Logistic regression with outcome probability based on month

[Loris Di Stefano]

I am performing a logistic regression to find out the probability of a given customer to click on one of my organizations emails.

The model looks thus like this:

y = β0 + β1X1 + β2X2 + ... +βnXn

where the outcome is the probability for the given observation/customer to click on a link in the email. The outcome variable I am using is a dummy called 'clicked'. The independent variables display the age, number of kids and many other information regarding the client.

I also have the time and date at which the emails where sent.

I am now curious to find out if a client is more likely to click on an email in a given month.

Am I correct to assume that in order to model this, I need to interact the 'clicked' variable with the dummy representing the month that I am interested in?

f.e. 'clicked' * 'month_july'

And set this interacted variable as the new outcome variable?

Or how would you proceed?

[Maarten Buis]

There are several things wrong. First, your model does not describe a logistic regression model.

You don't need to interact the month with the explained/dependent/left-hand-side/y-variable. That would be bad in many different ways. Instead just add the month variable without interaction. Why would a month variable be any different from all the other explanatory/independent/right-hand-side/x-variables you added to your model?

[Loris Di Stefano]

Absolutely right. sorry for the stupid question and thank you for the smart reply

I thought that by interacting the two I would be left with the clicks in the given month.
But you are correct, I can just look at the coefficients and see from there the effect.

I am trying to figure out a way to run the model with the different months in a ML algo and have it return the probability per customer per month.

Thank you for your corrections

[William Lisowski]

Instead of having a dummy for each separate month, you should create a Stata monthly date variable and - let's pretend you give it the name mon - then you include i.mon in your independent variables. This will simultaneously include indicator (dummy) terms in your model for each separate month.

help datetime
help factor variables

logistic y X1 X2 ... Xn i.mon