r - 如何从 nls 计算 95% 的预测区间

Question

从这里借用示例数据 question ，如果我有以下数据并且我拟合了以下非线性模型，我如何计算 95% 预测 间隔我的曲线？

library(broom)
library(tidyverse)

x <- seq(0, 4, 0.1)
y1 <- (x * 2 / (0.2 + x))
y <- y1 + rnorm(length(y1), 0, 0.2)

d <- data.frame(x, y)

mymodel <- nls(y ~ v * x / (k + x),
            start = list(v = 1.9, k = 0.19),
            data = d)

mymodel_aug <- augment(mymodel)

ggplot(mymodel_aug, aes(x, y)) +
  geom_point() +
  geom_line(aes(y = .fitted), color = "red") +
  theme_minimal()

例如，我可以轻松地从这样的线性模型计算预测区间:

## linear example

d2 <- d %>%
  filter(x > 1)

mylinear <- lm(y ~ x, data = d2)

mypredictions <-
  predict(mylinear, interval = "prediction", level = 0.95) %>%
  as_tibble()

d3 <- bind_cols(d2, mypredictions)

ggplot(d3, aes(x, y)) +
  geom_point() +
  geom_line(aes(y = fit)) +
  geom_ribbon(aes(ymin = lwr, ymax = upr), alpha = .15) +
  theme_minimal()

Answer 1

根据链接的问题，它看起来像 investr::predFit函数会做你想做的。

investr::predFit(mymodel,interval="prediction")

?predFit没有解释间隔是如何计算的，但是 ?plotFit说:

Confidence/prediction bands for nonlinear regression (i.e., objects of class ‘nls’) are based on a linear approximation as described in Bates & Watts (2007). This fun[c]tion was in[s]pired by the ‘plotfit’ function from the ‘nlstools’ package.

也称为 Delta method (例如，见 emdbook::deltavar )。