How to do feature reduction for a log-linear regression model

I’m building a log-linear regression model and I have 18 different variables in my model. 13 out of 18 variables I’m using are hot-encoded variables for holiday, e.g. showing which holiday it is. I think 18 variable for a log-linear model are a lot and I’d like to reduce them. I’m thinking of applying feature reduction, e.g. PCA or Autoencoder, on the holiday flags and convert them to 3 or 4 features. Does this makes sense or any better way or dealing with these number of features in my model?