p values and significance in RLM (MASS package) R

Question

I'm running some regression analyses and got pretty confused about R's output when it comes to robust regression models. When I run a OLS -- using the command lm() -- I get this as output:

Coefficients:

                Estimate Std. Error t value Pr(>|t|)

But when I run a robust linear model using the rlm() command, the output looks like so:

Coefficients:

                Value   Std. Error t value

How do I get the p-values and the significance-levels in an rlm then? Without that, the whole analysis is somewhat pointless. Unfortunately, I couldn't find an answer to that anywhere, so I hope someone around here can help me out. Thanks a lot!!

Answer 1

The sfsmisc package offers a helpful function for conducting a Wald test:

library(MASS)
library(sfsmisc)
summary(rsl <- rlm(stack.loss ~ ., stackloss))
#Call: rlm(formula = stack.loss ~ ., data = stackloss)
#Residuals:
#     Min       1Q   Median       3Q      Max 
#-8.91753 -1.73127  0.06187  1.54306  6.50163 
#
#Coefficients:
#            Value    Std. Error t value 
#(Intercept) -41.0265   9.8073    -4.1832
#Air.Flow      0.8294   0.1112     7.4597
#Water.Temp    0.9261   0.3034     3.0524
#Acid.Conc.   -0.1278   0.1289    -0.9922
#
#Residual standard error: 2.441 on 17 degrees of freedom

f.robftest(rsl, var = "Air.Flow")
#   robust F-test (as if non-random weights)
#
#data:  from rlm(formula = stack.loss ~ ., data = stackloss)
#F = 50.879, p-value = 1.677e-06
#alternative hypothesis: true Air.Flow is not equal to 0

f.robftest(rsl, var = "Acid.Conc.")
#   robust F-test (as if non-random weights)
#
#data:  from rlm(formula = stack.loss ~ ., data = stackloss)
#F = 1.0447, p-value = 0.3211
#alternative hypothesis: true Acid.Conc. is not equal to 0