I am designing a marketing campaign to raise money for a charity. I have a limited budget for my mailing campaign, so I have to send my mail to a selected group of people. I have data from past campaigns about who responded, and I will use logistic regression to select who shall receive my mail. The regression model will generate a probability of responding to the mail with a donation.
I will not include any interactions in my model; all covariates will be first-order effects.
Gender is a disproportionately significant covariate in my regression model. Because it is a binary variable, I am tempted to split my data set into male and female recipients, and build separate models for men and women. Hence, I have 2 possible approaches.
A) Use the entire data set, and use an indicator variable for gender in my regression model.
B) Split the data between men and women, and build 2 separate regression models for men and women.
1) A good lift curve decreases monotonically and smoothly. I don't know which method is better for this.
2) If I use Method B, then I will get better fits to the data. However, I will have smaller sample sizes for each model, resulting in less power. This thread already mentions this.
3) The response rates are very different between men and women. For women, the response rate is much, much lower. If I use Method B, then I worry that the predicted probability of responding (i.e. the "score") will be uniformly higher for men over women, even though some individual women may be very willing to respond and donate large amounts of money. I don't want to miss any of these women when selecting the recipients of my mailing campaign.
At this point, it is unclear to me which method is better, so my question is this: Are there any research articles in the statistical literature about regression modelling that talks about this issue and advises which method is better?