# Re: [R] testing coeficients of glm

From: peter salzman <peter.salzmanuser_at_gmail.com>
Date: Thu, 24 Jan 2008 14:51:17 -0500

thank you,
peter

On 1/24/08, Prof Brian Ripley <ripley_at_stats.ox.ac.uk> wrote:
>
> On Thu, 24 Jan 2008, peter salzman wrote:
>
> > Dear list,
> >
> > i'm trying to test if a linear combination of coefficients of glm is
> equal
> > to 0. For example :
> > class 'cl' has 3 levels (1,2,3) and 'y' is a response variable. We want
> to

> > test H0: mu1 + mu2 - mu3 =0 where mu1,mu2, and mu3 are the means for
> each
> > level.
> >
> > for me, the question is how to get the covariance matrix of the
> estimated
> > parameters from glm. but perhaps there is a direct solution in one of
> the
> > packages.
>
> See ?vcov .
>
> BTW, help.search("covariance matrix") finds it.
>
> >
> > i know how to solve this particular problem (i wrote it below) but i'm
> > curious about the covariance matrix of coefficient as it seems to be
> > important.
> >
> > the R code example :
> > ###
> > nObs <- 10
> > cl <- as.factor( sample(c(1,2,3),nObs,replace=TRUE) )
> > y <- rnorm(nObs)
> >
> > model <- glm(y ~ cl)
> > b <- model\$coefficients
> > H <- c(1,1,-1) # we want to test H0: Hb = 0
> >
> > ### the following code will NOT run unless we can compute covModelCoeffs
> >
> > #the mean of Hb is
> > mu = H %*% model\$coefficients
> > #the variance is HB is
> > var = H %*% covModelCoeffs %*% t(H)
> >
> > p.val <- 2 * pnorm( -abs(mu), mean=0, sd=sqrt(var),lower.tail = TRUE)
> >
> >
> > how do i get the covariance matrix of the estimated parameters ?
> >
> > thanks,
> > peter
> >
> > P.S. the simple solution for this particular problem:
> >
> > ## get the mean for each level
> > muV <- by(y,cl,mean)
> > ## get the variance for each level
> > varV <- by(y,cl,var)
> >
> > ## the mean of Hb is
> > muHb <- H %*% muV
> > ## because of independence, the variance of Hb is
> > varHb <- sum(varV)
> >
> > ## the probability of error, so-called p-value:
> > p.val <- 2 * pnorm( -abs(muHb), mean=0, sd=sqrt(varHb),lower.tail =
> TRUE)
> >
> > thanks again,
> > peter
> >
> >
> >
>
> --
> Brian D. Ripley, ripley_at_stats.ox.ac.uk
> Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
> University of Oxford, Tel: +44 1865 272861 (self)
> 1 South Parks Road, +44 1865 272866 (PA)
> Oxford OX1 3TG, UK Fax: +44 1865 272595
>

```--
Peter Salzman, PhD
Department of Biostatistics and Computational Biology
University of Rochester

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