Suppose I have an opinion survey on some topic. Both my dependent variable and independent variable are categorical variables. My question is, if I use the ordered probit model, how do I interpret the results? The independent variables are also categorical so I can't find the marginal effects either. Then, how do I interpret the coefficients and is there anything else I can do similar to finding the marginal effects?
Generally your are estimating probabilities for every category j of your dependent variable y. Similar to marginal effects, not as far as I know. You can estimate the probabilites for the response-categories with mfx in stata if I remember correctly.
Concerning the interpretation of the coefficients UCLA can help: "Standard interpretation of the ordered logit coefficient is that for a one unit increase in the predictor, the response variable level is expected to change by its respective regression coefficient in the ordered log-odds scale while the other variables in the model are held constant."