I'm learning to implement robust glms in R, but can't figure out why I am unable to get glmrob to predict values from my regression models when I have a model where some columns are dropped due to co-linearity. Specifically when I use the predict function to predict values from a glmrob, it always gives NA for all values. I don't observe this when predicting values from the same data & model using glm. It doesn't seem to matter what data I use -- as long as there is a NA coefficient in the fitted model (and the NA isn't the last coefficient in the coefficient vector), the predict does not work.
This behavior holds for all datasets and models I have tried where an internal column is dropped due to co-linearity. I include a fake data set where two columns are dropped from the model, which gives two NAs in the coefficient list. Both glm and glmrob give nearly identical coefficients, yet predict only works with the glm model. So my question is: what don't I understand about robust regression that would prevent my glmrob models from generating predicted values?
library(robustbase)
#Make fake data with two categorial predictors
df <- data.frame("category" = rep(c("A","B","C"),each=6))
df$location <- rep(1:6,each=3)
val <- rep(c(500,50,5000),each=6)+rep(c(50,100,25,200,100,1),each=3)
df$value <- rpois(NROW(df),val)
#note that predict works if we omit the newdata parameter. However I need the newdata param
#so I use the original dataframe here as a stand-in.
mod <- glm(val ~ category + as.factor(location), data=df, family=poisson)
predict(mod, newdata=df) # works fine
mod <- glmrob(val ~ category + as.factor(location), data=df, family=poisson)
predict(mod, newdata=df) #predicts NA for all values
I've been digging into this and have concluded that the problem does not lie in my understanding of robust regression, but rather the problem lies with a bug in the robustbase package. The predict.lmrob function does not correctly pick the necessary coefficients from the model before the prediction. It needs to pick the first x non-NA coefficients (where x=rank of the model matrix). Instead it merely picks the first x coefficients without checking if they are NA. This explains why this problem only surfaces for models where the NA isn't the last coefficient in the coefficient vector.
To fix this, I copied the predict.lmrob source using:
getAnywhere(predict.lmrob)
and created my own replacement function. In this function I made a single modification to the code:
...
p <- object$rank
if (is.null(p)) {
df <- Inf
p <- sum(!is.na(coef(object)))
#piv <- seq_len(p) # old code
piv <- which(!is.na(coef(object))) # new code
}
else {
p1 <- seq_len(p)
piv <- if (p)
qr(object)$pivot[p1]
}
...
I've run a few hundred datasets using this change and it has worked well.