Imputing Missing Data with MICE
2023-12-11
MCAR and MAR observations are called ignorable, while MNAR values are called non-ignorable or informative.
Work with the unbalanced data and use the ML or REML method for parameter estimation. This approach works best if all missing values are ignorable. However, for MNAR values, this strategy results in biased estimates.
Delete all incomplete cases, which are the subjects with at least one missing observation. It works best when the number of incomplete cases is not large, and there is no structure to the missing data (they are MCAR observations).
Impute the missing values and work with the resulting complete data set, including mean, last observation, and multiple imputation tech. The resulting parameter estimates are biased (unless that is MCAR).
Imputing Missing Data with MICE
Substitute the means for other variables with missingness, run a regression to get the imputed values for the first variable; next, run a regression for the second variable and imputed using the first variable’s updated values; repeat the above steps until all missing data was imputed by regression; that is the first iterate. repeat the above process by 50 iterates to get the first imputed dataset. repeat the above procedure 5 times to get 5 imputed datasets.
- Data summary
library(mice)##
## Attaching package: 'mice'## The following object is masked from 'package:stats':
##
## filter## The following objects are masked from 'package:base':
##
## cbind, rbinddata <- airquality
summary(data)## Ozone Solar.R Wind Temp
## Min. : 1.00 Min. : 7.0 Min. : 1.700 Min. :56.00
## 1st Qu.: 18.00 1st Qu.:115.8 1st Qu.: 7.400 1st Qu.:72.00
## Median : 31.50 Median :205.0 Median : 9.700 Median :79.00
## Mean : 42.13 Mean :185.9 Mean : 9.958 Mean :77.88
## 3rd Qu.: 63.25 3rd Qu.:258.8 3rd Qu.:11.500 3rd Qu.:85.00
## Max. :168.00 Max. :334.0 Max. :20.700 Max. :97.00
## NA's :37 NA's :7
## Month Day
## Min. :5.000 Min. : 1.0
## 1st Qu.:6.000 1st Qu.: 8.0
## Median :7.000 Median :16.0
## Mean :6.993 Mean :15.8
## 3rd Qu.:8.000 3rd Qu.:23.0
## Max. :9.000 Max. :31.0
## - Take a look at the variable and its distribution
md.pattern(data)
## Wind Temp Month Day Solar.R Ozone
## 111 1 1 1 1 1 1 0
## 35 1 1 1 1 1 0 1
## 5 1 1 1 1 0 1 1
## 2 1 1 1 1 0 0 2
## 0 0 0 0 7 37 44hist(data$Ozone)
- Imputed missing values using simple values
imputed_zero = replace(data$Ozone, is.na(data$Ozone), 0)
imputed_mean = replace(data$Ozone, is.na(data$Ozone), mean(data$Ozone, na.rm = TRUE))
