Standard errors GLM

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Standard errors GLM

D_Tomas
Dear userRs,

when applied the summary function to a glm fit (e.g Poisson) the parameter table provides the categorical variables assuming that the first level estimate (in alphabetical order) is 0.

What is the standard error for that variable then?

Are the standard errors calculated assuming a normal distribution?

Many thanks,

 
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Re: Standard errors GLM

Joshua Wiley-2
Hi,

See inline.

On Tue, Mar 13, 2012 at 6:38 AM, D_Tomas <[hidden email]> wrote:
> Dear userRs,
>
> when applied the summary function to a glm fit (e.g Poisson) the parameter
> table provides the categorical variables assuming that the first level
> estimate (in alphabetical order) is 0.
>
> What is the standard error for that variable then?

That is not a variable per se.  Say you have a 3 level factor, the
default coding is to create two 1/0 vectors, and the parameter
estimates and standard errors are for those 'dummy' vectors.
Information about the reference group is encoded, there is not an
explicit estimate for it with a standard error (notable exception when
there are no other variables, the intercept is essentially the
reference group, and the other estimates are deviations from that).

>
> Are the standard errors calculated assuming a normal distribution?

I am not completely sure I know what you mean by this.  It is assumed
that the z value (Estimate/Std. Error) is normally distributed, if
that answers your question?

Cheers,

Josh

>
> Many thanks,
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Standard-errors-GLM-tp4469086p4469086.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
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> and provide commented, minimal, self-contained, reproducible code.



--
Joshua Wiley
Ph.D. Student, Health Psychology
Programmer Analyst II, Statistical Consulting Group
University of California, Los Angeles
https://joshuawiley.com/

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Re: Standard errors GLM

David Winsemius
In reply to this post by D_Tomas

On Mar 13, 2012, at 9:38 AM, D_Tomas wrote:

> Dear userRs,
>
> when applied the summary function to a glm fit (e.g Poisson) the  
> parameter
> table provides the categorical variables assuming that the first level
> estimate (in alphabetical order) is 0.

Not really. It returns an estimate for the contrast of two Poisson  
parameters which have support on the real line. This is not really the  
correct list for fixing your misconceptions about GLMs. Your  
misconceptions are more of a conceptual character rather than an R  
coding problem. Maybe you should post follow-ups to:  
stats.stackexchange.com

>
> What is the standard error for that variable then?

It (meaning I assume the coefficient estimate) is not a variable, at  
least not in the sense of being a data element.

>
> Are the standard errors calculated assuming a normal distribution?

The standard errors are simply the square roots of the diagonals of  
the variance-covariance matrix (estimated from the deviations on the  
specified scale of the data from a best fit in a modeling framework).  
The assumption one makes when turning this into a confidence interval  
is that _parameters_ are approximately normally distributed using a  
glm method. You do not necessarily need to accept this method. The  
'confint' function in MASS will return CI's based on the profile  
likelihood.

>
> Many thanks,
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Standard-errors-GLM-tp4469086p4469086.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT

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Re: Standard errors GLM

Rubén Roa
In reply to this post by D_Tomas
You have a conceptual problem, as pointed out by previous helpers.
You don't have a standard error for the first level of your categorical variable because that level's effect is not estimated.
It is being used as a reference level against which the other levels of that categorical variable are being estimated (the default in R).
This is one way by which statisticians include categorical predictors into the regression framework, originally meant for relations between continuous quantitative variables.
You might want to read about regression, factors, and contrasts.
This paper about the issue is available online:
M.J. Davis, 2010. Contrast coding in multiple regression analysis: strengths, weaknesses and utility of popular coding structures. Journal of Data Science 8:61-73.
HTH
Ruben

-----Mensaje original-----
De: [hidden email] [mailto:[hidden email]] En nombre de D_Tomas
Enviado el: martes, 13 de marzo de 2012 14:39
Para: [hidden email]
Asunto: [R] Standard errors GLM

Dear userRs,

when applied the summary function to a glm fit (e.g Poisson) the parameter table provides the categorical variables assuming that the first level estimate (in alphabetical order) is 0.

What is the standard error for that variable then?

Are the standard errors calculated assuming a normal distribution?

Many thanks,

 

--
View this message in context: http://r.789695.n4.nabble.com/Standard-errors-GLM-tp4469086p4469086.html
Sent from the R help mailing list archive at Nabble.com.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.