[R] Calculation of slope for Poisson regression

[borealis_north]

Hello,

I am analyzing time-series data for multiple songbird species in northern
Canada where data were collected at 3 point count stations within a stand
(~150 stations) visited twice a year and with multiple observers. I am using
a linear mixed effects model (lme4) that includes year as a fixed effect and
observer, station nested within stand (to account for spatial
auto-correlation) and visit as random variables:

lme3<-lmer(Abundance ~ Year + (1|Site/Station)+ (1|Observer)+ (1|Visit),
data=AMRE, family = poisson(link=log))

To test the model, I simulated a data set (Poisson distribution) with a 50%
decline over 50 years (with a mean abundance at year 1 of 10 individuals of
species X).

The parameter estimates for the intercept and year are:

                Estimate Std. Error t value
(Intercept)  2.33181    0.03654   63.82
Yr             -0.17089    0.01685  -10.14

Since the data are log transformed during the analysis (link=log), I have to
apply an anti-log to the parameter estimates to get the 'true' value (i.e.,
exp(2.33181) = 10.29656 for the estimate of abundance and exp(-0.17089)=
0.8429143, so 1-0.8429143= 0.1570587, for the slope from the year 1 to year
2). Assuming that the method of back-transformation is correct, how do I
calculate the slope for the subsequent time steps (e.g., year 2 to year 3)
and for the overall trend (year 1 to year 5) using the parameter estimate
seeing as the slope should be ~ -1.25.

Your help is appreciated!

Kevin Kardynal, MSc
Environment Canada

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