Say we have 5 items, and people are asked which item they like. Multiple answers are possible, but also no answer is possible. The people are categorized according to factors like gender, age, and so on. One possible approach to analyze the differences between genders, age groups and so on is making use of the Generalized Estimating Equations.
I thus construct a dataset with a binary variable indicating whether the item was liked or not, and as predictor variables I have the items, the person id, the age,... i.e. :
Liked Item Person ... 0 1 1 1 2 1 0 3 1 0 4 1 1 5 1 1 1 2 ...
Then I apply a model with following form : $$Liked = Item + Gender + Item*Gender + Age + Item*Age + ... $$ with Person as random factor (called id in some applications) and a logit link function.
Now I like to give confidence intervals on the conditional fractions, i.e. the confidence interval of the fractions males and females that liked a particular item, corrected for age differences and the likes. I know I could use the estimated coefficients to get the results I want, but I'm a bit lost in how to do that. I can calculate the estimated odds, but I'm not sure on the standard error (SE) on those odds based on the SE of the coefficients. I'm not sure on how to deal with the random component of the variance for example.
1) Any pointers on how to calculate that SE from the SE of the coefficients?
2) Any alternatives for an approach? I've been thinking about mixed models, but a colleague directed me to GEE as more appropriate for these data. Your ideas?
Edit : for practical pointers, I'm using geepack in R for this. I tried
effect(), but the option
se.fit=T is not implemented. In any case, that would give the SE for every observation, which is not what I'm interested in.