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257
Sörbom’s Alternative to Analysis of Covariance
The following is the path diagram for Model X for the control group:
The path diagram for the experimental group is identical. Using the same parameter
names for both groups has the effect of requiring the two groups to have the same
parameter values.
Results for Model X
Model X would be rejected at any conventional level of significance.
The analyses that follow (Models Y and Z) are actually inappropriate now that we are
satisfied that Model X is inappropriate. We will carry out the analyses as an exercise in
order to demonstrate that they yield the same results as obtained in Example 9.
Model Y
Consider a model that is just like Model D but with these additional constraints:
Verbal ability at the pretest (pre_verbal) has the same variance in the control and
experimental groups.
The variances of eps1, eps2, eps3, eps4, and zeta are the same for both groups.
The covariance between eps2 and eps4 is the same for both groups.
Chi-square = 29.145
Degrees of freedom = 10
Probability level = 0.001
v_s1
pre_syn
v_o1
pre_opp
v_s2
post_syn
v_o2
post_opp
Example 16: Model X
Group-invariant covariance structure
Olsson (1973): control condition
Model Specification
c_s1o1
c_s2o2
c_s1s2
c
_
s
1
o
2
c
_
s
2
o
1
c_o1o2