I've established pretty conclusively that the residuals I'm generating with a standard lm() regression can be reasonably modeled by a t-distribution with 6-ish degrees of freedom. I'd like to use glm() with that error model, but I'm not seeing that the t fits into one of the families. Any recommendations on either alternatives to glm() that play well with t, or a family that would serve reasonably well as a substitute for (or superset of) t?
Package heavy can perform t-student regression models. Here is an example from the documentation:
library(heavy)
data(ereturns)
fit <- heavyLm(m.marietta ~ CRSP, data = ereturns, family = Student(df = 6))
summary(fit)
# Linear model under heavy-tailed distributions
# Data: ereturns; Family: Student(df = 2.83727)
#
# Residuals:
# Min 1Q Median 3Q Max
# -0.142237 -0.036156 0.003433 0.041310 0.546533
#
# Coefficients:
# Estimate Std.Error Z value p-value
# (Intercept) -0.0072 0.0082 -0.8876 0.3748
# CRSP 1.2637 0.1902 6.6459 0.0000
#
# Degrees of freedom: 60 total; 58 residual
# Scale estimate: 0.002520795
# Log-likelihood: 71.81294 on 3 degrees of freedom