imputed_median = replace(data$Ozone, is.na(data$Ozone), median(data$Ozone, na.rm = TRUE))- Check the distribution again
hist(imputed_zero)
hist(imputed_mean)
hist(imputed_median)
- Imputed missing values by different algorithm methods (MICE)
imputed_pmm = complete(mice(data, method = "pmm",seed=500))$Ozone #default the first imputed dataset##
## iter imp variable
## 1 1 Ozone Solar.R
## 1 2 Ozone Solar.R
## 1 3 Ozone Solar.R
## 1 4 Ozone Solar.R
## 1 5 Ozone Solar.R
## 2 1 Ozone Solar.R
## 2 2 Ozone Solar.R
## 2 3 Ozone Solar.R
## 2 4 Ozone Solar.R
## 2 5 Ozone Solar.R
## 3 1 Ozone Solar.R
## 3 2 Ozone Solar.R
## 3 3 Ozone Solar.R
## 3 4 Ozone Solar.R
## 3 5 Ozone Solar.R
## 4 1 Ozone Solar.R
## 4 2 Ozone Solar.R
## 4 3 Ozone Solar.R
## 4 4 Ozone Solar.R
## 4 5 Ozone Solar.R
## 5 1 Ozone Solar.R
## 5 2 Ozone Solar.R
## 5 3 Ozone Solar.R
## 5 4 Ozone Solar.R
## 5 5 Ozone Solar.Rimputed_cart = complete(mice(data, method = "cart",seed=500))$Ozone##
## iter imp variable
## 1 1 Ozone Solar.R
## 1 2 Ozone Solar.R
## 1 3 Ozone Solar.R
## 1 4 Ozone Solar.R
## 1 5 Ozone Solar.R
## 2 1 Ozone Solar.R
## 2 2 Ozone Solar.R
## 2 3 Ozone Solar.R
## 2 4 Ozone Solar.R
## 2 5 Ozone Solar.R
## 3 1 Ozone Solar.R
## 3 2 Ozone Solar.R
## 3 3 Ozone Solar.R
## 3 4 Ozone Solar.R
## 3 5 Ozone Solar.R
## 4 1 Ozone Solar.R
## 4 2 Ozone Solar.R
## 4 3 Ozone Solar.R
## 4 4 Ozone Solar.R
## 4 5 Ozone Solar.R
## 5 1 Ozone Solar.R
## 5 2 Ozone Solar.R
## 5 3 Ozone Solar.R
## 5 4 Ozone Solar.R
## 5 5 Ozone Solar.Rimputed_lasso = complete(mice(data, method = "lasso.norm",seed=500))$Ozone##
## iter imp variable
## 1 1 Ozone Solar.R
## 1 2 Ozone Solar.R
## 1 3 Ozone Solar.R
## 1 4 Ozone Solar.R
## 1 5 Ozone Solar.R
## 2 1 Ozone Solar.R
## 2 2 Ozone Solar.R
## 2 3 Ozone Solar.R
## 2 4 Ozone Solar.R
## 2 5 Ozone Solar.R
## 3 1 Ozone Solar.R
## 3 2 Ozone Solar.R
## 3 3 Ozone Solar.R
## 3 4 Ozone Solar.R
## 3 5 Ozone Solar.R
## 4 1 Ozone Solar.R
## 4 2 Ozone Solar.R
## 4 3 Ozone Solar.R
## 4 4 Ozone Solar.R
## 4 5 Ozone Solar.R
## 5 1 Ozone Solar.R
## 5 2 Ozone Solar.R
## 5 3 Ozone Solar.R
## 5 4 Ozone Solar.R
## 5 5 Ozone Solar.Rlasso is different with other two
- Check the distribution again
hist(data$Ozone)
hist(imputed_pmm)
hist(imputed_cart)
hist(imputed_lasso)
- Imputing the missing data using MICE
tempData <- mice(data,m=5,maxit=50,meth='pmm',seed=500) #m=5 refers to the number of imputed datasets.##
