A Kansas State University survey6 of 262 pig farmers asked “What are your primary sources of veterinary information?” The farmers were asked to select all relevant categories from (A) Professional Consultant, (B) Veterinarian, (C) State or Local Extension Service, (D) Magazines, and (E) Feed Companies and Reps. The Farmers data file at the text website shows results, listing the response for each source (1 = yes, 0 = no) as well as whether the farmer had at least some college education (1 = yes, 0 = no) and size of farm (number of pigs marketed annually, in thousands, with categories 1, 2, 3, 4 for < 1, 1–2, 2–5, > 5). In contingency table form, the data are a 25×2×4 table of (yes, no) counts for each of the five sources cross-classified with the farmers’ education and size of farm.

a. Explain why it is not proper to analyze the data by fitting a multinomial model to the counts in the 5×2×4 contingency table that cross-classifies information source by education and size of farm, treating source as the response variable. (Hint: This table contains 453 positive responses of sources from the 262 farmers.)

b. For a farmer with education i and size of farm s, let yist be the response on source t (1 = yes, 0 = no). Using GEE with exchangeable working correlation, estimate parameters and interpret effects in the model lacking an education effect, logit[P(Yist = 1)] = αt + βts, s = 1, 2, 3, 4.