Multiple imputation with regression is one step further from mean imputation (i.e. by a single value: the average of observed). In the case for continuous, normally distributed variable, linear regression can use information from other variables hence could be closer to the true missing values.
Imputation with mice
mice is a powerful R package developed by Stef van Buuren, Karin Groothuis-Oudshoorn and other contributors. Regression methods (continuous, normal outcome) are implemented in mice with methods starting with norm.
Here I use the small dataset nhanes included in mice package. It has 25 rows, and three out of four variables have missings.
The original NHANES data is a large national level survey, some are publicly available via R package nhanes.
library(mice)
Attaching package: 'mice'
The following object is masked from 'package:stats':
filter
The following objects are masked from 'package:base':
cbind, rbind
# load example dataset from micehead(nhanes)
age bmi hyp chl
1 1 NA NA NA
2 2 22.7 1 187
3 1 NA 1 187
4 3 NA NA NA
5 1 20.4 1 113
6 3 NA NA 184
summary(nhanes)
age bmi hyp chl
Min. :1.00 Min. :20.40 Min. :1.000 Min. :113.0
1st Qu.:1.00 1st Qu.:22.65 1st Qu.:1.000 1st Qu.:185.0
Median :2.00 Median :26.75 Median :1.000 Median :187.0
Mean :1.76 Mean :26.56 Mean :1.235 Mean :191.4
3rd Qu.:2.00 3rd Qu.:28.93 3rd Qu.:1.000 3rd Qu.:212.0
Max. :3.00 Max. :35.30 Max. :2.000 Max. :284.0
NA's :9 NA's :8 NA's :10
Examine missing pattern with md.pattern(data).
# 27 missing in total# by col: 8 for hyp, 9 for bmi, 10 for chl# by row: n missing numbersmd.pattern(nhanes)
We can also specify which imputed dataset to use as our complete data. Set index to 0 (action = 0) returns the original dataset with missing values.
Here we check which of the imputed data is being used as the completed dataset. First take a note of the row IDs (based on bmi, for example). Then we generate completed dataset.
if no action argument is set, then it returns the first imputation by default
action=0 corresponds to the original data with missing values
# check which imputed data is used for the final result, take note of row idid_missing <-which(is.na(nhanes$bmi))id_missing
[1] 1 3 4 6 10 11 12 16 21
nhanes_impr0_action0 <-complete(impr0, action =0) nhanes_impr0_action0[id_missing, ] # original data with missing bmi
age bmi hyp chl
1 1 NA NA NA
3 1 NA 1 187
4 3 NA NA NA
6 3 NA NA 184
10 2 NA NA NA
11 1 NA NA NA
12 2 NA NA NA
16 1 NA NA NA
21 1 NA NA NA
nhanes_impr0_action1 <-complete(impr0, action =1) nhanes_impr0_action1[id_missing, ] # using first imputation
Stef van Buuren, Karin Groothuis-Oudshoorn (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. DOI 10.18637/jss.v045.i03
