This may seem obvious to statisticians, but I could not find any documentation.
I ran a negative binomial model in R. My data for the response variable (PINDX) ranges from 0 to 15. PINDX was the count of the presence of a species in a survey with 15 segments, so technically, I could not have data >15.
Here is my model:
YBWS.fig <- glm.nb(PINDX ~ SF1 + SF9 + SF15 + SF17 + SF18 + RegArea + LndWinTemp + LndPercDev + RegPercDev + LndPercMix + LndMaxTemp*PercColleg, data = YB.fig)
Model R-square was 0.56. I looked at the predicted values from the model and found some of the predictions are >15 (my highest count value).
1 2 3 4 5 6 11.788032 10.041059 9.987404 11.131004 15.367862 9.499261
I also tried to predict for another dataset (contains the highest value of one interacting variable (LndMaxTemp), unique values (observed within the range of LndMaxTemp to avoid extrapolation) of the other interacting variable (PercColleg), and mean values of all other variables in the model). Here too, some of the predictions were >15.
tail(predict(YBWS.fig, type= "response", newdata=newY1))
135 136 137 138 139 140 13.95447 15.02475 13.87214 13.87373 14.55737 15.35829
The answer may be obvious to you, but is there a problem if my predictions are higher than my highest count value?
My understanding is that the predictions are being made for a specific combination (a set of numbers provided) of data which did not exist in my original dataset. I was also selecting the extreme value of one interacting variable (LndMaxTemp) for prediction. (For other values of LndMaxTemp all predictions were <15). The line of best fit may represent data values slightly above or below it, and the model error is reflected in the prediction. Also in count models, unlike in logistic models, there is no upper limit defined. Therefore, it makes sense that predictions vary and some are greater than my highest count in the dataset on which the model was based.
I want to be sure that I have not made any error before I start working on a manuscript. I may sleep better if I can get a logical explanation of why my predictions are higher than my largest count, or if someone can share a link to literature that is easy for a non-statistician to understand. Thank you.