r - 如何向ggplot添加对数非线性拟合？

Question

我想使用 nls 通过我的数据拟合对数曲线。

library(dplyr)
library(ggplot2)
a <- 3
b <- 2
Y <- data_frame(x = c(0.2, 0.5, 1, 2, 5, 10),
                y = a + b*log(x))

Y %>%
  ggplot(aes(x = x, y = y)) +
  geom_point(shape = 19, size = 2) +
  geom_smooth(method = "nls",
              formula = y ~ p1 + p2*log(x),
              start = list(a = a, b = b),
              se = FALSE,
              control = list(maxiter = 100))

这给了我一个错误:

Error in method(formula, data = data, weights = weight, ...) : number of iterations exceeded maximum of 100

出了什么问题？

Answer 1

这是我在执行 ?nls 后复制并粘贴的一些文本:

Warning

Do not use nls on artificial "zero-residual" data.

The nls function uses a relative-offset convergence criterion that compares the numerical imprecision at the current parameter estimates to the residual sum-of-squares. This performs well on data of the form

y = f(x, θ) + eps

(with var(eps) > 0). It fails to indicate convergence on data of the form

y = f(x, θ)

because the criterion amounts to comparing two components of the round-off error. If you wish to test nls on artificial data please add a noise component, as shown in the example below.

这启发了我尝试这个:

> library(dplyr)
> library(ggplot2)
> a <- 3
> b <- 2
> Y <- data_frame(x = c(0.2, 0.5, 1, 2, 5, 10),
+                 y = a + b*log(x)*(1 + rnorm(length(x), sd=0.001)))
> Y %>%
+   ggplot(aes(x = x, y = y)) +
+   geom_point(shape = 19, size = 2) +
+   geom_smooth(method = "nls",
+               formula = y ~ p1 + p2*log(x),
+               start = list(p1 = a, p2 = b),
+               se = FALSE,
+               control = list(maxiter = 100))

注意:你的代码有 start = list(a=a, b=b) 这是一个错字，因为 a 和 b 是' 在您的公式中定义。除此之外，添加 *(1 + rnorm(length(x), sd=0.001)) 是我唯一做的事。

生成的图表看起来一切正常。

不过，我通常建议单独进行拟合，然后使用 predict 绘制它。这样一来，您始终可以在绘图之前检查拟合的质量，看看它是否有效。

> fit <- nls(data=Y, formula = y ~ p1 + p2*log(x), start = list(p1 = a, p2 = b))
> summary(fit)

Formula: y ~ p1 + p2 * log(x)

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
p1 3.001926   0.001538    1952 4.14e-13 ***
p2 1.999604   0.001114    1795 5.78e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.003619 on 4 degrees of freedom

Number of iterations to convergence: 1 
Achieved convergence tolerance: 1.623e-08

> new_x = data.frame(x=seq(from=0.2, to=10, length.out=100))
> ggplot(data=Y, aes(x=x, y=y)) + 
       geom_point() + 
       geom_line(data=new_x, 
                 aes(x=new_x, y=predict(fit, newdata=new_x)), 
                 color='blue')