I used a Monte-Carlo approach to estimate the prediction interval for a new observation from a GLM using a Negative Binomial distribution. I used this method for linear models and got reliable estimations of the prediction interval but I am not enough confident with statistics to know if this method could also be applied for non-Gaussian distributions. Could you please tell me if it makes sens to use it or not?
- compute the se of the expected value with a Wald approach (on the link).
- to use this se to randomly simple 1000 values from a Gaussian distribution with the expected value as $\mu$ and se as $\sigma$.
- for each random value, to randomly sample 1000 values from a negative binomial distribution with the exponential of the random value as mu.
- The prediction interval was computed as the 2.5 & 97.5 quantile of the 1e6 random values obtained for a given expected value.
Does this methodology makes sense?