This is an extension of a previous question I asked; Logistic Regression - between 2 unrelated treatments? it's a separate question entirely, hence I thought I'd put up a separate post for it.
Context I'm testing the effects of various email interventions on getting people to sign up for a financial literacy event, and benchmarking them against a default, control intervention. The outcome variable is sign-up (i.e. Yes, or No). So it's a binary outcome, and I'm running a logistic regression.
- Control (T0) Email: A default email that the sponsoring agency has been using for years. ("Please sign up!")
- Treatment 1 (T1) Email: Same email, but adds an extra 'note'. (e.g., "By the way, did you know that.....")
- Treatment 2 (T2) Email: Same email again, with another type of 'note'.
- Treatment 3 (T3) Email: Same email again, with another type of 'note'.
- Treatment 4 (T4) Email: Same email again, with another type of 'note'.
Further to that, I have different demographic variables for age, income levels, and gender. I don't have a clear idea as to whether the odds of signup will vary linearly, so I decided to dummy code all of them. The picture below sums up the variables I've listed down.
As you can see, there are several variables, and after hand-coding coefficients for individual terms (and their interaction terms, for which I'm considering only age and income levels, given that there is literature evidence), I'm looking at ~40 coefficients. The picture below shows a sample (the interaction terms for t2,t3,t4 are not shown)
So my questions now are:
- Sanity Check: Am I on the 'right path' as far as capturing interaction terms is concerned? Anything I'm missing out?
- If I run a multiple logistic regression model - some coefficients will clearly be nonsignificant. I understand that it is still important to report them for integrity's sake - but for practical purposes, how would I calculate the log odds? simply pretend that the coefficient doesn't exist, and calculate only the significant coefficients?
- Do I need to do any Bonferroni corrections, since there are 40 coefficients and that there are 40 p-values?
Appreciate the guidance.