R help - Apr 2009 - predict "interval" for lmRob?

lm's "predict" function offers an "interval" parameter
to choose between 'confidence' and 'prediction' bands. In the
package "robust" and for "lmRob", there is also a
"predict" but it lacks such a parameter, and the documented
"type" parameter has only "response" offerred.  Is there
some way of obtaining prediction bands from lmRob?  Is there an alternative
robust (linear) regression package that offers such a capability?

Thanks for any and all help.

  - Jan Galkowski, Akamai Technologies, Cambridge, MA.

Your problem is related to the theory underlying linear models (and is an
example as to why it is important to understand the theory, not just know how to
plug numbers into a computer).

The lm function is based on theory that assumes the y variable in normally
distributed with the mean of that normal based on the model and the x values. 
This allows the predict function for lm to create prediction intervals based on
the normal distribution, the predicted mean of that distribution, the estimated
standard deviation, and the uncertainty in the predicted mean.  Note that if
your y variable is not normally distributed, but the sample size is large enough
for the Central Limit Theorem to hold, then the confidence intervals will be
approximately correct, but the prediction intervals will probably not be.

When you switch to a robust regression approach, the assumption is that the y
variable is not normal, so a prediction interval based on the normal
distribution does not make sense.  To get an appropriate prediction interval you
need some information on what the distribution of the y values is (conditional
on the model), but most robust techniques are not based on a specific
distribution, just some properties of the distribution.  Without some
information (or at least an assumption) on that distribution, the predict method
cannot create prediction intervals.

I know that this does not answer your question, but hopefully helps you to
understand what is happening.  Think about what your actual scientific question
is, it may be that you can answer the question without prediction intervals.

If you feel that you really need the prediction intervals, then you will need to
do some additional background research into what distribution you think the data
comes from, then you can proceed from there.  Some options include fitting a
model based on that distribution, simulating data from the distribution given
the model estimates and the uncertainty in those estimates, quantile regression,
mixture of regressions, and others.

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Galkowski, Jan
> Sent: Wednesday, April 08, 2009 9:32 AM
> To: r-help at r-project.org
> Subject: [R] predict "interval" for lmRob?
> 
> lm's "predict" function offers an "interval"
parameter to choose
> between 'confidence' and 'prediction' bands. In the package
"robust"
> and for "lmRob", there is also a "predict" but it lacks
such a
> parameter, and the documented "type" parameter has only
"response"
> offerred.  Is there some way of obtaining prediction bands from lmRob?
> Is there an alternative robust (linear) regression package that offers
> such a capability?
> 
> Thanks for any and all help.
> 
>   - Jan Galkowski, Akamai Technologies, Cambridge, MA.
> 
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