## iter imp variable
## 1 1 Ozone Solar.R
## 1 2 Ozone Solar.R
## 1 3 Ozone Solar.R
## 1 4 Ozone Solar.R
## 1 5 Ozone Solar.R
## 2 1 Ozone Solar.R
## 2 2 Ozone Solar.R
## 2 3 Ozone Solar.R
## 2 4 Ozone Solar.R
## 2 5 Ozone Solar.R
## 3 1 Ozone Solar.R
## 3 2 Ozone Solar.R
## 3 3 Ozone Solar.R
## 3 4 Ozone Solar.R
## 3 5 Ozone Solar.R
## 4 1 Ozone Solar.R
## 4 2 Ozone Solar.R
## 4 3 Ozone Solar.R
## 4 4 Ozone Solar.R
## 4 5 Ozone Solar.R
## 5 1 Ozone Solar.R
## 5 2 Ozone Solar.R
## 5 3 Ozone Solar.R
## 5 4 Ozone Solar.R
## 5 5 Ozone Solar.R
## 6 1 Ozone Solar.R
## 6 2 Ozone Solar.R
## 6 3 Ozone Solar.R
## 6 4 Ozone Solar.R
## 6 5 Ozone Solar.R
## 7 1 Ozone Solar.R
## 7 2 Ozone Solar.R
## 7 3 Ozone Solar.R
## 7 4 Ozone Solar.R
## 7 5 Ozone Solar.R
## 8 1 Ozone Solar.R
## 8 2 Ozone Solar.R
## 8 3 Ozone Solar.R
## 8 4 Ozone Solar.R
## 8 5 Ozone Solar.R
## 9 1 Ozone Solar.R
## 9 2 Ozone Solar.R
## 9 3 Ozone Solar.R
## 9 4 Ozone Solar.R
## 9 5 Ozone Solar.R
## 10 1 Ozone Solar.R
## 10 2 Ozone Solar.R
## 10 3 Ozone Solar.R
## 10 4 Ozone Solar.R
## 10 5 Ozone Solar.R
## 11 1 Ozone Solar.R
## 11 2 Ozone Solar.R
## 11 3 Ozone Solar.R
## 11 4 Ozone Solar.R
## 11 5 Ozone Solar.R
## 12 1 Ozone Solar.R
## 12 2 Ozone Solar.R
## 12 3 Ozone Solar.R
## 12 4 Ozone Solar.R
## 12 5 Ozone Solar.R
## 13 1 Ozone Solar.R
## 13 2 Ozone Solar.R
## 13 3 Ozone Solar.R
## 13 4 Ozone Solar.R
## 13 5 Ozone Solar.R
## 14 1 Ozone Solar.R
## 14 2 Ozone Solar.R
## 14 3 Ozone Solar.R
## 14 4 Ozone Solar.R
## 14 5 Ozone Solar.R
## 15 1 Ozone Solar.R
## 15 2 Ozone Solar.R
## 15 3 Ozone Solar.R
## 15 4 Ozone Solar.R
## 15 5 Ozone Solar.R
## 16 1 Ozone Solar.R
## 16 2 Ozone Solar.R
## 16 3 Ozone Solar.R
## 16 4 Ozone Solar.R
## 16 5 Ozone Solar.R
## 17 1 Ozone Solar.R
## 17 2 Ozone Solar.R
## 17 3 Ozone Solar.R
## 17 4 Ozone Solar.R
## 17 5 Ozone Solar.R
## 18 1 Ozone Solar.R
## 18 2 Ozone Solar.R
## 18 3 Ozone Solar.R
## 18 4 Ozone Solar.R
## 18 5 Ozone Solar.R
## 19 1 Ozone Solar.R
## 19 2 Ozone Solar.R
## 19 3 Ozone Solar.R
## 19 4 Ozone Solar.R
## 19 5 Ozone Solar.R
## 20 1 Ozone Solar.R
## 20 2 Ozone Solar.R
## 20 3 Ozone Solar.R
## 20 4 Ozone Solar.R
## 20 5 Ozone Solar.R
## 21 1 Ozone Solar.R
## 21 2 Ozone Solar.R
## 21 3 Ozone Solar.R
## 21 4 Ozone Solar.R
## 21 5 Ozone Solar.R
## 22 1 Ozone Solar.R
## 22 2 Ozone Solar.R
## 22 3 Ozone Solar.R
## 22 4 Ozone Solar.R
## 22 5 Ozone Solar.R
## 23 1 Ozone Solar.R
## 23 2 Ozone Solar.R
## 23 3 Ozone Solar.R
## 23 4 Ozone Solar.R
## 23 5 Ozone Solar.R
## 24 1 Ozone Solar.R
## 24 2 Ozone Solar.R
## 24 3 Ozone Solar.R
## 24 4 Ozone Solar.R
## 24 5 Ozone