predict2_nls: Prediction Bands for Nonlinear Regression

In nlraa: Nonlinear Regression for Agricultural Applications

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)

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.

The method currently works well for any nonlinear function, but if predictions are needed on new data, then it is required that a selfStart function is used.

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

See Also

predict.nls and predict_nls

Examples

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")
  
## This is equivalent 
fm2 <- nls(weight ~ Asym/(1 + exp((xmid - Time)/scal)), data = SoyF,
           start = c(Asym = 20, xmid = 56, scal = 8))
           
## 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_gnls(fmg1, 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")

nlraa documentation built on May 29, 2024, 2:01 a.m.