[R-sig-ME] mixed effects model proportion data that are not 0 and 1's

[M West]

Hello,

I am trying to decide the best approach for analyzing a short time series.

The goal is to see if there is a significant relationship between the
percentage change in females (# females/total population during epidemic -
# females/total population pre-epidemic) and disease prevalence (continuous
variable: percentage infected).

Samples are across 15 sites and 5 months. So a very short time series.

Here's the model and weights that I've used thus far.
v3 <- varComb(varIdent(form =~ 1 | Month) , varExp(form =~
Proportion_infected))
mod <- lme(Change_in_proportion_females ~ Proportion_infected + Month,
random = ~ 1 |Site/Month, weights = v3)

The main problems are:
1) If I plot the residuals vs. the fitted values, there is a strong
relationship demonstrating that the variance increase with the mean. How do
I account for this in a mixed effects model? I've tried the weights option
(with a couple of variations), however, I receive an error message:
"iteration limit reached without convergence"

2) I also have a question about the way that R treats proportion data that
are not 0 and 1's when using glm (or glmer) with the binomial distribution.
Crawley, for example, suggests that you create a y variable where you
account for the total number of observations (e.g., y <- cbind(total
females, (total population - total females)) and then run a glm (or in may
case, a generalized linear mixed model) using the binomial distribution.

But what is actually going on under the hood here? Is R running some sort
of proportion test?  All the examples that I have found for proportion data
or non-normal residuals suggest using a logistic regression approach with
the binomial distribution. Is this also the best option for proportion data
that are not 0 and 1's (i.e., my data on the percentage change would not
match the typical logistic regression plot)?

Many thanks in advance.
M.

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