how does R handle NA values vs deleted values with regressions - r

Question

Say I have a table and I remove all the inapplicable values and I ran a regression. If I ran the exact same regression on the same table, but this time instead of removing the inapplicable values, I turned them into NA values, would the regression still give me the same coefficients?

Answer 1

The regression would omit any NA values prior to doing the analysis (i.e. deleting any row that contains a missing NA in any of the predictor variables or the outcome variable). You can check this by comparing the degrees of freedom and other statistics for both models.
Here's a toy example:
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))
Comparing the two summaries you can see that they are identical, with the one exception that for the first model, there's a warning message that 5 csaes have been dropped due to missingness, which is exactly what we did manually in our mtcars_NA_omit example.
# 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