nlraa (version 0.98)

predict2_nls: Prediction Bands for Nonlinear Regression

Description

The method used in this function is described in Battes and Watts (2007) Nonlinear Regression Analysis and Its Applications (see pages 58-59). It is known as the Delta method.

Usage

predict2_nls(
  object,
  newdata = NULL,
  interval = c("none", "confidence", "prediction"),
  level = 0.95
)

Arguments

object

object of class ‘nls’

newdata

data frame with values for the predictor

interval

either ‘none’, ‘confidence’ or ‘prediction’

level

probability level (default is 0.95)

Value

a data frame with Estimate, Est.Error, lower interval bound and upper interval bound. For example, if the level = 0.95, the lower bound would be named Q2.5 and the upper bound would be name Q97.5

Details

This method is approximate and it works better when the distribution of the parameter estimates are normally distributed. This assumption can be evaluated by using bootstrap.

See Also

predict.nls and predict_nls

Examples

# NOT RUN {
require(ggplot2)
require(nlme)
data(Soybean)
SoyF <- subset(Soybean, Variety == "F" & Year == 1988)
fm1 <- nls(weight ~ SSlogis(Time, Asym, xmid, scal), data = SoyF)
## The SSlogis also supplies analytical derivatives
## therefore the predict function returns the gradient too
prd1 <- predict(fm1, newdata = SoyF)
## Gradient
head(attr(prd1, "gradient"))
## Prediction method using gradient
prds <- predict2_nls(fm1, interval = "conf")
SoyFA <- cbind(SoyF, prds)
ggplot(data = SoyFA, aes(x = Time, y = weight)) + 
   geom_point() + 
   geom_line(aes(y = Estimate)) + 
   geom_ribbon(aes(ymin = Q2.5, ymax = Q97.5), fill = "purple", alpha = 0.3) +
   ggtitle("95% Confidence Bands")
fm2 <- nls(weight ~ Asym/(1 + exp((xmid - Time)/scal)), data = SoyF,
           start = c(Asym = 20, xmid = 56, scal = 8))
## Using predict.nls on this object will not return a gradient 
## so predict2_nls will fail
predict(fm2)
## For this reason, functions which use a selfStart are recommended
## Prediction interval
prdi <- predict2_nls(fm1, interval = "pred")
SoyFA.PI <- cbind(SoyF, prdi) 
## Make prediction interval plot
ggplot(data = SoyFA.PI, aes(x = Time, y = weight)) + 
   geom_point() + 
   geom_line(aes(y = Estimate)) + 
   geom_ribbon(aes(ymin = Q2.5, ymax = Q97.5), fill = "purple", alpha = 0.3) + 
   ggtitle("95% Prediction Band")
## For these data we should be using gnls instead with an increasing variance
fmg1 <- gnls(weight ~ SSlogis(Time, Asym, xmid, scal), 
             data = SoyF, weights = varPower())
IC_tab(fm1, fmg1)
prdg <- predict_nlme(fmg1, plevel = 1, interval = "pred")
SoyFA.GPI <- cbind(SoyF, prdg) 
## These prediction bands are not perfect, but they could be smoothed
## to eliminate the ragged appearance
 ggplot(data = SoyFA.GPI, aes(x = Time, y = weight)) + 
   geom_point() + 
   geom_line(aes(y = Estimate)) + 
   geom_ribbon(aes(ymin = Q2.5, ymax = Q97.5), fill = "purple", alpha = 0.3) + 
   ggtitle("95% Prediction Band. NLS model which \n accomodates an increasing variance")
# }