Prediction interval for generalized linear model

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Discussion Overview

The discussion revolves around obtaining the prediction distribution of the response variable in a generalized linear model (GLM). Participants explore methods for estimating prediction intervals and the associated uncertainties, focusing on simulation techniques and the specifics of model parameters.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks assistance with the simulation procedure for obtaining prediction uncertainty in a GLM.
  • Another participant inquires about the specific GLM model being used, including the distributions and link functions involved.
  • A participant mentions using a Gamma distribution with a reciprocal link function and questions whether the simulation procedure is applicable to other distribution-link function pairs.
  • There is a discussion about whether the goal is to estimate parameters from data or to simulate specific distributions to derive parameters like mean and variance.
  • A participant clarifies that estimating the response variable involves measuring the mean related to the link function and estimating coefficients for predictors, suggesting the use of matrix algebra and iterative techniques.
  • Another participant notes the importance of having already decided on constraints for the response variable in terms of its distribution and link function.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the simulation procedures and the specifics of GLM modeling, with no consensus reached on the best approach or methodology.

Contextual Notes

Participants express uncertainty about the standard analytical forms for various distribution-link function pairs and the specific procedures for obtaining prediction intervals.

Rizer
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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?
 
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Hey Rizer.

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

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