I am estimating the effect of future expectations of profits on hospital admissions and days of hospital stays. The situation is as follows: Hospitals are paid a fixed tariff for the first x number of days of hospital stay, at x+1 days the tariff increases considerably. I am testing whether the relative increase in tariffs (or the ratio of tariff_1 and tariff_2) affects the decision whether to admit the patient today and how long the patient will be kept in the hospital.
My dataset includes number of hospital stays, tariff1 and tariff2 along with a complete set of individual health characteristics.
Due to the large number of "zero" hospital days, I would like to run a hurdle model with negative binomial distribution.
Here is a play example:
days <- c(rep(0, 30) , sample(0:100, 70, replace=TRUE)) tariff1 <- sample(1000:2000, 100, replace=TRUE) tariff2 <- sample(2000:4000, 100, replace=TRUE) dta <- data.frame(days=days, tariff1=tariff1, tariff2=tariff2) dta$rate <- (dta$tariff2 - dta$tariff1)/dta$tariff1 library(pscl) model <- hurdle(days ~ tariff1 + rate , data = dta, dist = "negbin") summary(model)
After this I would like to estimate what this distribution would look like if tariff1=tariff2.
# Prediction: new <-dta new$rate <- 0 pred_old <- predict(model,data=dta, type = "response") pred_new <- predict(model,data=new, type = "response") pred <-cbind(pred_old, pred_new) # the two predictions are equal
My questions are as follows:
- I was told that this kind of adjustment is incorrect. I would like to understand why this is.
- What would be a correct way to evaluate a situation of tariff1=tariff2?
- If correct, then why am I getting the same predictions for both?