# [R] Form of the equation produced by a GLM with Poisson family and log link function

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat Jan 27 08:28:05 CET 2007

```Have you looked at the references on ?glm ?  They will all explain this to
you (the first and last are simpler than the other two).

The short answer is that predictions from the linear part of your model
are for the natural log of the mean response.  That is the default option
for predict() on a glm fit, but there is also predict(fit,
type="response") which predicts mean response.  The Poisson family is an
assumption you have supplied about how the response counts vary about the
mean, that they are Poisson and independent with a mwan predicted by the
model (for the 'true' coefficients).

These are statistical (and not 'math') issues.

On Fri, 26 Jan 2007, Marianne Gilbert wrote:

> Hi everyone,
>
> My background is not math and I am trying to figure out exactly what
> equation to use to map a response variable in GIS based on the
> coefficients obtained from the GLM and the values of the independent
> variables in each grid cell of my study area. Most specifically, I want
> to know how to incorporate the Poisson family and log link function in
> the equation. I would really appreciate if someone could help me with
> this or direct me towards literature that would help me do this.
>
> Here are the coefficients from my model:
>
> Call:  glm(formula = count ~ slope + sst + chl + dist + ice, family = poisson,      data = dfo2003cc)
>
> Coefficients:
> (Intercept)        slope          sst          chl         dist          ice
> -6.884e-01   -6.740e-01    5.644e-01   -2.694e+00   -7.278e-05    1.044e-01
> Degrees of Freedom: 412 Total (i.e. Null);  407 Residual
> Null Deviance:      544.7
> Residual Deviance: 413.2        AIC: 512.2
>
>
>
> Marianne Gilbert, M.Sc., R.P.Bio.
> Environmental Scientist - Marine Biology
> Jacques Whitford
> 4370 Dominion St., 5th Floor
> Burnaby, B.C.
> Tel. (604) 436-3014, ext. 253
> Fax. (604) 436-3752
>
> *****************************************************
>
> This e-mail message, including attachments, is confidential ...{{dropped}}
>
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> and provide commented, minimal, self-contained, reproducible code.
>

--
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

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