loglinear analysis, assumptions met?

Question

We've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical arrangement; 0,1) and the number of items on the plate (3 scallops or 4). For each pair of plates+food, we ask the individual which they prefer. A person will only ever get trials where there are 3 vs 4 items on a plate. Below are our frequencies.

edit:

• I have added 'test' which details which item x plate x arrangement was tested with which other such grouping.
• where 'weight' is the number of times the people decided one grouping (item x plate x arrangement) was preferred over another in a given text.

items,plate,arrangement,test,weight

3,1,1,1,249

3,1,0,1,177

3,0,1,2,282

3,0,0,2,184

4,1,1,3,243

4,1,0,3,297

4,0,1,4,185

4,0,0,4,281

I originally used loglinear analysis. I have a doubt though about this study. It feels as if some assumption has not been met. My question is: do you think this data is valid for such an analysis? Our criteria of only showing participants plates where there were 3 vs 4 items of food is bothersome.

For the curious, here is the loglinear model output (pdf).

Answer 1

edit: this answer needs to be updated given new information provided in the question

I say you're meeting the assumptions of the test. Your intuition about 3 vs 4 scallops as a predictor variable might come from this:

As I've read it, you've got a series of categorical variables predicting a binomial preference dependent variable (preferring a plate or not).

This design doesn't violate assumptions (as long as you're treating number scallops as categorical) but it might end up being under-powered (depending on n) as compared to a design that had integer predictors (like if you had 1-2-3-4-5 as number-of-scallops sub-conditions). I think that's what might be bothering you, but not much to do about it now, as these are the sub-conditions chosen for the experiment.

You might argue that the number-of-scallops predictor could be included as a numeric variable but consider that baked into that is the assumption that 0, 10, 50 100 scallops are possible values for the number-of-scallops predictor variable.

So if my read is correct, it's a logistic regression predicting plate preference with 3 categorical variables and I'd say you're using the technique appropriately.