Hi,
Thanks for your reply. I have a few more follow-up questions.
You recommended demeaning each questionnaire, creating the interactions
based on these demeaned evs, and not worrying about any further
orthogonalization. Our understanding is that orthogonalizing EV 1 wrt to EV
2 gives all the shared variance to EV 2. We had originally planned to
orthogonalize the interactions wrt the questionnaires so that the variance
shared by the interaction and questionnaire evs would go to the
questionnaires. How would creating the interactions from demeaned
questionnaires accomplish the same goal?
Also, we have been doing some testing of orthogonalization procedures. Say,
for example, we have a model with EVs for the group mean and for two
questionnaires (A and B). We add in an EV representing the interaction
between the two questionnaires and orthogonalize this EV wrt the EVs for
questionnaires A and B. Since adding in a new EV will account for more
error variance, we would predict that the zstats for the two questionnaires
will change. However, since the interaction EV is orthogonalized wrt to the
questionnaire EVs, we think the PEs for questionnaires A and B should be
unaffected by the addition of the interaction to the model. Is that correct?
We did some tests of the hypothesis that the PEs will remain unchanged and
have found some confusing results.
We first ran two HLA's using raw (i.e. not demeaned) questionnaire scores.
Model 1: Composed of 3 EVs. One EV for the group mean, one for
questionnaire A, and one for questionnaire B. None of the EVs were
orthogonalized to each other.
Model 2: Composed of 4 EVs. One EV for the group mean, one for
questionnaire A, one for questionnaire B, and one for the interaction of
questionnaire A and B (created by multiplying A and B together). The
interaction EV was orthogonalized wrt to the EVs for questionnaire A and B (
i.e. clicked the buttons underneath the interaction EV corresponding to A
and B).
We compared the questionnaire A PE for model 1 to the questionnaire A PE for
model 2 and found that they were not identical. The max difference in
intensity between PEs for model 1 and model 2 was 8.67. Since the maximum
intensity of PEs for model 1 and model 2 was approximately 9, the difference
of 8.67 seems large. We repeated this for questionnaire B and found a
similar difference.
We are unclear about the source of this large difference in questionnaire
PEs between the two models. We then repeated this test, but this time we
orthogonalized all EVs wrt to the group mean ( i.e. we clicked the button
under each EV corresponding to the group mean). We again compared the
questionnaire PEs for the two models and found that they were still not
identical, but this time the difference was smaller (the max difference in
intensity was 3.8, the maximum intensity of both PEs was approximately 9).
We are left confused about how to set up our model and have a few questions.
1. Why is there a difference in questionnaire PEs for model 1 and 2?
2. Why does orthogonalizing wrt to the group mean reduce this difference?
3. Is there a way to make the PEs for model 1 and 2 equivalent (and is this
a desirable goal)?
4. Given that there is a difference, which model is more appropriate for
interpreting the effects of questionnaire A and B?
Thanks for your help,
~Anna
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