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

[M West]

Thanks all for these great answers - I really appreciate it!

M

On Mon, Oct 12, 2015 at 2:16 PM, Ben Bolker <bbolker at gmail.com> wrote:

> On 15-10-12 01:42 PM, M West wrote:
> > 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"
>
>   weights= is the right way to go about it; we'd have to see more
> details to know what the problem is in your particular case.
>
>  Your model looks like it might be overfitted: if you only have one
> observation per Site/Month combination, then the Site-by-Month
> interaction term (Site/Month expands to "Site plus Site-by-Month")
> will be confounded with the residual variance.  I have found in the
> past that lme may allow you to fit the overfitted model without
> complaining; one way of diagnosing this problem is to try intervals() on
> your fitted model (try it without the weights= argument for
> simplicity) and see if you get warnings/errors.
>
> >
> > 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)?
>
>   Binomial and Bernoulli (binary) logistic regression are basically
> equivalent; when you have multiple individuals observed for a particular
> set of predictor variables (e.g. month/site), it's practical
> and computationally efficient to collapse them to a binomial regression.
> Under the hood there is indeed the equivalent of a proportion test --
> not necessarily quite as accurate for small numbers of counts as some
> classical proportion tests, but much more flexible.  In lme4 (the
> successor to nlme, which implements generalized linear MMs that can
> handle a binomial response), the 'weights' argument is simpler/can be
> used to specify the denominator or total number of counts:
>
> library(lme4)
>  mod <- glmer(Change_in_proportion_females ~ Proportion_infected + Month
> + (1 |Site/Month),
> family=binomial, weights = total_counts, data=...)
>
>  (here, including the site-by-month interaction is OK -- it represents
> the possibility of extra-binomial variance (overdispersion).)
>
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