Analysis of residuals from generalized linear model with binomial family

Question

I have fit a GLM where the response variable represents ratio and used Binomial family. Below is my model

library(foreign)
df <- read.dta("http://fmwww.bc.edu/ec-p/data/wooldridge/401k.dta")
df$prate <- df$prate/100

myglm <- glm(prate ~ mrate + age + sole, data = df, family = binomial)
summary(myglm)

Now I want to get quantile residuals of above fit. As per the discussion in the paper https://www.researchgate.net/publication/2647151_Randomized_Quantile_Residuals, in order to estimate quantile residuals, I need to convert the response variable to standard normal variable.

However, given that in my case I only have ratios (not actual realization of binomial distribution), I could not figure out how exactly I should estimate the quantile residuals in this case.

Is there any direct or approximate method available to obtain such residuals for this type of model fit?

Any pointer will be very helpful.

Answer 1

You cannot compute randomized quantile residuals without the binomial numbers. In fact you cannot fit a binomial glm corrrectly without them either.

But the dataset you have loaded does include the binomial realizations. You need:

library(foreign)
df <- read.dta("http://fmwww.bc.edu/ec-p/data/wooldridge/401k.dta")
df$prate <- df$totpart / df$totelg
myglm <- glm(prate ~ mrate + age + sole, data = df, family = binomial, weights = totalelg)
library(statmod)
qr <- qresid(myglm)