[RsR] "standard deviation" for slope in rlm rather than standard error

[Robert Chatfield]

I wish to give general information about confidence in estimates of the
slope in single-variate rlm         where I try to estimate “emissions factors” which scale
pollutant fire-tracer amounts with amounts of fuel burned.  

emissiions.rlm = rlm ( tracer ~ burn.amount + 1)    (default method)

tracer = a * burn.amount + b

Please help with these naive questions: I have found no previous posts
and am hardly sure that I will find the answers directly in the literature references.


Is there a way to associate a “standard deviation” rather than a “standard error”
to the slope estimate.   From the remarks about the value df.residual regarding the 
predicted-variable standard error, I understand that there must be intricacies.

I do notice that the standard errors for the   slope a   printed  from summary(emissions.rlm) 
are rather smaller than those from  what I would get from  summary( lm ( tracer ~ burn.amount + 1) )
with or without omitting completely down weighted cases or using sum( emissiions.rlm$w -2 )
for the situations I investigate.  When there are no down-weighted observations, they
seem similar.

I would like to have standard deviations rather than standard errors, since the individual
observations are not likely completely independent, and it would be difficult and probably
unwise to attach an independence estimate. (By the way, “independent” takes on several
meanings, “instruments provide independent results” vs “meteorological variability is or is
not great”, and the latter idea has several interpretations also.) Those independence 
questions are at least addressed by separate methods.


Now my purpose is to make   _generalized_ comparisons     between similar situations,
lm using an old estimation methodology for burn.amount
rlm using the same old estimation methodology for burn.amount
and
lm and rlm using what I believe is a better methodology for burn.amount

and where I have several variables to use for “tracer” in the very same context.

(Also a colleague in an earlier paper has quoted only a standard deviation in using the old
estimation methodology for burn.amount, … no doubt for very similar reasons.)


Of course I give a warning that the quoted standard deviations or standard errors must 
used carefully and mostly compared to one another.

Perhaps there are ways to guess intent in the rlm R code, but I hesitate a bit.

Bob Chatfield





Robert Chatfield, Research Scientist
Earth System Science, Atmospherics
Mail Stop 245-5
NASA Ames Research Center
Moffett Field, CA 94035  USA
ph: 650-604-5490  cell: 650-793-5227