如何计算r中的非线性最小二乘法的置信区间？

Question

我在预测r中的nls的置信区间时遇到麻烦。

pl <- ggplot(data) +  geom_point(aes(x=date, y=cases),size=2, colour="black") + xlab("Date") + ylab("Cases")  
model = nls(cases ~ SSlogis(log(date), Asym, xmid, scal), data= data )


new.data = data.frame(date=c(1:100))
interval <- predict(model, newdata = new.data, se.fit = TRUE, interval = "confidence", level= 0.9)

new.data[c("fit","lwr.conf", "upr.conf")] <- interval 

pl +   
  geom_ribbon(data=new.data, aes(x=date, ymin=lwr.pred, ymax=upr.pred), alpha=0.05, inherit.aes=F, fill="blue")

[当我运行它时，它没有显示任何错误，但是我得到的间隔只是一个带有拟合的向量，没有上下置信区间。

Answer 1

非线性置信区间可以通过使用包propagate进行仿真来获得：

library("propagate")

x  <- c(25, 25, 10, 10, 5, 5, 2.5, 2.5, 1.25, 1.25)
y <- c(0.0998, 0.0948, 0.076, 0.0724, 0.0557,
       0.0575, 0.0399, 0.0381, 0.017, 0.0253)

m <- nls(y ~ SSmicmen(x, Vm, K), trace = TRUE)

x1 <- seq(0, 25, length = 100)
plot(x, y, xlim = c(0, 25), ylim = c(0, 0.1))
lines(x1, predict(m, data.frame(S = x1)), col = "red")

y.conf <- predictNLS(m, newdata=data.frame(x=x1), interval="confidence", alpha=0.05, nsim=10000)$summary
y.pred <- predictNLS(m, newdata=data.frame(x=x1), interval="prediction", alpha=0.05, nsim=10000)$summary

matlines(x1, y.conf[,c("Sim.2.5%", "Sim.97.5%")], col="red", lty="dashed")
matlines(x1, y.pred[,c("Sim.2.5%", "Sim.97.5%")], col="blue", lty="solid")