Re: Repeated measures analysis of fractions summing to a constant

Posted by Kirill Orlov on Apr 05, 2013; 3:36pm
URL: http://spssx-discussion.165.s1.nabble.com/Repeated-measures-analysis-of-fractions-summing-to-a-constant-tp5719257p5719286.html

Thank you for all your answers that came so far. I haven't read them carefully yet.

But here is what meanwhile came to my own mind after a little meditation.
It is very simple: I just thought that (PLEASE correct me if I'm mistaken!) that there is no problem at all. The constraint that repeated-measures sum to a constant within individuals *does not* refute using common RM-ANOVA model. If only ANOVA distributional and spericity assumptions hold, no need for GEE or other procedures arise at all.

Let's have some data: between-subject grouping factor GROUP and within-subject factor RM with 3 levels summing up to a constant (100).

group rm1 rm2 rm3 sum

1 50 30 20 100
1 24 42 34 100
1 34 16 50 100
1 61 28 11 100
1 46 46 8 100
1 23 18 59 100
2 55 22 23 100
2 27 39 34 100
2 44 36 20 100
2 28 40 32 100

Run usual Repeated-measures ANOVA:

GLM rm1 rm2 rm3 BY group
/WSFACTOR= rm 3
/METHOD= SSTYPE(3)
/WSDESIGN= rm
/DESIGN= group.

Summing up to a constant just means that upon collapsing the RM levels, all respondents appear to be the same: there exist no between-subject variation at all, or in other words, the "respondent ID" factor's effect is zero. Hence, in the table "Tests of Between-Subjects Effects" Error term is zero. Also, the effect of GROUP factor is zero too - of course, because the constant sum (100) in our data is the same for both groups 1 and 2.

Now, - I'd ask you, - does these results invalid in any way? Do we say that ANOVA is misused when an error variation - which is left unxplained - is zero? I would not say it, and so RM-ANOVA *is* an appropriate method for fractions (i.e values summing up to a constant). If I'm wrong, please explain me why.