如何獲取R中GLM中二次項的頂點值？

Question

我在 GLM 中有一個二次項，我對二次項的頂點值（+ 頂點的標准誤差和置信區間）感興趣。 據我所知，在 R 中沒有用於此目的的自動 function，我無法手動計算，因為我沒有足夠的統計知識和 ZE1E1D3D40573127E9EE0480CAF1283D。 有沒有人可以幫助並構建代碼以獲取感興趣的值？

GLM <- glm(Y ~ X1 + I(X1^2) + X2 + X3 + X4 + X5, family="binomial", data=DF)

帶有來自 Stata 的代碼的所需 output 示例

Answer 1

除了警告，因為我不習慣為這些類型的問題模擬數據。 這是一個基於 Bonferroni CI 參數的帶有 CI 的頂點。 由於我們需要兩個參數，我們需要調整兩個 CI 的乘積，使得x^2=1-alpha -> x=(1-alpha)^(1/2)

set.seed(1)
library(dplyr, warn.conflicts = F)
library(ggplot2, warn.conflicts = F)
logit_trans <- function(x) 1/(1/exp(x)+1)

sim_data <- tibble(
  x = rep(seq(0,20,.1), 10),
  y = round(logit_trans(20 - 8*x + .4*x^2 + rnorm(2010, 0, 1)))
)

model <- glm(
  y ~ x + I(x^2),
  binomial(),
  sim_data
)
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

find_vertex <- function(model_pars){
  a <- model_pars[2]
  b <- model_pars[3]
  if(2*b>0){ #Check second deriv.
    -a/(2*b)
  } else{ # concave down
    NA
  }
}

ci_vertex <- function(model){
  mean_vertex <- model %>% 
    coef() %>% 
    find_vertex()
  ci <- model %>% 
    confint(parm = 2:3, level = (1-.05)^(1/2))
  lower_ci <- ci %>% 
    magrittr::extract(,1) %>% 
    c(0, .) %>% 
    find_vertex()
  upper_ci <- ci %>% 
    magrittr::extract(,2) %>% 
    c(0, .) %>% 
    find_vertex()
  list(
    lower_ci = lower_ci,
    mean_vertex = mean_vertex,
    upper_ci = upper_ci
  )
}

ci <- ci_vertex(model)
#> Waiting for profiling to be done...
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

sim_data %>% 
  mutate(
    x2 = x^2,
    y_expected = logit_trans(c(matrix(c(rep(1, n()), x, x2), ncol = 3) %*% matrix(coef(model))))
  ) %>% 
  ggplot(aes(x, y_expected)) + 
  geom_point() +
  geom_line() +
  geom_vline(xintercept = ci$lower_ci, color = 'red', linetype = 'dashed') +
  geom_vline(xintercept = ci$upper_ci, color = 'red', linetype = 'dashed') +
  geom_vline(xintercept = ci$mean_vertex, color = 'red')

^{由reprex package (v2.0.1) 於 2022 年 8 月 19 日創建}

正如我們對y的輸入 function 所期望的那樣，平均頂點幾乎正好是10 。 由於某種原因，上下 CI 是倒置的，下一個比預期的稍大。 我猜這是由於 model 無法識別。