Mixed Model or Growth Curve Model?

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Hi all,
I am working with repeated, unbalanced, and hierarchical data. I have results (NFI) for both eyes from a same individual (level 1 = eye, level 2 =patient) (though not all individuals had both eyes included). Each eye was examined several times, from 3 to 8 times (Visits). The order of these are important as I'm studying exactly the progressive changes for each eye, comparing two groups assessed by an independent method (Progr). And the interval between these visits is variable.

So far, this is how it is:

MIXED NFI BY EYE PATIENT WITH PROGR
/FIXED PROGR |SSTYPE(3)
/RANDOM INTERCEPT EYE*PATIENT | COVTYPE(ID)
/REPEATED VISITS | SUBJECT(EYE*PATIENT) COVTYPE(AR1)
/PRINT SOLUTION TESTCOV.

Question:

I need to know if there was a general trend related with time. I have for each measure the "time since baseline", that would be how many months elapsed between the first measure and that determined measure. I was planning to include this information (Time) as a covariate on each measure level. But I'm not managing to find the best way to do it. Shall I just add it as a random effect, for each eye, with an AR1 Covtype? Something like: /RANDOM TIME | SUBJECT(EYE*PATIENT) COVTYPE(AR1)

Hope I'm not too lost in the concepts here, I'll appreciate any help.

Luciana

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关键词：mixed model Growth model Mixed curve individual comparing important included repeated

As I understand what you said

>>Each eye was examined several times, from 3 to 8 times (Visits). ... And the interval between these visits is variable. I was planning to include this information (Time) as a covariate on each measure level. ... Shall I just add it as a random effect, for each eye, with an AR1 Covtype? Something like: /RANDOM TIME | SUBJECT(EYE*PATIENT) COVTYPE(AR1)

You are going to have trouble because you are treating visits as a repeated factor while it is repeated, persons have a different number of visits. Thus missing data problems.

I think a better way to do this would be to use a three level model of visit within in eye within person. Basically a growth curve model for each eye with the interval beween visits being used to construct the scaling of the time coefficients. The slight familiarity I have with such models is wholely in the context of Mplus. I think example 6 in the Mixed documetation will bring you pretty close. Among others Judith Singer and John Willet's recent book might be quite useful. All that said, I defer in my recommendations to
persons on the list more experienced with mixed.

Gene Maguin

I will agree with most of what Gene has said.  But, you should probably consider a model with only 2 levels - repeated measures nested within individuals.  Eye should not be a level.  It should be used as a predictor
(factor/covariate) of intercept and slope parameters.

I agree that visits within persons is the best way, but you could consider modeling eye as a dyad, a multivariate (2-level) measure about which you wish to know the average as well as the difference between the eyes (eye level must be ordered: e.g., L v R, or Dominant v Non-dominant if neurologically sensible).

Aileen Sayer (a former student of Willett) presents this eloquently, and has some papers out where she and her co-authors use couples as the multivariate dyad. HLM will model this remarkably well. There is a key concept about how to model the dyad that allows for the intraclass coefficient, as well as the use of Intercept and Slope to be used to model both the average as well as the difference, respectively, between the dyads, a very clever assumption, but not necessarily an intuitive one. Singer and Willett do not discuss this in their book, although, I, too, would highly recomment reading their book (at least the first 40% which deals with continuous metric DV's).

Unfortunately, I also have the HLM examples. But my understanding of it leads me to believe that SPSS could do it as well.

Joe Burleson

Would this work considering that "eye" is my unit of interest? All the data I have is given for each eye. We have no hypothesis of differences related to side (right eye vs. left eye). The only reason I leveled them under "patient" is to account for the correlation among eyes of a same patient.
I have no experience using dyads, I'm going to have to do some research on the topic. I got some papers on the subject by Aileen Sayer and I'll give it a look. Thank you on the hint.

Luciana