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Sörbom’s Alternative to Analysis of Covariance
Model B
The largest modification index obtained with Model A suggests adding a covariance
between eps2 and eps4 in the experimental group. The modification index indicates
that the chi-square statistic will drop by at least 10.508 if eps2 and eps4 are allowed to
have a nonzero covariance. The parameter change statistic of 4.700 indicates that the
covariance estimate will be positive if it is allowed to take on any value. The suggested
modification is plausible. Eps2 represents unique variation in pre_opp, and eps4
represents unique variation in post_opp, where measurements on pre_opp and
post_opp are obtained by administering the same test, opposites, on two different
occasions. It is therefore reasonable to think that eps2 and eps4 might be positively
correlated.
The next step is to consider a revised model, called Model B, in which eps2 and eps4
are allowed to be correlated in the experimental group. To obtain Model B from Model A:
E Draw a double-headed arrow connecting eps2 and eps4.
This allows eps2 and eps4 to be correlated in both groups. We do not want them to be
correlated in the control group, so the covariance must be fixed at 0 in the control
group. To accomplish this:
E Click control in the Groups panel (at the left of the path diagram) to display the path
diagram for the control group.
E Right-click the double-headed arrow and choose Object Properties from the pop-up
menu.
E In the Object Properties dialog box, click the Parameters tab.
E Type 0 in the Covariance text box.
E Make sure the All groups check box is empty. With the check box empty, the constraint
on the covariance applies to only the control group.