# Interpretation of hurdle model with negative binomial distribution

I envisage to employ a hurdle model in R, as for instance described here.

Question: how I can derive marginal effects from the hurdle model?

With linear regression, it is easy to get a marginal effect, as for instance, increasing healthpoor by one unit in the regression below, will increase visits by 1.84532 units. Or gendermale is associated with a decrease of visits by -0.63185 (other things equal).

I wonder how to derive such marginal effects in a hurdle model.

library(AER)
library(pscl)

data("NMES1988")
nmes <- NMES1988[, c(1, 6:8, 13, 15, 18)]  # select certain columns; Col 1 is number of visits
plot(table(nmes$visits)) ols <- lm(visits ~ ., data = nmes) summary(ols) --- Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.63203 0.33480 4.875 1.13e-06 *** hospital 1.61976 0.13264 12.211 < 2e-16 *** healthpoor 1.84532 0.31234 5.908 3.72e-09 *** healthexcellent -1.33140 0.36257 -3.672 0.000243 *** chronic 0.94440 0.07693 12.276 < 2e-16 *** gendermale -0.63185 0.19454 -3.248 0.001171 ** school 0.14345 0.02726 5.262 1.49e-07 *** insuranceyes 1.10397 0.24362 4.532 6.01e-06 *** ---  Here is an example of a hurdle model and the model summary. I understand that the lower part of the output (Zero hurdle model) is the binary model to identify $$(0,1)$$, so I suppose a simple logistic regression. However, I'm interested in interpreting the upper part (Count model) in the way like marginal effects as described above. The log-link hints that an interpretation as in the linear regression case is not valid. How can I calculate marginal effects from the Count model? I know that Stata has built-in functions to derive marginal effects from log-link models. Is there a way to do this in R as well? mod.hurdle.nb <- hurdle(visits ~ ., data = nmes, dist = "negbin") summary(mod.hurdle.nb) --- Count model coefficients (truncated negbin with log link): Estimate Std. Error z value Pr(>|z|) (Intercept) 1.197699 0.058973 20.309 < 2e-16 *** hospital 0.211898 0.021396 9.904 < 2e-16 *** healthpoor 0.315958 0.048056 6.575 4.87e-11 *** healthexcellent -0.331861 0.066093 -5.021 5.14e-07 *** chronic 0.126421 0.012452 10.152 < 2e-16 *** gendermale -0.068317 0.032416 -2.108 0.0351 * school 0.020693 0.004535 4.563 5.04e-06 *** insuranceyes 0.100172 0.042619 2.350 0.0188 * Log(theta) 0.333255 0.042754 7.795 6.46e-15 *** Zero hurdle model coefficients (binomial with logit link): Estimate Std. Error z value Pr(>|z|) (Intercept) 0.043147 0.139852 0.309 0.757688 hospital 0.312449 0.091437 3.417 0.000633 *** healthpoor -0.008716 0.161024 -0.054 0.956833 healthexcellent -0.289570 0.142682 -2.029 0.042409 * chronic 0.535213 0.045378 11.794 < 2e-16 *** gendermale -0.415658 0.087608 -4.745 2.09e-06 *** school 0.058541 0.011989 4.883 1.05e-06 *** insuranceyes 0.747120 0.100880 7.406 1.30e-13 *** ---  • Visits range from 0-89. Despite mod.hurdle.nb$model, does that look like a glm binomial family regression? – Richard Careaga Nov 7 '19 at 5:41
• my question is about plain interpretation of effects. The model is just a minimal example on playdata – Peter Nov 7 '19 at 6:56