r - R 如何通过回归处理 NA 值与删除的值

Question

假设我有一张表，我删除了所有不适用的值，然后进行了回归。如果我在同一张表上运行完全相同的回归，但这次不是删除不适用的值，而是将它们转换为 NA 值，回归是否仍会给出相同的系数？

Answer 1

在进行分析之前，回归将忽略任何 NA 值(即删除任何包含任何预测变量或结果变量中缺失 NA 的行)。您可以通过比较两个模型的自由度和其他统计数据来检查这一点。
这是一个玩具示例:

head(mtcars)

# check the data set size (all non-missings)
dim(mtcars) # has 32 rows

# Introduce some missings
set.seed(5)
mtcars[sample(1:nrow(mtcars), 5), sample(1:ncol(mtcars), 5)] <- NA

head(mtcars)

# Create an alternative where all missings are omitted
mtcars_NA_omit <- na.omit(mtcars)

# Check the data set size again
dim(mtcars_NA_omit) # Now only has 27 rows

# Now compare some simple linear regressions
summary(lm(mpg ~ cyl + hp + am + gear, data = mtcars))
summary(lm(mpg ~ cyl + hp + am + gear, data = mtcars_NA_omit))

比较这两个摘要，您可以看到它们是相同的，唯一的异常(exception)是对于第一个模型，有一条警告消息表明 5 个 csaes 由于缺失而被丢弃，这正是我们在 mtcars_NA_omit 中手动执行的操作。例子。

# First, original model

Call:
lm(formula = mpg ~ cyl + hp + am + gear, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0835 -1.7594 -0.2023  1.4313  5.6948 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 29.64284    7.02359   4.220 0.000352 ***
cyl         -1.04494    0.83565  -1.250 0.224275    
hp          -0.03913    0.01918  -2.040 0.053525 .  
am           4.02895    1.90342   2.117 0.045832 *  
gear         0.31413    1.48881   0.211 0.834833    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.947 on 22 degrees of freedom
  (5 observations deleted due to missingness)
Multiple R-squared:  0.7998,    Adjusted R-squared:  0.7635 
F-statistic: 21.98 on 4 and 22 DF,  p-value: 2.023e-07

# Second model where we dropped missings manually    

Call:
lm(formula = mpg ~ cyl + hp + am + gear, data = mtcars_NA_omit)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0835 -1.7594 -0.2023  1.4313  5.6948 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 29.64284    7.02359   4.220 0.000352 ***
cyl         -1.04494    0.83565  -1.250 0.224275    
hp          -0.03913    0.01918  -2.040 0.053525 .  
am           4.02895    1.90342   2.117 0.045832 *  
gear         0.31413    1.48881   0.211 0.834833    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.947 on 22 degrees of freedom
Multiple R-squared:  0.7998,    Adjusted R-squared:  0.7635 
F-statistic: 21.98 on 4 and 22 DF,  p-value: 2.023e-07