# [R] Estimate of intercept in loglinear model

Mark Difford mark_difford at yahoo.co.uk
Mon Nov 7 20:04:02 CET 2011

On Nov 07, 2011 at 7:59pm Colin Aitken wrote:

> How does R estimate the intercept term \alpha in a loglinear
> model with Poisson model and log link for a contingency table of counts?

Colin,

If you fitted this using a GLM then the default in R is to use so-called
treatment contrasts (i.e. Dunnett contrasts). See ?contr.treatment. Take the
first example on the ?glm help page

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())
anova(glm.D93)
summary(glm.D93)

< snip >
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  3.045e+00  1.709e-01  17.815   <2e-16 ***
outcome2    -4.543e-01  2.022e-01  -2.247   0.0246 *
outcome3    -2.930e-01  1.927e-01  -1.520   0.1285
treatment2   1.338e-15  2.000e-01   0.000   1.0000
treatment3   1.421e-15  2.000e-01   0.000   1.0000
< snip >

> levels(outcome)
 "1" "2" "3"
> levels(treatment)
 "1" "2" "3"

So here the intercept represents the estimated counts at the first level of
"outcome" (i.e. outcome = 1) and the first level of "treatment" (i.e.
treatment = 1).

> predict(glm.D93, newdata=data.frame(outcome="1", treatment="1"))
1
3.044522

Regards, Mark.

-----
Mark Difford (Ph.D.)
Research Associate
Botany Department
Nelson Mandela Metropolitan University
Port Elizabeth, South Africa
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