My question pertains to this Cross Validated post, but I specifically aim to compare the effect size of an independent variable between categories of the dependent variable.
In practice, I have a non-ordinal dependent variable with four categories representing cultural consumption clusters. I have three independent predictors: Gender (binary), Age (continuous), and Social Origin (categorized into three groups). I want to assess whether the effect of social origin on the probability of belonging to one cluster differs for each cluster.
Should I use multinomial logistic regression or one-vs-rest binary logistic regression for each category of the dependent variable? Or perhaps there's another model I'm not aware of?
