Filter
Top Products
150
Example 9
Requesting modification indices with a threshold of 4 produces the following
additional output:
According to the first modification index in the M.I. column, the chi-square statistic
will decrease by at least 13.161 if the unique variables eps2 and eps4 are allowed to be
correlated (the actual decrease may be greater). At the same time, of course, the
number of degrees of freedom will drop by 1 because of the extra parameter that will
have to be estimated. Since 13.161 is the largest modification index, we should
consider it first and ask whether it is reasonable to think that eps2 and eps4 might be
correlated.
Eps2 represents whatever pre_opp measures other than verbal ability at the pretest.
Similarly, eps4 represents whatever post_opp measures other than verbal ability at the
posttest. It is plausible that some stable trait or ability other than verbal ability is
measured on both administrations of the Opposites test. If so, then you would expect a
positive correlation between eps2 and eps4. In fact, the expected parameter change (the
number in the Par Change column) associated with the covariance between eps2 and
eps4 is positive, which indicates that the covariance will probably have a positive
estimate if the covariance is not fixed at 0.
It might be added that the same reasoning that suggests allowing eps2 and eps4 to
be correlated applies almost as well to eps1 and eps3, whose covariance also has a
fairly large modification index. For now, however, we will add only one parameter to
Model A: the covariance between eps2 and eps4. We call this new model Model B.
Model B for the Olsson Data
Below is the path diagram for Model B. It can be obtained by taking the path diagram
for Model A and adding a double-headed arrow connecting eps2 and eps4. This path
diagram is saved in the file Ex09-b.amw.
Modification Indices (Group number 1 - Default model)
Covariances: (Group number 1 - Default model)
M.I. Par Change
eps2
<-->
eps4
13.161
3.249
eps2
<-->
eps3
10.813
-2.822
eps1
<-->
eps4
11.968
-3.228
eps1
<-->
eps3
9.788
2.798