Re: [R] diagnostic functions to assess fitted ols() model: Confidence is too narrow?!

From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>
Date: Sun 18 Dec 2005 - 00:03:40 EST

Jan Verbesselt wrote:
> Dear all,
>
> When fitting an "ols.model", the confidence interval at 95% doesn't cover
> the plotted data points because it is very narrow.
>
> Does this mean that the model is 'overfitted' or is there a specific amount
> of serial correlation in the residuals?
>
> Which R functions can be used to evaluate (diagnostics) major model
> assumptions (residuals, independence, variance) when fitting ols models in
> the Design package?
>
> Regards,
> Jan

Confidence intervals for means are not supposed to cover the data points. This interval shrinks to zero as the sample size goes to infinity. Confidence intervals that are 'individual' should cover the majority of data points.

You can see the case study on ols in my book for examples of diagnostics. See biostat.mc.vanderbilt.edu/rms

Frank Harrell

>
> # -->OLS regression
> library(Design)
> ols.1 <- ols(Y~rcs(X,3), data=DATA, x=T, y=T)
> summary.lm(ols.1) # --> non-linearity is significant
> anova(ols.1)
>
> d <- datadist(Y,X)
> options(datadist="d")
> plot(ols.1)
> #plot(ols.1, conf.int=.80, conf.type=c('individual'))
> points(X,Y)
> scat1d(X, tfrac=.2)
>
> When plotting this confidence interval looks normal:
> #plot(ols.1, conf.int=.80, conf.type=c('individual'))
>
> Workstation Windows XP
> // R version 2.2 //
>
>
>
>
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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Received on Sun Dec 18 00:09:08 2005

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