Logistic Regression - Only Dummy Variables

Question

I'm working on a problem where all my variables are dummy variables (i.e. I have 5 dummy variables and a binary dependent variable). I'm exploring how each variable affects my dependent variable. My dataset is from a questionnaire with a sample size of around 2000. All the responses are either yes (= 1) or no (= 0). Therefore, I'm only able to use dummy variables for both my dependent and independent variables.

I came across the logistic regression and this model seems to fit my dataset (my data has independence of observations, my data does not follow a normal distribution and the dependent variable is mutually exclusive). However, I do have a concern with regard to the fact that I do not have any continuous variables and I have yet to come across an example of a logistic regression where all the variables are dummies.

Is a logistic regression model appropriate for my data?

Thank you!

Answer 1

As @John Madden said, there is nothing wrong with that.

Basically, your model will look like this:

$$\mathbb{P}(Y_i=1)=f(X_i)$$

Usually, $f$ is defined like this:

$$f(X_i)=\frac{e^{\sum_{j=0}^k \beta_j x_{i,j}}}{1+e^{\sum_{j=0}^k \beta_j x_{i,j}}}$$ where $x_{i,j}$ is the $i^\text{th}$ observation of the $k^\text{th}$ variable.

Having $x_{i,j}\in \{0,1\}$ is not an issue.

Answer 2

As previously stated, yes, you can use logistic regression even when there are no continuous variables.

Your model will then find additive relations (how much does X1 increase the probability of Y=1).

You can enrich it by adding interaction features of the form X1*X2 which will add nonlinear effects to the model (maybe the effect of X1 and X2 are small on their own but if they are both 1 there's a large effect?)