specification of logistic regression model

[Melli Heger]

Hey everyone,

I need some help with the specification of a log. reg. model for my thesis, it would be awesome if someone could give me a hint.
I have the following dummy-variables:

Test (= are you applying this test?) --> if the answer is yes, the following filterquestions appear:

Internal (=are you applying the Test for internal applicants?),
External (=are you applying the Test for external applicants?)

My hypothesis is "Tests are more likely to be applied for external applicants than for internal applicants"

But how can I test this hypothesis within a log. reg model ? I tried Test as dependent variable, and External and Both (=created for Internal & External) as independent variables, but Stata says "outcome does not vary".... I think it's because External and Internal are filterquestions answered only by people that use Tests....Can someone help?

Thank you!!

[Stephen Jenkins]

If I understandand you correctly, you appear to have 3 binary outcomes, and 2 of them are observed only if the binary "Test" outcome = "yes". The standard way of modelling this would be to use a "trivariate probit model with (one) selection". NB probit, not logit, because one typically wants to allow for non-zero correlations in the errors across the 3 equations and the multivariate normal distribution provides a way of doing this. (There is no multivariate logistic counterpart.) Have a look at Cappellari & Jenkins, Stata Journal, 2006, 6(2) [free download from Stata Journal website] where we discuss multivariate probit models including those with selection, and provide examples of likelihood expressions and code. Also check out David Roodman's cmp on SSC. There are also issues regarding the identification of such models that you probably need to consider.