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GLM and blogit for proportion variable: different results

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Dear Stata users,

In order to model a proportional dependent variable, I used a GLM model and a blogit model. All data are on the group level (85 neighborhoods).


For the GLM, I used a proportion variable: Airbnb_prop = count of Airbnb houses / count total number of houses.

Code:
 
glm prop_airbnb cohesion WO_eig afstand_weg TK_GL gemb_ink HH_alleenstaand, link(logit) family (binomial) robust nolog
For the Blogit, I used the count of airbnb houses (Airbnb) and total count of houses (WO_totaal). The blogit is designed for group data and equipped to handle proportion variables, so this seemed appropriate.

Code:
 
blogit airbnb WO_totaal cohesion WO_eig afstand_weg TK_GL gemb_ink HH_alleenstaand
The problem:
- I'm not sure which of the two models to use.
My questions:
- The results between both models differ (see output below). It seems to me these models should produce (more) similar results. Why isn't that the case?
- I find it very hard to assess the model fit of these models in a way that I can compare them. What would be the best way to do so?



I hope this is enough to go on, if you would need any additional information I would be happy to provide it. Thank you in advance!
Lydia






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