We asked 60 people to list as many restaurant franchises in Atlanta as they could. The overall list included over 70 restaurants, but we eliminated those that were mentioned by fewer than 10% of the people, leaving us with 45. For these 45, we calculated the proportion of informants who listed the franchise, and we're interested in modeling this proportion as a function of the franchises's (log-transformed) advertising budget and years since becoming a franchise.
So I wrote this code:
model <- glm ( cbind (listed, 55-listed) ~ log.budget + years, family = binomial, data = list.45)
As predicted, both variables exhibit strong, significant effects.
But even though I know that proportional data should never be modeled with OLS regression, I subsequently wrote this code:
model.lm <- lm ( proportion.55 ~ log.budget + years, data = list.45)
In this case, "budget" is still a significant predictor, but "years" is relatively weak and not significant.
It makes me worried that the confidence in the estimates is artificially inflated by the aggregation. Doesn't the binomial glm essentially vectorize the data such that the model is based on 45 * 55 = 2,475 rows? Is that appropriate given that there are really only 45 restaurants and 55 informants? Would this call for mixed-effects modeling?