Solar.R
## 25 1 Ozone Solar.R
## 25 2 Ozone Solar.R
## 25 3 Ozone Solar.R
## 25 4 Ozone Solar.R
## 25 5 Ozone Solar.R
## 26 1 Ozone Solar.R
## 26 2 Ozone Solar.R
## 26 3 Ozone Solar.R
## 26 4 Ozone Solar.R
## 26 5 Ozone Solar.R
## 27 1 Ozone Solar.R
## 27 2 Ozone Solar.R
## 27 3 Ozone Solar.R
## 27 4 Ozone Solar.R
## 27 5 Ozone Solar.R
## 28 1 Ozone Solar.R
## 28 2 Ozone Solar.R
## 28 3 Ozone Solar.R
## 28 4 Ozone Solar.R
## 28 5 Ozone Solar.R
## 29 1 Ozone Solar.R
## 29 2 Ozone Solar.R
## 29 3 Ozone Solar.R
## 29 4 Ozone Solar.R
## 29 5 Ozone Solar.R
## 30 1 Ozone Solar.R
## 30 2 Ozone Solar.R
## 30 3 Ozone Solar.R
## 30 4 Ozone Solar.R
## 30 5 Ozone Solar.R
## 31 1 Ozone Solar.R
## 31 2 Ozone Solar.R
## 31 3 Ozone Solar.R
## 31 4 Ozone Solar.R
## 31 5 Ozone Solar.R
## 32 1 Ozone Solar.R
## 32 2 Ozone Solar.R
## 32 3 Ozone Solar.R
## 32 4 Ozone Solar.R
## 32 5 Ozone Solar.R
## 33 1 Ozone Solar.R
## 33 2 Ozone Solar.R
## 33 3 Ozone Solar.R
## 33 4 Ozone Solar.R
## 33 5 Ozone Solar.R
## 34 1 Ozone Solar.R
## 34 2 Ozone Solar.R
## 34 3 Ozone Solar.R
## 34 4 Ozone Solar.R
## 34 5 Ozone Solar.R
## 35 1 Ozone Solar.R
## 35 2 Ozone Solar.R
## 35 3 Ozone Solar.R
## 35 4 Ozone Solar.R
## 35 5 Ozone Solar.R
## 36 1 Ozone Solar.R
## 36 2 Ozone Solar.R
## 36 3 Ozone Solar.R
## 36 4 Ozone Solar.R
## 36 5 Ozone Solar.R
## 37 1 Ozone Solar.R
## 37 2 Ozone Solar.R
## 37 3 Ozone Solar.R
## 37 4 Ozone Solar.R
## 37 5 Ozone Solar.R
## 38 1 Ozone Solar.R
## 38 2 Ozone Solar.R
## 38 3 Ozone Solar.R
## 38 4 Ozone Solar.R
## 38 5 Ozone Solar.R
## 39 1 Ozone Solar.R
## 39 2 Ozone Solar.R
## 39 3 Ozone Solar.R
## 39 4 Ozone Solar.R
## 39 5 Ozone Solar.R
## 40 1 Ozone Solar.R
## 40 2 Ozone Solar.R
## 40 3 Ozone Solar.R
## 40 4 Ozone Solar.R
## 40 5 Ozone Solar.R
## 41 1 Ozone Solar.R
## 41 2 Ozone Solar.R
## 41 3 Ozone Solar.R
## 41 4 Ozone Solar.R
## 41 5 Ozone Solar.R
## 42 1 Ozone Solar.R
## 42 2 Ozone Solar.R
## 42 3 Ozone Solar.R
## 42 4 Ozone Solar.R
## 42 5 Ozone Solar.R
## 43 1 Ozone Solar.R
## 43 2 Ozone Solar.R
## 43 3 Ozone Solar.R
## 43 4 Ozone Solar.R
## 43 5 Ozone Solar.R
## 44 1 Ozone Solar.R
## 44 2 Ozone Solar.R
## 44 3 Ozone Solar.R
## 44 4 Ozone Solar.R
## 44 5 Ozone Solar.R
## 45 1 Ozone Solar.R
## 45 2 Ozone Solar.R
## 45 3 Ozone Solar.R
## 45 4 Ozone Solar.R
## 45 5 Ozone Solar.R
## 46 1 Ozone Solar.R
## 46 2 Ozone Solar.R
## 46 3 Ozone Solar.R
## 46 4 Ozone Solar.R
## 46 5 Ozone Solar.R
## 47 1 Ozone Solar.R
## 47 2 Ozone Solar.R
## 47 3 Ozone Solar.R
## 47 4 Ozone