[R] Plotting confidence bands around regression line

[David Winsemius]

On Aug 10, 2010, at 12:12 PM, Michal Figurski wrote:

> David,
>
> I would consider myself intermediate in R, but a beginner in  
> statistics. I need a formula that would allow me to calculate  
> confidence boundaries of the regression line given the slope,  
> intercept and their CIs (and *any* range).

There are some worked examples:

rhelpSearch <- function(string,
                   restrict = c("Rhelp10", "Rhelp08", "Rhelp02",  
"functions" ),
                   matchesPerPage = 100, ...) {
          RSiteSearch(string=string,  restrict = restrict,
                       matchesPerPage = matchesPerPage, ...) }

rhelpSearch("plot prediction intervals regression")

... produces 131 hits and the first one led me to install and load  
asbio which produced a nice looking graph with your data that  
illustrates the quadratic depepndence on x and the difference between  
prediction intervals and confidence intervals on parameters
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plotCI.reg(a$x, a$y)

--  
David

>
> Passing-Bablok regression doesn't yet exist in R - I am developing  
> it. Therefore I am sure there is no predict method for it ;)
>
> I believe I have provided sufficient data to address this problem,  
> but if that would help anyone, here is more:
>
> # data frame
> > a <- structure(list(x = c(0.1, 1.43, 4.21, 3.67, 3.23, 7.72, 5.99,  
> 9.16, 10.6, 9.84, 11.94, 12.03, 12.89, 11.26, 15.54, 15.58, 17.32,  
> 17.65, 19.52, 20.48, 20.44, 20.51, 22.27, 23.58, 25.83, 26.04,  
> 26.92, 28.44, 30.73, 28.78), y = c(1.08, 1.39, 1.84, 0.56, 7.23,  
> 4.91, 3.35, 7.09, 3.16, 8.98, 16.37, 7.46, 15.46, 23.2, 4.63, 11.13,  
> 15.68, 13.92, 26.44, 21.65, 21.01, 20.22, 22.69, 22.21, 23.6, 17.24,  
> 45.24, 30.09, 40, 49.6)), .Names = c("x", "y"), row.names = c(NA,  
> -30L), class = "data.frame")
>
> Then I run the regression procedure (in development - now part of  
> the 'MethComp' package):
> > print(PBreg(a))
>
> # And the result of the Passing-Bablok regression on this data frame:
>           Estimate      5%CI     95%CI
> Intercept -4.306197 -9.948438 -1.374663
> Slope      1.257584  1.052696  1.679290
>
> The original Passing & Bablok article on this method has an easy  
> prescription for CIs on coefficients, so I implemented that. Now I  
> need a way to calculate CI boundaries for individual points - this  
> may be a basic handbook stuff - I just don't know it (I'm not a  
> statistician). I would appreciate if anyone could point me to a  
> handbook or website where it is described.
>
> Regarding 2 - the predict method for 'nls' class currently *ignores*  
> the interval parameter - as it is stated in documentation.
>
> Regards
>
> --
> Michal J. Figurski, PhD
> HUP, Pathology & Laboratory Medicine
> Biomarker Research Laboratory
> 3400 Spruce St. 7 Maloney
> Philadelphia, PA 19104
> tel. (215) 662-3413
>
> On 2010-08-10 11:38, David Winsemius wrote:
>>
>> On Aug 10, 2010, at 11:23 AM, Michal Figurski wrote:
>>
>>> David,
>>>
>>> I may have stated my problem incorrectly - my problem is to *obtain
>>> the coordinates* for confidence boundary lines. As input data I have
>>> only CIs for slope and intercept.
>>
>> Wouldn't you also need to specify the range over which these  
>> estimates
>> might be valid and to offer the means for the X values? What level  
>> of R
>> knowledge are you at? You have provided no data or code. Many R  
>> methods
>> offer predict methods that return CI's.
>>

David Winsemius, MD
West Hartford, CT