I have made an analysis to test whether the weight of a mice population has changed between two periods. Data have been collected in the period 1978-81 and 2005-07. Many mice were captured through the whole set of years (all months) in the first period and a much smaller number was captured in the second period. The unbalanced data are due to a different capture effort in the field and to a strong reduction of mice population size.
Weight may vary according to: (i) sex, (ii) age class, (iii) month of capture, (iv) total body length, and (iv) type of capture (e.g. individuals captured by live- and death-traps, both used, may tend to provide data on individuals of different average conditions or age). Moreover, a random deviation in weight may be result of environmental stochasticity with some years "better" and other "worse". For this reason, to test whether weight has changed BETWEEN the two periods I have chosen to use a GLMM for each sex by including all the predictors I mentioned before (using notation of package lme4 in R):
weight ~ age + month + TBL + TypeCap + year + (1|yearF) where all the predictors are categorical except TBL (total body length, continuous variable) and year (integer variable, i.e. 1978,1979,1980,1981,2005,2006,2007 - yearF is categorical). I have checked my model visually as usually and looked also for influential point (individuals or years). The model seems really OK, it converges well, it has good fit to data, and does not seem overfitted.
I find a strong and significant decrease over time (year effect highly significant). According to the first and last year (1978 and 2007) point estimates and net of the above mentioned controlling variables, it would correspond to a decrease of about 30% (similar for both females and males).
So, what is my question about? I feel fine with this approach and the interpretation I am doing of the results but, until now, reviewers (this forms part of a scientific manuscript) do not seem to agree. There have been already three reviewers who claim against using the GLMM because there are not data in the middle and suggest some type of ANOVA test. I do not agree and would like to convince them that there is nothing wrong in using a GLMM to test whether there has been a change between the beginning and final of period study even if we do not have data in the middle. What actually matters is that we cannot say nothing about what happens in the middle (and in fact we do not) but we can do it about the change in weight between 1978 and 2007. We never talk about any linear trend or anything similar. By using the GLMM we can control for several potential confounding variables (e.g age, month, capture type, etc.) and also for random effect as that of year. However, I don't see an immediate way of doing that by using some kind of t-test.
I would appreciate any thought, commentary or suggestion (even some reference I could cite) on this.