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Example 6
The column heading M.I. in this table is short for Modification Index. The modification
indices produced are those described by Jöreskog and Sörbom (1984). The first
modification index listed (5.905) is a conservative estimate of the decrease in
chi-square that will occur if eps2 and delta1 are allowed to be correlated. The new
chi-square statistic would have 5 degrees of freedom and would be no
greater than 65.639 ( ). The actual decrease of the chi-square statistic
might be much larger than 5.905. The column labeled Par Change gives approximate
estimates of how much each parameter would change if it were estimated rather than
fixed at 0. Amos estimates that the covariance between eps2 and delta1 would be
. Based on the small modification index, it does not look as though much would
be gained by allowing eps2 and delta1 to be correlated. Besides, it would be hard to
justify this particular modification on theoretical grounds even if it did produce an
acceptable fit.
Changing the Modification Index Threshold
By default, Amos displays only modification indices that are greater than 4, but you
can change this threshold.
E From the menus, choose View > Analysis Properties.
E In the Analysis Properties dialog box, click the Output tab.
E Enter a value in the Threshold for modification indices text box. A very small threshold
will result in the display of a lot of modification indices that are too small to be of
interest.
The largest modification index in Model A is 40.911. It indicates that allowing eps1
and eps3 to be correlated will decrease the chi-square statistic by at least 40.911. This
is a modification well worth considering because it is quite plausible that these two
variables should be correlated. Eps1 represents variability in anomia67 that is not due
to variation in 67_alienation. Similarly, eps3 represents variability in anomia71 that is
not due to variation in 71_alienation. Anomia67 and anomia71 are scale scores on the
same instrument (at different times). If the anomia scale measures something other
than alienation, you would expect to find a nonzero correlation between eps1 and eps3.
In fact, you would expect the correlation to be positive, which is consistent with the
fact that the number in the Par Change column is positive.
61–=()
71.544 5.905–
0.424–