# How to best analyze non-mutually-exclusive categorical outcome with categorical predictor and categorical blocking factors?

Here is an example: I have a set of observations of different individuals from lots of different families of grasses:

individual#, Fam, Genus, Factor1(3 levels), Factor2(7 levels), Factor3(5 levels), Response1(3 levels), Response2(3 levels)


What I am hoping to discover is whether the frequency of occurrences of Response1 and 2 are linked to family groups, and whether Factors 1 - 3 (things like soil type, sun exposure etc) have an impact.

Example:

family,  resp1a,  resp1b,   resp1c
1,       14%(20), 16%(24),  67%(98),  Total N = 147
2,       38%(98), 86%(220), 48%(123), Total N = 256
...


First, I need to see whether these differences in responses between families is significant (chi-squared?). Secondly, I need to see if one of the 3 factors has an effect on the response.

Now it seems in my basic understanding, that if the response(s) were continuous measurement, ANOVA/MANOVA would work. Easy-peasy. However, since everything is discreet categories (including the independent and dependent variables) I can't do this. Additionally, since the responses are not mutually exclusive, this seems to violate an assumption of the log-linear model.

I've scoured, and keep bouncing around between Multinomial Logistic Regression, or just independent Chi-Square tests, or... hell I don't know anymore.

And yes, I am trying to swim before learning to float.

Oh, and this is all happening in R.

• Did you look at log-linear models as well? Should be loglin in R.
– psj
Dec 7 '11 at 12:35
• Hmmm - log-linear models seem to assume mutually exclusive categories. Although my blocking factors are, the response variables are not. Dec 8 '11 at 6:20
• "multiple response data" could then be the term to search for. If your data fall into this category then you're right: Standard log linear models cannot handle that (TMK). But there have been proposals to modify them. (see stats.stackexchange.com/questions/3676/… or On the Log-Linear Analysis of Multiple Response Data by Declaro et al). There are also some simpler strategies, e.g. constructing a new variable holding all possible combinations of resp1a, resp1b and resp1c and therefore get around the multiple responses.
– psj
Dec 13 '11 at 23:13
• Thanks @psj - knowing the terminology definitely helps. Am I correct in assuming that if I collapse the responses into an uber-combined response, I would lose any ability to look at whether the responses are interacting... Perhaps I could look at that separately, before considering the factors... Dec 14 '11 at 3:54