# Prediction Bands for Nonlinear Regression 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. ```r 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) ## Returns 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. 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. ## Examples ```r 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") ``` ## See Also `predict.nls` and `predict_nls`

predict2_nls function