On Sep 13, 2009, at 1:19 PM, Tal Galili wrote:
Hello dear r-help group
I am turning for you for help with FAQ number 7.31: "Why doesn't R
think
these numbers are equal?"
http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f
*My story* is this:
I wish to run many lm predictions and need to have them run fast.
Using predict.lm is relatively slow, so I tried having it run faster
by
doing the prediction calculations manually.
But doing that gave me problematic results (I won't go into the
details of
how I found that out).
I then discovered that the problem was that the manual calculations
I used
for the lm predictions yielded different results than that of
predict.lm,
*here is an example*:
predict.lm.diff.from.manual.compute <- function(sample.size = 100)
{
x <- rnorm(sample.size)
y <- x + rnorm(sample.size)
new <- data.frame(x = seq(-3, 3, length.out = sample.size))
aa <- lm(y ~ x)
predict.lm.result <- sum(predict(aa, new, se.fit = F))
manual.lm.compute.result <- sum(aa$coeff[1]+ new * aa$coeff[2])
# manual.lm.compute.result == predict.lm.result
return(all.equal(manual.lm.compute.result , predict.lm.result, tol=0))
}
# and here are the results of running the code several times:
predict.lm.diff.from.manual.compute(100)
[1] "Mean relative difference: 1.046407e-15"
predict.lm.diff.from.manual.compute(1000)
[1] "Mean relative difference: 4.113951e-16"
predict.lm.diff.from.manual.compute(10000)
[1] "Mean relative difference: 2.047455e-14"
predict.lm.diff.from.manual.compute(100000)
[1] "Mean relative difference: 1.294251e-14"
predict.lm.diff.from.manual.compute(1000000)
[1] "Mean relative difference: 5.508314e-13"
Are these meaningfully different? You are using different datasets and
didn't even set a seed for your RNG. They seem really quite close. Why
should we care?
> .Machine$double.eps
[1] 2.220446e-16
And that leaves me with *the question*:
Can I reproduce more accurate results from the manual calculations
(as the
ones I might have gotten from predict.lm) ?
Maybe some parameter to increase the precision of the computation ?
Many thanks,
Tal
--
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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