Hello,
I am having trouble fitting a distribution to my mixed model for meadow
vole catch per unit effort (CPUE) data. I have tried several families and
cannot find one that does not violate both the homogeneity and normality
assumptions. NOTE: The data set is zero-inflated (no captures).
Here is my study design:

I am trying to determine if the CPUE of meadow voles differ among lines
(line = near,mid, or far) at increasing distances from a linear feature
(type = road, trail or powerline corridor) in two different habitat types
(habitat=forest or barren).
Response variable: catch per unit effort (non-integer values)
Fixed explanatory variables: line (3 categories), habitat (2 categories),
type (3 categories)
Random explanatory variable: site (8 categories), cycle (2 categories)
The random variable site is for the 8 different sites I sampled in (4
barren and 4 forest) and the cycle is there because I visited each site
twice.
Here is an excerpt of my data set:
   CE2  catch effort site line   cycle habitat      type
0.000000     0   57.5    A near  first   forest     trail
3.278689     2   61.0    A   mid   first   forest     trail
0.000000     0   60.5    A   far   first   forest     trail
0.000000     0   66.5    G near  first   barren       road
0.000000     0   74.5    G   mid   first   barren       road
0.000000     0   74.0    G   far   first   barren       road
1.449275     1   69.0    E near second  barren powerline
0.000000     0   73.0    E   mid second  barren powerline
0.000000     0   71.5    E   far second  barren powerline


I tried the lme4 package using the following syntax:

Model1<-lmer(CPUE~line+habitat+type+(1|site)+(1|cycle))

However, analysis of the residuals and fitted values showed extreme
violation of the homogeneity assumption and mild violation of the normality
assumption.

I then tried using a poisson error structure using catch (the actual number
of animals) as the response and incorporated effort as an offset. Effort as
an offset is commonly used for analysis of CPUE data.

Model2<-
glmer(catch~line+habitat+type+(1|site)+(1|cycle)+offset(effort),family=poisson)

This turned out to be a worse fit than the previous.

I tried transforming the data using a popular CPUE transformation
ln(CPUE+1) and once again did not get a good fit using lmer.

Next, since the data set is zero-inflated, I tried the tweedie distribution
in package CPLM.

Model3<-cpglmm(CE2~line+habitat+type+(1|site)+(1|cycle))

Once again, this did not fit the data very well.

Does anyone have any suggestions on how I can analyze zero-inflated CPUE
data? I have been trying to figure out how to do a Monte Carlo permutation
test for a mixed model but I am having trouble figuring out the syntax. Any
help would be greatly appreciated.

Thank you,

Karla

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