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GLMs - definition

D

DanielZ

Member
In page 2 of chapter 16, GLMs are defined as "a flexible generalisation of ordinary least squares regression. The GLM generalises linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value."

Can anyone please explain the part I have highlighted in bold? Be gentle!

Dan
 
DanielZ said:
In page 2 of chapter 16, GLMs are defined as "a flexible generalisation of ordinary least squares regression. The GLM generalises linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value."

Can anyone please explain the part I have highlighted in bold? Be gentle!

Dan
Click to expand...

I think the flexibility refers to the ability of GLMS to allow the variance to depend on the value you are trying to predict rather than the more restrictive assumption that the variance is independent of predicted value.

If you are modelling claims severity for example, you would naturally want your model to allow for the fact the the variablity of claim amounts is greater for larger claims than for smaller ones.

It's been a while since I did ST8 so I could be wrong but that's my understanding.
 
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