On Aug 29, 2012, at 4:08 PM, John Thaden wrote:
Draper & Smith sections (3.2, 9.6) address prediction interval
issues, but
I'm also concerned with the linear fit itself. The Model II regression
literature
Citations?
makes it abundantly clear that OLS regression of x on y
frequently yields a different line than of y on x. The example below
is not
so extreme, but those given e.g. by Ludbrook, J. (2012)
... to a source that does not require a fee of US$30?
certainly are. Rui
notes the logical problem of imputing an unknown x using a calibration
curve where the x values are without error. Regression x on y
doesn't help
that. But on a practical level, I definitely recall (years ago) using
predict.lm and newdata to predict x terms. I wish I remembered how.
You may be thinking of "orthogonal regression" or or "Deming
regression" or one of its many other names. There is abundant code in
the (free) archives regarding this topic. Please do be clear about
what you really do desire. If you think there is a correct answer to
your problem in a particular case, then by all means ... post that.
Just saying predict)lm)...)) is not right, is not sufficient.
--
David
require(stats)
#Make an illustrative data set
set.seed(seed = 1111)
dta <- data.frame(
area = c(
rnorm(6, mean = 4875, sd = 400),
rnorm(6, mean = 8172, sd = 800),
rnorm(6, mean = 18065, sd = 1200),
rnorm(6, mean = 34555, sd = 2000)),
concn = rep(c(25, 50, 125, 250), each = 6))
model <- lm(area ~ concn, data = dta)
inv.model <- lm(concn ~ area, data = dta)
plot(area ~ concn, data = dta)
abline(model)
inv.new = cbind.data.frame(area = c(1600, 34000))
inv.pred <- predict(inv.model, newdata = inv.new)
lines(x = inv.pred, y = unlist(inv.new), col = "red")
_____________________________
Ludbrook, J. (2012). "A primer for biomedical scientists on how to
execute
Model II linear regression analysis." Clinical and Experimental
Pharmacology and Physiology 39(4): 329-335.
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David Winsemius, MD
Alameda, CA, USA
______________________________________________
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and provide commented, minimal, self-contained, reproducible code.
