为什么 geom_smooth nls 和独立的 nls 给出不同的拟合结果？

Question

当我使用 geom_smooth nls 拟合数据时，我得到了非常好的拟合。但是，如果我使用独立的 nls 函数使用相同的方程和起始值来拟合我的数据，我的拟合效果会差得多。我想提取拟合参数，所以真的需要独立的 nls 来生成与 geom_smooth nls.

相同的拟合

任何suggestion/hint可能会发生什么？


df <- data.frame("x" = c(4.63794469, 1.54525711, 0.51508570, 0.17169523, 0.05737664, 5.11623138, 1.70461130, 0.56820377, 0.18940126, 0.06329358, 0.02109786), 
                 "y" = c(0.1460101, 0.7081954, 0.9619413, 1.0192286, 1.0188301, 0.3114495, 0.7602488, 0.8205661, 0.9741323, 1.0922553, 1.1130464))

fit <- nls(data = df, y ~ (1/(1 + exp(-b*x + c))), start = list(b=1, c=0))
df$stand_alone_fit <- predict(fit, df)

df %>% ggplot() +
  geom_point(aes(x = x, y = y)) +
  scale_x_log10() +
  ylim(0,1.2) +
  geom_smooth(aes(x = x, y = y), method = "nls", se = FALSE, 
              method.args = list(formula = y ~ (1/(1 + exp(-b*x + c))), start = list(b= 1, c=0))) +
  geom_line(aes(x = x, y = stand_alone_fit), color = "red") +
  labs(title = "Blue: geom_smooth nls fit\nRed: stand alone nls fit")

Answer 1

这里有两个问题，首先，预测（红线）仅在 x 点处执行，导致曲线看起来四四方方且不平滑。

第二个问题的原因。两条拟合曲线不相等是因为这条线 scale_x_log10() 在 x 轴上有变换，所以 geom_smooth 内的 nls 函数执行的拟合与独立拟合不同。

看看移除 x 轴变换后会发生什么。（绿线是外部拟合的更精细预测）。

df <- data.frame("x" = c(4.63794469, 1.54525711, 0.51508570, 0.17169523, 0.05737664, 5.11623138, 1.70461130, 0.56820377, 0.18940126, 0.06329358, 0.02109786), 
                 "y" = c(0.1460101, 0.7081954, 0.9619413, 1.0192286, 1.0188301, 0.3114495, 0.7602488, 0.8205661, 0.9741323, 1.0922553, 1.1130464))


fit <- nls(data = df, y ~ (1/(1 + exp(-b*x + c))), start = list(b=0, c=0))
df$stand_alone_fit <- predict(fit, df)

#finer resolution (green line)
new <- data.frame(x=seq(0.02, 5.1, 0.1))
new$y <-predict(fit, new)

df %>% ggplot() +
   geom_point(aes(x = x, y = y)) +
#   scale_x_log10() +
   ylim(0,1.2) +
   geom_smooth(aes(x = x, y = y), method = "nls", se = FALSE, 
               method.args = list(formula = y ~  (1/(1 + exp(-b*x + c))), start = list(b=0, c=0))) +
   geom_line(aes(x = x, y = stand_alone_fit), color = "red") +
   geom_line(data=new, aes(x, y), color="green") +
   labs(title = "Blue: geom_smooth nls fit\nRed: stand alone nls fit")

或者在你原来的 ggplot 定义中使用这个：method.args = list(formula = y ~ (1/(1 + exp(-b*10^(x) + 2*c))), start = list(b=-1, c=-3)))

为什么 geom_smooth nls 和独立的 nls 给出不同的拟合结果？

Why do geom_smooth nls and the standalone nls give different fit results?

r

nls

ggplot2

data-fitting