Hello,
I am fitting a Poisson mixed effects model. I have the number of eggs
(Eggs) laid by a quail and looking at the effect of dosage of a chemical
(Dose) in the study. I have counts of eggs laid by week of the study,
so I am including the week number (Week) as a random effect. I'm using
the lme4 package.
I have,
> mod1 <- lmer(Eggs~Dose + (1|Week),family=poisson)
> summary(mod1)
Generalized linear mixed model fit using PQL
Formula: Eggs ~ Dose + (1 | Week)
Family: poisson(log link)
AIC BIC logLik deviance
112.2 117.8 -53.11 106.2
Random effects:
Groups Name Variance Std.Dev.
Week (Intercept) 0.011693 0.10813
number of obs: 48, groups: Week, 12
Estimated scale (compare to 1) 1.339789
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.699e+00 3.656e-02 128.53 <2e-16 ***
Dose -4.768e-04 4.177e-05 -11.41 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
Dose -0.324
My problem is that I need to find the lower limit on the dose that
causes a 10% effect. I can get the dose that causes a 10% effect, but
getting the lower-limit is not straightforward. Thus, I have
reparameterized the model in terms of this dosage and want to re-fit.
The reparameterized model is:
Log(E(Eggs)) = A - (B/A*0.1)*Dose
where E(Eggs) is the expected value from the Poisson distribution, A is
the intercept and B is the dose causing a 10% reduction. Is it possible
to directly fit A and B in this case within lmer (and other R models)?
I don't see how to code this? Can someone point me to documentation that
shows how to do this?
Thanks.
Rick
