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combining varIdent variance function with mixed effects model
2 messages · Belinda Burns, Ben Bolker
3 days later
Belinda Burns <10517197 at ...> writes:
Dear all, I hope this is the correct place for my question, if not, my apologies! I am analysing several behaviour variables obtained by observing captive gibbons. The raw values are in the form proportion of ten minutes spent doing the behaviour, and most of the behaviours are zero-inflated and negatively skewed. At the moment I am interested in modelling the proportion of time that adult gibbons spend grooming their mates, such that the models take the form: Grooms_mate~Age+Species*Sex+Family_composition+Repro_phase*Sex where species is a factor with 3 levels, family composition is a binary variable (they either have offspring or not) and repro_phase is the reproductive phase of the female (4 levels).
Ideally I should be including individual and group as random effects (individuals are nested within groups) and so I would like to use a mixed model approach; however, diagnostic plots of residuals vs fitted values show heteroscedasticity (increasing spread with increasing fitted values) and plots of residuals vs predictors suggests that one species is less variable than the other two and gibbons with offspring are more variable than those without. The inclusion of a species*family_composition weighted variance function (using the weights= varIdent(form~1|Species*Family_composition) in a gls model) seems to improve the homogeneity of the residuals...
I therefore have two questions (among a million others!): Can I include the two random effects in gls, or, vice versa, a varIdent structure in lmer? (the only contact I know doing mixed modelling in R uses lmer with MCMC estimation of p-values and so I am most comfortable using that to include the random effects) How do I write individual and group in as random effects considering individual is nested in group?
lmer does not handle "R-side" effects (heteroscedasticity/varStruct/etc.) at present. You should be able to use random=~1|group/individual in lme to account for individuals nested in groups. However, heteroscedasticity is also a common feature of lognormal data: could you get away with some transformation of the form log(small_number+proportion) (realizing that picking small_number is a bit of a can of worms)? Or plogis(small_number+proportion)? (Should be roughly equivalent if the proportions are typically small.) Ben Bolker