# Prediction interval for generalized linear model

1. Jul 19, 2013

### Rizer

I am currently working on a prediction problem using generalized linear model, My goal is to get the prediction distribution of the response variable.

I read a thread (https://stat.ethz.ch/pipermail/r-help/2003-May/033165.html) saying the prediction uncertainty of a generalized linear model can be obtained by simulation, but I couldn't find any description of the procedure. Can anyone please help me on this?

2. Jul 19, 2013

### chiro

Hey Rizer.

What is your GLM model specifically? What distributions and link functions are you using?

3. Jul 19, 2013

### Rizer

Hi Chiro

My current model uses Gamma distribution and a reciprocal link function. I think the same simulation procedure can be applied to any distribution-link function pairs? Or are there standard analytical forms for the commonly used pairs? Thanks

4. Jul 19, 2013

### chiro

Are you trying to estimate a set of parameters from your data or are you just trying to run a simulation of specific distributions (and possibly their parameters) to get some parameters (like mean, variance, etc)?

5. Jul 20, 2013

### Rizer

I am trying to estimate the response variables from the newly observed predictors. I have built the GLM using R and Matlab, but I have no idea how to get the prediction interval/distribution for the response variable.

6. Jul 20, 2013

### chiro

In a GLM you estimate specific parameters: in particular, you measure the mean that is involved in the link function and you also estimate co-efficients that correspond to predictors in the linear model.

There is some theory that is used that allows one to obtain the estimate of the mean and the co-efficients using matrix algebra and iterative techniques and if you are needing to implement custom code yourself, you might want to look at either a book on GLM's or perhaps the R code that implements these techniques.

If you are estimating the response through a GLM, then you would have already decided some constraints for the response variable (in terms of its distribution and link function).