From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Tue 03 May 2005 - 16:54:39 EST

Date: Tue 03 May 2005 - 16:54:39 EST

On Mon, 2 May 2005, Charles Annis, P.E. wrote:

> I have tried everything I can think of and hope not to appear too foolish

*> when my error is pointed out to me.
**>
**> I have some real data (18 points) that look linear on a log-log plot so I
**> used them for a comparison of lm() and survreg. There are no suspensions.
**>
**> survreg.df <- data.frame(Cycles=c(2009000, 577000, 145000, 376000, 37000,
**> 979000, 17420000, 71065000, 46397000, 70168000, 69120000, 68798000,
**> 72615000, 133051000, 38384000, 15204000, 1558000, 14181000), stress=c(90,
**> 100, 110, 90, 100, 80, 70, 60, 56, 62, 62, 59, 56, 53, 59, 70, 90, 70),
**> event=rep(1, 18))
**>
**>
**> sN.lm<- lm(log(Cycles) ~ log10(stress), data=survreg.df)
**>
**> and
**> vvvvvvvvvvv
**> gaussian.survreg<- survreg(formula=Surv(time=log(Cycles), event) ~
**> log10(stress), dist="gaussian", data=survreg.df)
**>
**> produce identical parameter estimates and differ slightly in the residual
**> standard error and scale, which is accounted for by scale being the MLE and
**> thus biased. Correcting by sqrt(18/16) produces agreement. Using predict()
**> for the lm, and predict.survreg() for the survreg model and correcting for
**> the differences in stdev, produces identical plots of the fit and the upper
**> and lower confidence intervals. All of this is as it should be.
*

I trust you called predict() on both and let R choose the method.

*> And,
*

> vvvvvv

*> lognormal.survreg<- survreg(formula=Surv(time=(Cycles), event) ~
**> log10(stress), dist="lognormal", data=survreg.df)
**>
**> produces summary() results that are identical to the earlier call to
**> survreg(), except for the call, of course. The parameter estimates and SE
**> are identical. Again this is as I would expect it.
**>
**> But since the call uses Cycles, rather than log(Cycles) predict.survreg()
**> returns $fit in Cycles units, rather than logs, and of course the fits are
**> identical when plotted on a log-log grid and also agree with lm()
**>
**> Here is the fly in the ointment: The upper and lower confidence intervals,
**> based on the $se.fit for the dist="lognormal" are quite obviously different
**> from the other two methods, and although I have tried everything I could
**> imagine I cannot reconcile the differences.
*

How did you do this? (BTW, I assume you mean upper and lower confidence

*>limits< for the predicted means.) For the predictions and standard
*

errors are (or should be) on the response scale, a non-linear function of
the parameters. In that case it is normal to form confidence limits on
the linear predictor scale and transform.

> I believe that the confidence bounds for both models should agree. After

*> all, both calls to survreg() produce identical parameter estimates.
*

They will, if computed on the same basis. On log-scale (to avoid large numbers)

pr1 <- predict(lognormal.survreg, se.fit=T) log(cbind(pr1$fit - 1.96*pr1$se.fit, pr1$fit + 1.96*pr1$se.fit)) pr2 <- predict(gaussian.survreg, se.fit=T) cbind(pr2$fit - 1.96*pr2$se.fit, pr2$fit + 1.96*pr2$se.fit)

are really pretty close. The main difference is a slight shift, which comes about because the mean of a log(X) is not log(mean(X)). Note that the second set at the preferred ones. Transforming to log scale before making the confidence limits:

cbind(log(pr1$fit) - 1.96*pr1$se.fit/pr1$fit, log(pr1$fit) + 1.96*pr1$se.fit/pr1$fit)

does give identical answers.

Consider care is needed in interpreting what predict() is actually predicting in non-linear models. For both glm() and survreg() it is closer to the median of the uncertainty in the predictions than to the mean.

-- Brian D. Ripley, ripley@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 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Tue May 03 17:02:57 2005

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