Mixed-effects Generalised Linear Model (GLMM) to detect significant differences in bird observation data I am trying to analyse a set of bird count data associated with an environmental impact assessment I am running, but require experts to get this right. I am unsure how to formulate the model and complete the test, and determine a statistical difference where one is present. Thus my questions are:
1) How should the model be formulated in R, specifically which factors should be assigned as random factors; and
2) How can the test for significant differences between treatments be accomplished?
The data can be described thus:


*

*Observations are counts of birds made by surveyors in the field. An observation can be a single bird, or a flock of 2 or more birds. Data are heavily overdispersed and a negative binomial model seems to fit the data best when comparing AICs (better than the alternative, a quasi-poisson model).

*There are three fixed factors: Location (observations were made at two sites, "south" and "north"), Month (birds at each location were counted once a month over 6 months) and Tide (at each site and each month, separate counts were made at low and high tide).

*Counts were made over a 10 minute survey period (often used in the literature), repeated 6 times to sample the population at each site and tide in each month; counting therefore lasted a total of one hour. Thus it seems right to consider the bird counts from each 10 minute sample as the random factor.


Data can be found here:
http://www.zen134994.zen.co.uk/glmm_bird_data.xlsx
The R code I have been using for my analysis is below:
birdglmm <- glmer.nb(bird_count ~ month + site + tide + (1|sample_no), data = glmm_bird_data)
birdglmmoutput <- summary(birdglmm)
birdglmmanova <- anova(birdglmm)
birdglmmdrop1 <- drop1(birdglmm, test = "Chi")
summary(birdglmm)
anova(birdglmm)
drop1(birdglmm, test = "Chi") 

 A: After consulting a few statisticians whom colleagues directed me to, clearly my question is flawed, and is trying to (wrongly) coerce a classical frequentist approach to statistics with one based on information theory.
The model will determine which factors are most important in describing the data, this being done by the use of comparing AICs. Significance testing in the Fisherian-Neymann/Pearson sense is not a part of the workflow, although such tests could be employed post-hoc to answer specific questions.
In this case, I reformulated the analysis to generate successively more complex models and compared AICs, for example:
bird_glmm_site <- glm.nb(bird_count ~ site, data = glmm_bird_data)
bird_glmm_month <- glm.nb(bird_count ~ month, data = glmm_bird_data)
bird_glmm_tide <- glm.nb(bird_count ~ tide, data = glmm_bird_data)
bird_glmm_sitexmonth <- glm.nb(bird_count ~ site + month, data = glmm_bird_data)
bird_glmm_sitextide <- glm.nb(bird_count ~ site + tide, data = glmm_bird_data)
bird_glmm_monthxtide <- glm.nb(bird_count ~ month + tide, data = glmm_bird_data)

Etc, incorporating more combinations of factors. The lowest AIC was for the bird_count ~ site model (909), with other models showing AICs of 924 and above. P values for factors other than site were non-significant, showing they were not significantly different from zero.
Thus I conclude that there is a relationship between bird counts and study site (one supporting higher numbers of birds than another), but no evidence for a relationship between bird counts and month or tide.
