在R中计算预测均值(或预测概率)和多重补偿后的SE

Question

我想要计算预测值和标准误差，但我不能简单地使用predict()，因为我使用了15个倍数推算的数据集(生成的Amelia包)。我在每个数据集上运行回归模型。然后，使用Amelia函数mi.meld()将结果合并到一组模型系数和标准误差中，该函数使用鲁宾规则。

示例数据和代码：

dd<-list()
for (i in 1:15){
dd[[i]] <- data.frame(
  Age=runif(50,20,90),
  Cat=factor(sample(0:4, 50, replace=T)),
  Outcome = sample(0:1, 50, replace=T)
)}

b.out<-NULL
se.out<-NULL
for(i in 1:15) {
  ols.out<-glm(Outcome~Age+factor(Cat), data=dd[[i]],family="binomial")
  b.out <- rbind(b.out, ols.out$coef)
  se.out <- rbind(se.out, coef(summary(ols.out))[,2])}
mod0 <- mi.meld(q = b.out, se = se.out)

> mod0
$q.mi
     (Intercept)         Age factor(Cat)1 factor(Cat)2 factor(Cat)3 factor(Cat)4
[1,]   0.0466825 -0.00577106    0.5291908  -0.09760264    0.4058684    0.3125109

$se.mi
     (Intercept)        Age factor(Cat)1 factor(Cat)2 factor(Cat)3 
factor(Cat)4
[1,]    1.863276 0.02596468     1.604759     1.398322     1.414589     
1.332743

现在是有问题的部分了。我想要计算以下一组预测值的预测值(在本例中为预测概率)和标准误差：

data.predict <- data.frame(Cat=as.factor(c(0:4)), Age=53.6)
print(data.predict)
  Cat  Age
1   0 53.6
2   1 53.6
3   2 53.6
4   3 53.6
5   4 53.6

如果我在1个数据集上拟合一个模型，我会简单地这样做：

prediction<- predict(mod1, data.predict, type="response",se.fit=T)

但是，我没有模型对象，我只存储了系数。现在我已经研究了两种解决这个问题的方法，第一种是以这种方式手动计算预测：predict() with arbitrary coefficients in r然而我不知道如何获得标准误差。我的另一个想法是创建一个假的模型对象，就像这个函数创建的：https://gist.github.com/MrFlick/ae299d8f3760f02de6bf并在predict()中使用它，但是由于没有使用模型的标准误差，也没有办法计算预测的标准误差。

有没有人有解决这个问题的建议？我已经尝试用示例代码清楚地解释我的问题，但是如果我的问题不是很清楚，请让我知道，这样我就可以提供额外的信息。谢谢你的帮助!

Answer 1

我确信你在近几年后不再需要这个答案，但我刚刚解决了一个类似的问题，我想我应该把答案放在这里留给后人。

Andrew Heiss把这个解决方案放在gisthub上-- https://gist.github.com/andrewheiss/a3134085e92c6607db39c5b14e1b879e

我对它做了一点修改(部分原因是因为我认为，自从他写了这篇文章后，tidyverse中'nest‘的默认行为可能已经改变了?)

代码(辛苦的工作！)几乎完全来自安德鲁·海斯。这里的注释混合了我的和他的。

这是使用Amelia非洲数据集，对于我的实际问题，我有一个不同的数据集(显然)，并且在开始的几个步骤中做了一些不同的事情，这一切都很好。

library(tidyverse)
library(Amelia)
library(broom)

# Use the africa dataset from Amelia
data(africa)
set.seed(1234)
imp_amelia <- amelia(x = africa, m = 5, cs = "country", ts = "year", logs = "gdp_pc", p2s = 0) # do the imputations -- for me, it was fine to do this bit in 'mice'

# Gather all the imputed datasets into one data frame and run a model on each
models_imputed_df <- bind_rows(unclass(imp_amelia$imputations), .id = "m") %>%
  group_by(m) %>%
  nest() %>% 
  mutate(model = data %>% map(~ lm(gdp_pc ~ trade + civlib, data = .)))

# again - for my real life problem the models looked very different to this, and used rms - and this was also totally fine.

models_imputed_df
#> # A tibble: 5 x 3
#>   m     data               model   
#>   <chr> <list>             <list>  
#> 1 imp1  <tibble [120 × 7]> <S3: lm>
#> 2 imp2  <tibble [120 × 7]> <S3: lm>
#> 3 imp3  <tibble [120 × 7]> <S3: lm>
#> 4 imp4  <tibble [120 × 7]> <S3: lm>
#> 5 imp5  <tibble [120 × 7]> <S3: lm>


# We want to see how GDP per capita varies with changes in civil liberties, so
# we create a new data frame with values for each of the covariates in the
# model. We include the full range of civil liberties (from 0 to 1) and the mean
# of trade.

# ie. this is a 'skelton' data frame of all your variables that you want to make predictions over.

new_data <- data_frame(civlib = seq(0, 1, 0.1), 
                       trade = mean(africa$trade, na.rm = TRUE))
new_data
#> # A tibble: 11 x 2
#>    civlib trade
#>     <dbl> <dbl>
#>  1  0.     62.6
#>  2  0.100  62.6
#>  3  0.200  62.6
#>  4  0.300  62.6
#>  5  0.400  62.6
#>  6  0.500  62.6
#>  7  0.600  62.6
#>  8  0.700  62.6
#>  9  0.800  62.6
#> 10  0.900  62.6
#> 11  1.00   62.6

# write a function to meld predictions

meld_predictions <- function(x) {
  # x is a data frame with m rows and two columns:
  #
  # m  .fitted  .se.fit
  # 1  1.05     0.34
  # 2  1.09     0.28
  # x  ...      ...

  # Meld the fitted values using Rubin's rules
  x_melded <- mi.meld(matrix(x$.fitted), matrix(x$.se.fit))

  data_frame(.fitted = as.numeric(x_melded$q.mi),
             .se.fit = as.numeric(x_melded$se.mi))
}

# We augment/predict using new_data in each of the imputed models, then we group
# by each of the values of civil liberties (so each value, like 0.1 and 0.2 has
# 5 values, 1 from each of the imputed models), and then we meld those 5
# predicted values into a single value with meld_predictions()

predict_melded <- data_frame(models = models_imputed_df$model) %>%
  mutate(m = 1:n(),
         fitted = models %>% map(~ augment(., newdata = new_data))) %>% 
  unnest(fitted) %>% 
  dplyr::select(-models) %>% #### I needed to add this row to make the code work, once you've used the models to get the fit you don't need them in the data object anymore.  I took this line out because it was slowing everything down, then realised the code only works with this line... not sure why?
  group_by(civlib) %>%  
  nest(data=c(m, .fitted, .se.fit)) %>%  # needed to change this here from gisthub to make the nested 'data' have all the imputations in it, not just estimates from one of the imputations.
  mutate(fitted_melded = data %>% map(~ meld_predictions(.))) %>% 
  unnest(fitted_melded) %>% 
  mutate(ymin = .fitted + (qnorm(0.025) * .se.fit),
         ymax = .fitted + (qnorm(0.975) * .se.fit))


## NB. this is still on the link scale -- you'd need to write an extra few lines to exponentiate everything and get your predictions and se's on the response scale
# Plot!
ggplot(predict_melded, aes(x = civlib, y = .fitted)) +
  geom_line(color = "blue") +
  geom_ribbon(aes(ymin = ymin, ymax = ymax), alpha = 0.2, fill = "blue")

希望这至少能对其他偶然发现这篇文章的人有所帮助。