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I have fit a two-part model, where the first part is using a logistic regression to model the probability of seeing Y, and the second part is using a Gamma GLM regression with a log link to model the value of Y, conditional on it being positive.

I have then calculated predictions of Y for new values of X by multiplying the probability predicted from the logistic regression, by the value of Y predicted from the Gamma GLM regression for each value of X. How can I go about computing the prediction interval for specific values of X?

I was thinking of using bootstrapping, using the method suggested at the following link. However, I am not sure how I would bake in residual uncertainty over two models. https://stats.stackexchange.com/a/501275/360160

user16993967
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  • So if you have from logistic regression the probability of "seeing Y" being 0.1 and from glm regression a y-value of e.g. 100, then you would predict y to be 10? – frank Jul 14 '22 at 12:37
  • @frank That is the logic, I am using - yes – user16993967 Jul 14 '22 at 12:38

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