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Sörbom’s Alternative to Analysis of Covariance
as verbal ability at the beginning of the study, and post_verbal is interpreted as verbal
ability at the conclusion of the study. This is Sörbom’s measurement model. The
structural model specifies that post_verbal depends linearly on pre_verbal.
The labels opp_v1 and opp_v2 require the regression weights in the measurement
model to be the same for both groups. Similarly, the labels a_syn1, a_opp1, a_syn2,
and a_opp2 require the intercepts in the measurement model to be the same for both
groups. These equality constraints are assumptions that could be wrong. In fact, one
result of the upcoming analyses will be a test of these assumptions. As Sörbom points
out, some assumptions have to be made about the parameters in the measurement
model in order to make it possible to estimate and test hypotheses about parameters in
the structural model.
For the control subjects, the mean of pre_verbal and the intercept of post_verbal are
fixed at 0. This establishes the control group as the reference group for the group
comparison. You have to pick such a reference group to make the latent variable means
and intercepts identified.
For the experimental subjects, the mean and intercept parameters of the latent
factors are allowed to be nonzero. The latent variable mean labeled pre_diff represents
the difference in verbal ability prior to treatment, and the intercept labeled effect
represents the improvement of the experimental group relative to the control group.
The path diagram for this example is saved in Ex16-a.amw.
Note that Sörbom’s model imposes no cross-group constraints on the variances of
the six unobserved exogenous variables. That is, the four observed variables may have
different unique variances in the control and experimental conditions, and the
variances of pre_verbal and zeta may also be different in the two groups. We will
investigate these assumptions more closely when we get to Models X, Y, and Z.
Results for Model A
Text Output
In the Amos Output window, clicking Notes for Model in the tree diagram in the upper
left pane shows that Model A cannot be accepted at any conventional significance level.
Chi-square = 34.775
Degrees of freedom = 6
Probability level = 0.000