nlstools (version 2.1-0)

nlsBootPredict: Prediction from Bootstrap resampling

Description

Computation of confidence intervals on predictions from Bootstrap resampling

Usage

nlsBootPredict(nlsBoot, newdata, interval = c("confidence", "prediction"))

Value

nlsBoot returns a matrix of predictions with three columns respectively corresponding to the 50, 2.5 and 97.5 percentiles of bootstrap predictions.

Arguments

nlsBoot

An object of class 'nlsBoot'.

newdata

A data frame in which to look for values of independent variables for the predictions.If omitted, the data used for fitting are used.

interval

Type of interval to compute, "confidence", or "prediction".

Author

Florent Baty, Marie-Laure Delignette-Muller

Details

nlsBootPredict produces confidence intervals on predicted values that can be obtained using predict.nls for values of the independent variable(s) defined in the data frame newdata. Non-parametric bootstrapping is used (results of nlsBoot). For confidence intervals the bootstrap sample of predictions is simply computed from the bootstrap sample of estimations of the model parameters, by evaluating the mean value of the model on each new data. For prediction intervals, to take into account the residual errors, a residual error sampled in the mean centered residuals is added to each mean predicted value. In both cases, bootstrap predictions are summarized by the median and 95 percent confidence intervals (50, 2.5, and 97.5 percentiles of the bootstrapped values).

References

Huet S, Bouvier A, Poursat M-A, Jolivet E (2003) Statistical tools for nonlinear regression: a practical guide with S-PLUS and R examples. Springer, Berlin, Heidelberg, New York.

See Also

See nlsBoot and predict.nls.

Examples

formulaExp <- as.formula(VO2 ~ (t <= 5.883) * VO2res + (t > 5.883) * 
                        (VO2res + (VO2peak - VO2res) * 
                        (1 - exp(-(t - 5.883) / mu))))
O2K.nls1 <- nls(formulaExp, start = list(VO2res = 400, VO2peak = 1600, mu = 1), data = O2K)
niter <- 200

### To reach stable prediction intervals use far greater niter (>> 1000)
O2K.boot1 <- nlsBoot(O2K.nls1, niter = niter)
newdata <- data.frame(t = seq(0, 12, length.out = 50))
(pred.clim <- nlsBootPredict(O2K.boot1, newdata = newdata, interval = "confidence"))
(pred.plim <- nlsBootPredict(O2K.boot1, newdata = newdata, interval = "prediction"))

plotfit(O2K.nls1, smooth = TRUE, ylim = c(200, 1800))
lines(newdata$t, pred.clim[, 2], col = "red")
lines(newdata$t, pred.clim[, 3], col = "red")
lines(newdata$t, pred.plim[, 2], col = "blue")
lines(newdata$t, pred.plim[, 3], col = "blue")

### An example without giving newdata

# plot of data
plot(O2K$t, O2K$VO2)

# add of predictions computed using predict.nls()
pred <- predict(O2K.nls1)
points(O2K$t, pred, pch = 16)

# add of prediction intervals using nlsBootPredict()
(pred.plim <- nlsBootPredict(O2K.boot1, interval = "prediction"))
segments(O2K$t, pred.plim[, 2], O2K$t, pred.plim[, 3], col = "blue")