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I am interested in the relationship between body mass and thyroid hormones in male and female birds. I have a sample size of 77 males and 28 females. Of these individual, 6 males and 1 females were measured more than once. Initially I was going to examine the relationship between thyroid hormones and body mass in males and females using separate mixed effect models for each sex with bird ID as a random factor to control for repeated measures, but is it appropriate considering so few individuals have been sampled more than once? Or, is it better to randomly select one measure from the repeated sampling?

  M1<-lmer(log10(Mass)~log10(TT3)+ (1|Band),REML=TRUE, data= THmassM)

It was recommended I look at sexes separately by a reviewer considering my sample size is skewed. Would a more appropriate model include sex as a predictor instead of examining males and females separately?

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  • $\begingroup$ Your sample doesn't have the needed information for estimation of random effects. I would just sample one observation from each of the 7 subjects, using a sampling tactic that mimics how the individual responses were sampled for the other subjects. $\endgroup$ Dec 9, 2021 at 12:40

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The choice of main effect versus stratification should be based on model fit and the research question of interest. Stratifying by sex implies the population variance is different between men and women and, in the case of your model, that the (approximate) percentage change in mean mass for a 1% change in hormone is different between men and women. (If your data follow a log-normal distribution then the coefficient could be interpreted as the change in median mass for a 1% change in hormone.) A similar stratified model is achieved by including an interaction term between sex and hormone and requesting separate variance terms for each sex. I suggest fitting both a main effect model and a stratified (interaction) model and comparing their fit to the data.

It's been a while since I have thought about a log-log model. I'm wondering if using a generalized linear model for the untransformed dependent variable would be better while incorporating a log$_e$ link function. The exponentiated coefficient would then be the percentage change in mean mass for a 1% increase in hormone.

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