[R-sig-eco] mixed model on proportion data

[Thierry Onkelinx]

Dear Mariano,

The logit transformation will fail in case the damage is 0% or 100%. The
correct distribution for ratios between 0 and 1 is a beta distribution.
When 0 or 1 is present you'll need a zero and/or one-inflated beta
distribution. This is currently non available in lme4.
It looks like you measure the damage in steps of 5%. So you use the
binomial distribution as a workaround. That is: assume that each leave has
20 'trials' (20 * 5% = 100%), each 5% damage is one successful trial.

glmer(cbind(dam / 5, 20 - dam / 5) ~  treat + day + (1|pair/plant),
data=gaston, family = binomial)

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2017-03-06 21:17 GMT+01:00 Mariano Devoto <mdevoto at agro.uba.ar>:

> Hello again. This is a query which follows up on the very useful answer
> provided by Drew Tyre who suggested creating new variables and adding the
> random term you'll see in the model below.
> Quick reminder: the analysis aims at understanding how the presence of
> "bodyguard" ants regulates leaf damage caused by lepidopteran herbivores on
> a focal plant species.
> For this, I set up fourteen pairs of plants in a nature reserve and then
> assigned each plant in each pair to one of two treatments, either "with
> ants" or "without ants", by applying a physical barrier at the base of the
> plant.
> In the following nine weeks I measured four response variables once a week
> on a subsample of ten randomly chosen leaves of each plant. I thus have
> nine repeated measures on each plant.
>
> >From analyses done over the weekend I know excluding ants from the plants
> (variable "treat" in the dataset) has a positive effect on the number of
> butterfly eggs and larvae found on plants.
> Now I want to know if this results in a reduced damage to the leafs
> (variable "dam" in the data set), which is measured as the percentage of
> the area eaten by herbivores.
>
> My response variables are:
> ants: number of ants (this was measured just to check the physical barrier
> had worked OK)
> eggs: number of butterfly eggs
> larve: number of butterfly larvae
> dam: percent leaf damage (percentage eaten by larvae)
>
> My explanatory variables are:
> treat: treatment (two levels: "con" and "sin" mean with and without ants,
> respectively)
> pair: plant pair
> date
>
> #I provide a workable example below
> require(lme4); require(tidyverse); require(lubridate)
>
> #read data from Google drive
> id <- "0Bzd8I1jr8z_iU0h6R0hxaElseDA" # google file ID
> gaston <- read.table(sprintf("
> https://docs.google.com/uc?id=%s&export=download", id), head=T)
>
> #create variables following suggestion by Drew Tyre
> gaston <- mutate(gaston,
>                  plant = paste0(pair,treat),
>                  date = dmy(date),
>                  day = as.numeric((date - min(date))))
>
> #After a few hours of scavenging through books, articles, blogs and R-lists
> I ended up with the following model which turns the % damage into a
> proportion and then logit transforms it so I can use lmer.
>
> M1 <- lmer(logit(dam/100) ~ treat + day + (1|pair/plant), data=gaston)
> summary(M1)
>
> #Am I headed in the right direction? Any advice would be greatly
> appreciated.
>
> Best,
>
> Mariano
>
> *Dr. Mariano Devoto*
>
> Profesor Adjunto - Cátedra de Botánica General, Facultad de Agronomía de la
> UBA
> Investigador Adjunto del CONICET
>
> Av. San Martín 4453 - C1417DSE - C. A. de Buenos Aires - Argentina
> +5411 4524-8069
> http://www.agro.uba.ar/users/mdevoto/
>
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>
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