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I have two surveys of business owners. One is a sample (sample 1) of business owners who were not members of the association, done using a random digit dialing approach. The other is a sample (sample 2) of business owners who were members of an association (used the list of members for the frame). Both samples were stratified by state. Sample 1 was weighted using state and gender. Sample 2 was weighted for non-response and weighted to reflect the association characteristics. As it turns out, there is a greater proportion of males in the association data (sample 2) than in the non-member data (sample 1 data). At first look, it appears that the association appeals to males more than females. We have 500 responses for each sample.

I want to use a probit regression to find the factors (mostly demographic type of factors) influencing association membership. What is the best way to do this? I was hoping I could just combine the samples. However the samples were done independently. Clearly there is a huge difference in the size of the populations - sample 1 is huge (all owners in the country) and sample 2 is just the members. The survey instrument (questions) was almost identical - there were some extra questions for the members of the association (sample 2) related to the satisfaction with the association.

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  • $\begingroup$ I'm wondering why you want to use probit. Logistic regression is standard for relating covariates to a discrete binary response. Should you be interested, I wrote a good deal about all that here: difference-between-logit-and-probit-models. $\endgroup$
    – gung - Reinstate Monica
    Commented Aug 25, 2012 at 18:18

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This looks like a case-control study (all cases are sampled, a similar number of controls are sampled at a much lower rate) -- read up Alastair Scott and Chris Wild's s work on this (book chapter, invited lecture). I second gung's opinion about logistic regression being somewhat more suitable (the theoretical advantages being the exponential family and sufficient statistics).

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  • $\begingroup$ Thanks to everyone for the answers. I'm now clear on what I need to do and I've found a couple of very useful papers. You're correct,it is logistic regression I want - to get the odds ratios out. Thanks!! $\endgroup$
    – eliz
    Commented Aug 26, 2012 at 21:20

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