# Comparing linear mixed effects models using ANOVA - underlying assumptions

I am trying to analyze some CPUE (Catch Per Unit Effort) data for a fisheries related analysis with lme models in R. So I have total of six models that are tested in groups of two to determine the effects of both fixed variables and their interaction separately. The models are:

M1 : CPUE = area + year + area*year + (1|location)

M2 : CPUE = area + year + (1|location)

M3 : CPUE = area + (1|location)

M4 : CPUE = ~1 +(1|location)

M5 : CPUE = year + (1|location)

M6 : CPUE = ~1 +(1|location)

The testing is done so that model 1 is tested against model 2 to test for interaction between the fixed variables, and models 3 vs 4 and models 5 vs 6 against each other for the effect of both fixed variables year and area.

The models are fitted with lme (from nlme -package) using 'ML' as method and the testing is done with anova.

So my questions are:

1) The CPUE data is not normally distributed. As I fit the models I see that the residuals also deviate from normal distribution, as do the plotted random effects. Do I need to transform my data to produce models with normally distributed residuals and random effects to use ANOVA for model comparison?

2) If I should transform my data can I be done simply by using for example log or sqrt if this seems to produce models with residuals and random effects that are approximately normally distributed? Does using a boxcox transformation fitted on a linear model without random effects produce erroneous results if used for lme models in this context? What I mean is using the estimate for lambda with the maximum log-likelihood obtained from the models without random effects to transform the data.

I am not the person who designed this analysis and have no resources or competence to change it. Therefore I am only interested in producing the results without making errors. Any help is appreciated!

• Look into the literature. A quick look shows that GLMs with log-link and normal distribution have been used to model CPUE but I'm not sure if that is the best distribution since CPUE is an abundance measure, i.e., something similar to a count variable. – Roland Dec 6 '18 at 14:11
• Thanks for the input. You have some literature recommendations on GLM for an ecologist with very basic understanding in statistics? – mihy Dec 6 '18 at 15:06