GLM and blogit for proportion variable: different results

[Lidia Stulen]

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.

 
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.

 
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

[Clyde Schechter]

If you look at the number of observations in each analysis you will see that these are running on very different estimation samples. I'm not entirely sure why that is the case, but it is clearly true.

Perhaps related to the above, and perhaps not, I think your -glm- model is not properly specified for your kind of data. I think that you actually need to run it more analogous to the way bilogit works. Specifically I think it should be:

glm airbnb cohesion WO_eig afstand_weg TK_GL gemb_ink HH_alleenstaand, link(logit) family (binomial WO_totaal) robust nolog

In fact, I think that should give you the exact same results as your -blogit- version.

In any case, in -glm-, specifying -family(binomial)- without a number or varname giving a denominator, the denominator is assumed to be 1. And in any case, I don't know what Stata does with your proportion outcome variable here. This command is not designed to work with proportions when used with -family(binomial)-: it expects 0/1 outcomes.

[Nick Cox]

fracreg and betareg now offer direct support for proportional responses.

Binomial/logit/robust is an orthodox combination for continuous proportions.

I can't advise on the specific question here on the comparison with blogit