What is the proper interpretation of the coefficients for the positive count part of a hurdle model (truncated Poisson or Negative Binomial)? I have read that the interpretation of the coefficients for a nontruncated Poisson (one unit increase in x results in an e^β factor increase in the expected count of y, controlling for other predictors) is not appropriate since the expected value is not equal to lambda in the truncated Poisson distribution:
This is supported by information on the glmmAdaptive package in R:
"...it has been noted that the fixed-effects coefficients for the positive counts part relate to the mean μ of Poisson distribution that includes the zeros, not the mean for those who experience the event. The mean for those who experience more than one events is μ/(1−e^−μ). Hence, a β=0.1 cannot be interpreted as reflecting a e^β= 10% increase in the mean of the subjects who experience the events."
However, these sources appear to be contradicted by an article on RPubs related to the pscl package:
"(Positive count model) Given the response is positive (among those who have positive counts), the average count is 3.3. This is increased by a unit increase in hospital stay by 1.24 among those who have positive counts. Poor health increases it by 1.37 times, whereas excellent health decreases it by 0.72, both among those who have positive counts."
What is the appropriate interpretation? Or does it depend on the package used (e.g., glmmAdaptive, pscl, or glmmTMB)?