Background: Multi-model inference with glmulti
glmulti is a R function/package for automated model selection for general linear models that constructs all possible general linear models given a dependent variable and a set of predictors, fits them via the classic glm function and allows then for multi-model inference (e.g., using model weights derived from AICc, BIC). glmulti works in theory also with any other function that returns coefficients, the log-likelihood of the model and the number of free parameters (and maybe other information?) in the same format that glm does.
My goal: Multi-model inference with robust errors
I would like to use glmulti with robust modeling of the errors of a quantitative dependent variable to guard against the effect out outliers.
For example, I could assume that the errors in the linear model are distributed as a t distribution instead of as a normal distribution. With its kurtosis parameter the t distribution can have heavy tails and is thus more robust to outliers (as compared to the normal distribution).
However, I'm not committed to using the t distribution approach. I'm happy with any approach that gives back a log-likelihood and thus works with the multimodel approach in glmulti. But that means, that unfortunately I cannot use the well-known robust linear models in R (e.g., lmRob from robust or lmrob from robustbase) because they do not operate under the log-likelihood framework and thus cannot work with glmulti.
The problem: I can't find a robust regression function that works with glmulti
The only robust linear regression function for R I found that operates under the log-likelihood framework is heavyLm (from the heavy package); it models the errors with a t distribution. Unfortunately, heavyLm does not work with glmulti (at least not out of the box) because it has no S3 method for loglik (and possibly other things).
To illustrate:
library(glmulti)
library(heavy)
Using the dataset stackloss
head(stackloss)
Regular Gaussian linear model:
summary(glm(stack.loss ~ ., data = stackloss))
Multi-model inference with glmulti using glm's default Gaussian link function
stackloss.glmulti <- glmulti(stack.loss ~ ., data = stackloss, level=1, crit=bic)
print(stackloss.glmulti)
plot(stackloss.glmulti)
Linear model with t distributed error (default is df=4)
summary(heavyLm(stack.loss ~ ., data = stackloss))
Multi-model inference with glmulti calling heavyLm as the fitting function
stackloss.heavyLm.glmulti <- glmulti(stack.loss ~ .,
data = stackloss, level=1, crit=bic, fitfunction=heavyLm)
gives the following error:
Initialization...
Error in UseMethod("logLik") :
no applicable method for 'logLik' applied to an object of class "heavyLm".
If I define the following function,
logLik.heavyLm <- function(x){x$logLik}
glmulti can get the log-likelihood, but then the next error occurs:
Initialization...
Error in .jcall(molly, "V", "supplyErrorDF",
as.integer(attr(logLik(fitfunc(as.formula(paste(y, :
method supplyErrorDF with signature ([I)V not found
The question: Which function/package for robust linear regression works with glmulti (i.e., behaves like glm)?
There is probably a way to define further functions to get heavyLm working with glmulti, but before embarking on this journey I wanted to ask whether anybody
- knows of a robust linear regression function that (a) operates under the log-likelihood framework and (b) behaves like glm (and will thus work with glmulti out-of-the-box).
- got heavyLm already working with glmulti.
Any help is very much appreciated!
