I am thinking of trying to use the logit model to determine the probability of whether patients will participate in a particular health program. My observation is the individual patient. My independent variables pertain to the characteristics of the patient (Male/Female, Age, Region, etc). My dependent variable is dichotomous (whether patients participate or not in the particular health program). There are 3 health programs total and patients can choose to participate in 0 (none), 1, 2, 3 (all) of the programs. The decision to participate in one program can be dependent on the decision to participate in another (I don’t have the data to back this statement up but this assumption makes sense); participation in one program does not exclude participation in another. In fact if one participates in one of the programs it may be easier to participate in another.

I would like to take all my observations and create 3 logit regression equations (one for each health program the patients can participate in). However I would like to then compare the three regression equations to determine if there is a statistical difference between the three. The problem is that I cannot use an ANOVA/ANCOVA type test in which I include the “health program” as a dummy variable because the data from the three different regression equations overlaps. For example Patient A who participates in Program 1 can also participate in Program 2. If I were to use data from all three regressions, I would be counting Patient A twice.

Is there any way for me to compare these three logit regressions? I am undergraduate economics major so my knowledge of advanced econometric and statistical topics is limited.

I have thought about doing a multinomial logit model with each combination of participation possibilities as a discrete choice. However the problem is that not all 3 of the programs were available to all of the patients.

I would like to take all my observations and create 3 logit regression equations (one for each health program the patients can participate in). However I would like to then compare the three regression equations to determine if there is a statistical difference between the three. The problem is that I cannot use an ANOVA/ANCOVA type test in which I include the “health program” as a dummy variable because the data from the three different regression equations overlaps. For example Patient A who participates in Program 1 can also participate in Program 2. If I were to use data from all three regressions, I would be counting Patient A twice.

Is there any way for me to compare these three logit regressions? I am undergraduate economics major so my knowledge of advanced econometric and statistical topics is limited.

I have thought about doing a multinomial logit model with each combination of participation possibilities as a discrete choice. However the problem is that not all 3 of the programs were available to all of the patients.

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