Given the ordered logistic regression model:
$outcome=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_1*X_2$
Can I test linear restrictions on the parameters? For example I would like to test $H_0: \beta_2+\beta_b3=0, H_1: Otherwise$. I can formally test after fitting an OLS model, and I would like to know if I can also do this test after fitting an ordered logistic model.
An ordinal model will have more than one intercept, not just $\beta_{0}$. But to answer your question, an ordinal model is treated just like any other multivariable model when testing contrasts involving the non-intercept regression coefficients. Form your contrast and compute the standard error of the contrast using the usual matrix operation on the variance-covariance matrix.
It appears that your hypothesis may be for an $X_{2}$ effect for a given value of $X_{1}$ you can also get this test automatically using the contrast.rms function in the R rms package, once you fit the ordinal model with the orm or lrm function. contrast expects two sets of predictor settings to compare (or 4 if testing a double difference (interaction)). It will compute the standard error that goes along with the contrast.
