We are having problems running generalized linear models with proportional data.
For example, we have data like this:
Species Trait(Diet) IndividualsinForest TotalIndividuals ProportionForest X Insectivore 300.5 500.7 0.60 Y Frugivore 32.3 47.6 0.67
And we want to determine whether trait influences the proportion of individuals in forest. Note that the individual numbers are continuous (have decimals), because the original counts have been DISTANCE-adjusted.
Most on the models that we have seen in R deal with count data. For example, see M.J. Crawley Statistics: An Introduction using R, Chapter 10: Analyzing proportion data (pdf).
These models use the
cbind statement to bind together the number of successes and the number of failures and then relate that to the predictor:
model.1 <- glm (cbind(IndividualsinForest, (TotalIndividuals-IndividualsinForest))~Diet, family=binomial)
However, there seems to be two problems to using this approach for our situation:
We are using
cbindthat combined vectors with continuous (decimal point) values; it is not clear whether this is allowed, although it runs in R. We have played around with multiplying everything by 1000 to get rid of the decimals, but find the results change a lot with such a technique (very different results if multiply by 10, by 100, by 1000)
cbindruns a weighted regression, as explained by Crawley. This means that the model will weight the data of Species X, above, with 500.7 total individuals more heavily than the data of Species Y, with 47.6 individuals.
But conceptually, we do not want a weighted regression, because we want to treat all species equally: a rare species’ data is as important to us as an abundant species’ data. Species is the unit of replication here.
We tried to force a non-weighted regression using the same code, by adding columns to the data, for example,
Species ProportionForest PInForest PTotal X .60 60 100 Y .67 67 100
And then running:
model.3 <- glm(cbind(PInForest, (PTotal-PInForest))~Diet, family=binomial)
But the resulting analyses are very overdispersed, and running them with
family=quasibinomial gives strange results (completely non-sensitive tests, with large p-values for fairly clear differences).
Hence our current analytical strategy is to fall back on arcsine transforming the proportion and then running a general linear model. But we'd prefer though to run a generalized linear model because the arcsine transformation seems to be a relict of old pre-computer statistics.