# Offset variable seemingly not factored into GEE

#### titopuente

##### New Member
In SPSS I am using a repeated measures, negative binomial generalized estimating equation (GEE) to analyze my study where I counted animals on repeatedly sampled forest transects that sample 2 habitats. The habitats were not evenly sampled (it wasn't possible) so I have an offset variable of area sampled. Area sampled could vary both between transects and between replicates of individual transects when bad weather caused a sample to be truncated, so I created a separate area sampled variable to use as my offset:
GENLIN NumbIndividuals BY Habitat (ORDER=ASCENDING)

/MODEL Habitat INTERCEPT=YES OFFSET=lnAreasampled

/CRITERIA METHOD=FISHER(1) SCALE=1 MAXITERATIONS=100 MAXSTEPHALVING=5 PCONVERGE=1E-006(ABSOLUTE) SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 LIKELIHOOD=FULL
/EMMEANS TABLES=Habitat SCALE=ORIGINAL COMPARE=Habitat CONTRAST=PAIRWISE PADJUST=LSD
/REPEATED SUBJECT=TransectName WITHINSUBJECT=Replicates SORT=YES CORRTYPE=AR(1) ADJUSTCORR=YES COVB=ROBUST MAXITERATIONS=100 PCONVERGE=1e-006(ABSOLUTE) UPDATECORR=1
/MISSING CLASSMISSING=EXCLUDE
/PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.

The parameter Habitat is significant in the model effects and the EMMs output then gives me a significant difference with:
Habitat A: 0.54 (SE 0.071)
Habitat B: 0.16 (SE 0.067)

Means are reported for the response, so this should be the average number of individuals per transect replicate in each habitat. The problem is that A and B were not evenly sampled, so when I divide the average number of individuals per habitat above by the average area sampled per habitat to get individuals/square kilometer I end up with:

Habitat A: 6.30 individuals/km2
Habitat B: 11.01 individuals/km2

In effect the relationship between the variables has been flipped (also, the "# individuals/km2" estimates show the same relationship as the raw data whereas the "# of individuals" estimates are reversed). The direction of the regression coefficients also line up with the relationship between the "number of individuals" and not with the relationship between the "number of individuals/km2" like I think they should.

This makes me think that the EMMs test is not properly accounting for the offset.

Any ideas on how I incorporate area into this model? I was under the impression that using the natural log of an exposure variable in SPSS should allow for analyses that factor in area sampled and provide a density.