# What family should I use when my response variable is humidity vs temperature?

I am trying to understand what factors influence temp and humidity but I am not sure what family argument I should be using in my GLM The humidity data is a proportion 0-1 and temp is continuous my model code is as such:

mod4<-glm(average.humid~Age + Mine.size.km2 + canopy.cover.E + canopy.cover.100 +
avarage.sapling.height.in.mine + avarage.canopy.height.at.edge +
avarage.canopy.height.100m + number.of.saplings.M +
number.of.saplings.E + number.of.saplings.100m +
Large.trees.Mine + Large.trees.Edge +
Large.trees.100,
data = datal, family = gaussian())

I am not sure if Gaussian is the correct code to be used for humidity. It seems to work fine with temp. Is this correct?

• Maybe binomial family. Aug 9 at 5:40
• You will puzzle or irritate fewer people by reporting values bounded between 0 and 1 as proportions or fractions, and never as percentages. It's a case where everybody should understand what you mean, but somebody such as myself will dislike the terminology. Aug 22 at 10:57
• A more serious issue is that I understand that relative humidity, which is what you're talking about, is sometimes reported as above 100% or above 1. I've forgotten the physics here, but no statistical routine will understand this except as impossible. Aug 22 at 10:59

I believe that a beta regression is what you need.

You have two issues to deal with:

1. your response variable is bound between 0 (0% humidity) and 1(100% humidity), so the model predictions need to account for that;
2. the closer the average model predictions are to 0 and 1, the more asymmetrical the distribution of the single observations become around the expected mean. For an average predicted mean humidity of 0%, observed variability can only be 0% or more; for an average predicted mean humidity of 100%, observed variability can only be 100% or less.

Beta regression accounts for these two issues as follows:

1. it fits a logistic model to the data. A logistic model is sigmoidal i.e. S-shaped and bound between 0 (0%) and 1 (100%);
2. it assumes that the model residuals follow a beta distribution, which is usually a good approximation when data are rates and proportions (see, for example: https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/1365-2745.13200).

You can fit such a model in R with function betareg() from package betareg: https://www.rdocumentation.org/packages/betareg/versions/3.1-4/topics/betareg

It should also be possible to do so with function glmmTMB() from package glmmTMB: