I have a dependent variable that is technically ordinal, so I ran a ordered probit model (
However, an ordered probit model does not produce any residuals which I needed (post). I thought maybe I can compare a couple of models (that do produce residuals) and see to what extent the estimate of my variable of interest differs (especially since I read that an ordinal probit is essentially a special case of a glm (answer by @suncoolsu)).
Crime is in this example a dummy variable (I have recoded it to a dummy)
I decided to, in addition to an ordered probit model, also run GLM from the quasipoisson family. My output (only showing the variable of interest) looks as follows:
polr_1st <- polr(polr_form_1st, Hess=TRUE, method="probit", data=full) ;summary(polr_1st) Value Std. Error t value Crime 0.45799229 0.0253234 18.08573 glm_1st <- glm(glm_form_1st, family="quasipoisson", data=full); summary(glm_1st) Estimate Std. Error t value Pr(>|t|) (Intercept) -0.2140713 0.0875054 -2.446 0.014438 * Crime 0.3524041 0.0221681 15.897 < 0.0000000000000002 **
So the estimates are quite a bit different, but I thought lets look at the
polr_1st_margins <- summary(margins(polr_1st, variables = "Crime")) factor AME SE z p lower upper Crime -0.1546 0.0084 -18.3506 0.0000 -0.1712 -0.1381 summary(margins(glm_1st, variables = "Crime")) factor AME SE z p lower upper Crime 0.3302 0.0209 15.7771 0.0000 0.2892 0.3712
To my surprise, the marginal effect of the bigger (
polr) coefficient is negative (see also this post).
Does this mean that these models are in the end so different that I just cannot compare them? If yes, is there any model that comes close to
polr which produces residuals?