I'm running a regression with a set of 3 dummy variables (for four categories of a variable) and these 3 dummies interacted with a continuous variable. I want to impose the restriction that the vector of the coefficients of the interacted dummies is proportional to the coefficients of the dummies, e.g. each interaction term has a coefficient 2x larger than the coefficient on it's non-interacted dummy.
Is it possible to impose these restrictions with a linear regression model? or will I have to use non-linear least squares?
(P.S. the proportionality is a ratio to be estimated, so that would be another free parameter in the model)