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Can anyone please explain the identity link and log link in Poisson regression with simple example? For example, I have run a script using the mtcars data set in R. 

head(mtcars) 
glm(mpg~disp+hp+wt, data=mtcars, family=poisson(link="‌​identity"))

mpg, disp, and wt are variables in the data set. I got the results: 

(Intercept)= 35.205669
Coefficient of disp=-0.004313
Coefficient of hp=-0.028214
Coefficient of wt=-3.102409

How do I interpret these coefficients? How does the model look like mathematically? What does link="identity" mean in the model?

gung - Reinstate Monica
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Bilal Para
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    Can you clarify what you mean by "explain"? As it stands your question is rather vague. What is it you need to know? – Glen_b Feb 26 '16 at 07:10
  • In Poisson regression i have heard , some times we employ log link and some times identity link. In addition if we build new model how manually we can use it in R. For example, If we have build Poisson distribution, i i want manually use it as regression model in R for any count variable. how to do that?.I mean if there is no specific package build for Poisson, can we manually write a script to run Poisson regression..Thanks in Advance – Bilal Para Feb 26 '16 at 15:56
  • you fit Poisson regression models using `glm` in R. e.g. if you had data in a data frame `mydat`, then `glm(y~x1+x2,data=mydat,family=poisson(link="identity"))` would fit a Poisson regression with identity link. See `?glm` and `?family`. Questions purely about how to do something in R code (rather than the corresponding statistical aspects) are usually [off topic](http://stats.stackexchange.com/help/on-topic) here. Can you rephrase your question in a way that makes it both about statistics and so that it's clear what you seek? – Glen_b Feb 27 '16 at 01:06
  • For example i have run a script for mtcars data set in R. as head(mtcars) glm(mtcars$mpg~mtcars$disp+mtcars$hp+mtcars$wt,data=mtcars,family=poisson(link="identity")). mpg,disp,wt are variables in data set mtcars. I got the result (Intercept)= 35.205669 ,Coefficient of disp=-0.004313, Coeff of hp=-0.028214, Coeff of wt=-3.102409 . How to interpret these coefficients? how the model look like? what does link="identity" mean in the model?...Thanks in advance – Bilal Para Feb 27 '16 at 06:29
  • Thanks Bilal -- Please edit that clarification into your question – Glen_b Feb 27 '16 at 12:50
  • Thanks Glen for attention ...For example i have run a script for mtcars data set in R. as head(mtcars) glm(mpg~disp+hp+wt,data=mtcars,family=poisson(link="‌​identity")). mpg,disp,wt are variables in data set mtcars. I got the result (Intercept)= 35.205669 ,Coefficient of disp=-0.004313, Coeff of hp=-0.028214, Coeff of wt=-3.102409 . How to interpret these coefficients? how the model look like mathematically? what does link="identity" mean in the model?...Thanks in advance. – Bilal Para Feb 28 '16 at 15:24
  • Please *edit your question*. Don't reply to me in comments, fix the original question.-- by clicking "edit" If you only clarify in comments your question won't re-open – Glen_b Feb 28 '16 at 22:50
  • These course notes on generalized linear models by German Rodriguez are very good, & there are some example R scripts: http://data.princeton.edu/wws509. See also [Interpreting coefficients for Poisson regression](http://stats.stackexchange.com/q/24821/17230), & [OLS vs. Poisson GLM with identity link](http://stats.stackexchange.com/q/167588/17230). – Scortchi - Reinstate Monica Feb 29 '16 at 16:08

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