Solar.R
## 47 5 Ozone Solar.R
## 48 1 Ozone Solar.R
## 48 2 Ozone Solar.R
## 48 3 Ozone Solar.R
## 48 4 Ozone Solar.R
## 48 5 Ozone Solar.R
## 49 1 Ozone Solar.R
## 49 2 Ozone Solar.R
## 49 3 Ozone Solar.R
## 49 4 Ozone Solar.R
## 49 5 Ozone Solar.R
## 50 1 Ozone Solar.R
## 50 2 Ozone Solar.R
## 50 3 Ozone Solar.R
## 50 4 Ozone Solar.R
## 50 5 Ozone Solar.Rsummary(tempData)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## Ozone Solar.R Wind Temp Month Day
## "pmm" "pmm" "" "" "" ""
## PredictorMatrix:
## Ozone Solar.R Wind Temp Month Day
## Ozone 0 1 1 1 1 1
## Solar.R 1 0 1 1 1 1
## Wind 1 1 0 1 1 1
## Temp 1 1 1 0 1 1
## Month 1 1 1 1 0 1
## Day 1 1 1 1 1 0tempData$imp$Ozone## 1 2 3 4 5
## 5 14 8 6 19 8
## 10 11 20 20 18 44
## 25 8 18 19 19 18
## 26 13 13 37 37 13
## 27 37 13 12 11 21
## 32 59 40 44 47 45
## 33 30 59 13 45 36
## 34 37 32 37 32 1
## 35 63 20 89 35 40
## 36 59 89 39 78 89
## 37 36 16 30 16 41
## 39 61 79 97 50 82
## 42 50 115 77 61 78
## 43 79 50 76 91 79
## 45 45 46 45 28 45
## 46 52 47 35 63 46
## 52 35 59 96 59 35
## 53 48 39 78 39 96
## 54 40 49 110 89 49
## 55 59 64 110 78 39
## 56 28 45 59 44 52
## 57 47 16 48 16 47
## 58 23 21 39 41 30
## 59 52 44 35 16 28
## 60 21 23 23 9 21
## 61 96 48 79 39 110
## 65 36 16 29 23 23
## 72 46 28 35 32 32
## 75 48 40 37 35 48
## 83 49 49 48 71 78
## 84 35 59 59 49 71
## 102 61 85 82 61 82
## 103 28 31 20 45 35
## 107 41 14 16 21 23
## 115 36 13 20 16 23
## 119 66 61 97 79 122
## 150 41 21 36 21 11- Get back a completed dataset
completedData <- complete(tempData,1)
# completed <- complete(tempData) - Inspecting the distribution of original and imputed data
xyplot(tempData,Ozone ~ Wind+Temp+Solar.R,pch=18,cex=1) #?
densityplot(tempData)
- Pooling the results
modelFit1 <- with(tempData,lm(Temp~ Ozone+Solar.R+Wind))
summary(pool(modelFit1))## term estimate std.error statistic df p.value
## 1 (Intercept) 72.401478102 2.901648707 24.9518413 107.46161 1.620476e-46
## 2 Ozone 0.172964671 0.026685861 6.4815099 59.50153 1.963992e-08
## 3 Solar.R 0.007473364 0.007686916 0.9722187 47.48152 3.358687e-01
## 4 Wind -0.329208428 0.207845499 -1.5839093 131.96400 1.156080e-01Using logistic regression to indentify if it is missing completely at random;
How well is your imputation working? Remove all missing rows; Run statistics on your dataset from #1;Randomly remove values from your dataset; Impute values, calculate statistics, and compare to #2; Repeat steps 3 and 4 with many different removed values + imputation methods;