[Rd] se.fit from predict.lm

[Prof Brian Ripley]

On Fri, 15 Oct 2004, Hiroyuki Kawakatsu wrote:

> i noticed that se.fit from predict.lm is the same whether interval="conf"
> or interval="pred". it is not clear to me from ?predict.lm whether this is
> intended or not. i suggest that se.fit should match the type of interval
> requested, if interval is specified. suggested change in lm.R line 700

It is intended.  It has been that way in S for many years, and lots of 
code relies on it.  Why would it be useful to have the standard error of a 
prediction interval called se.fit?
                              ^^^
   
>     if(se.fit || interval != "none") se <- sqrt(ip)
> to
>     if(se.fit || interval != "none") se <- switch(interval, none = ,
> confidence = sqrt(ip), prediction = sqrt(ip+res.var) )
> 
> 
> #---sample code to illustrate issue---
> 
> x <- rnorm(5);
> y <- x + rnorm(5);
> out <- lm(y~x);
> 
> xf <- data.frame(x=1);
> # expected y
> ye <- predict(out, xf, se.fit=TRUE, interval="conf");
> print(ye$fit);
> print( paste("se=", ye$se.fit) );
> # actual y
> ya <- predict(out, xf, se.fit=TRUE, interval="pred");
> print(ya$fit);
> print( paste("se=", ya$se.fit) );
> 
> #---end of sample code---
> 
> h.
> p.s. suggestion for ?predict.lm. i don't know whether the
> distinction between interval="confidence" and interval="prediction" is
> standard terminology. 

It is, just as capitalizing is standard usage and you seem not to know.

> it would be clear if the help page had something
> like
>   interval="confidence" accounts only for coefficient uncertainty,
>   whereas interval="prediction" accounts for both coefficient and
>   innovation uncertainty.

But `innovation' is not standard terminology, and it is not the
coefficients that uncertain, but their estimates.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595