This is not exactly a psych question, but I thought this was the forum wher I would find the most knowledge about log-linear models. If i shold relocate the question, please let me know.

If you have catagorical count data from a large survey, with reported varience estimates fo each cell corrected for for survey design (stratification and clustering) does this imply that one should change the cell mean estimates, test the fit of models, or select between nested models?

I have categorical count data that comes from a complex survey. Each unit of analysis in the survey (household, individual, etc.) is put into one and only category per dimension, with the number of categories per dimension ranging from 2 to 20. The number of dimensions exceeds 50. The in addition to the cell counts, the survey reports a variance estimate for each cell corrected based on the clustering and stratification in the survey design. Thus the variances are generally above the level suggested buy the Poisson distribution given the cell means, and are not uniformly proportional to the means.

I have three related questions:

1. Do the reported cell variance numbers suggest any change in how one should use the data to estimate the population mean for each cell from the sample?

2. If I am fitting a model – say, a hierarchical log-linear model – do reported cell variances at odds with the standard Poisson variences imply that I should accept or reject different models than I would in the Poisson case? For example, if the independence model fits well in all cells but one, but that one is sufficient to make you reject independence at standard levels of significance, might one accept it if the variance estimate for that cell is sufficiently great?

3. If the answer to the preceding question is “yes,” how should the tests for accepting or rejecting nested models be reformulated to account for the variances?

Any insights anyone could offer would be greatly appreciated.

Sincerely, andrewH