters, for a difference of 8. In
other words, if Model A is correct, 11.547 is an observation on a chi-square variable
with 8 degrees of freedom. A chi-square table can be consulted to see whether this chi-
square statistic is significant.
Function of log likelihood = 1363.586
Number of parameters = 27
Implied (for all variables) Covariances (Group number 1 - Model 1)
wordmean sentence paragrap lozenges cubes visperc
wordmean 73.974
sentence 29.577 25.007
paragrap 23.616 13.470 13.570
lozenges 29.655 10.544 9.287 67.901
cubes 3.470 1.678 2.739 17.036 16.484
visperc 14.665 14.382 8.453 31.173 17.484 49.584
Implied (for all variables) Means (Group number 1 - Model 1)
wordmean sentence paragrap lozenges cubes visperc
18.263 18.802 10.976 14.962 25.154 28.883