Rmarkdown: Missing Data
Wenyue Ma
Introduction
Welcome to this R demo session! Here, I will demonstrate how to use R to deal with missing data.
Missing data can be a not so trivial problem when analysing a dataset and accounting for it is usually not so straightforward either.
If the amount of missing data is very small relatively to the size of the dataset, then leaving out the few samples with missing features may be the best strategy in order not to bias the analysis, however leaving out available datapoints deprives the data of some amount of information and depending on the situation you face, you may want to look for other fixes before wiping out potentially useful datapoints from your dataset.
While some quick fixes such as mean-substitution may be fine in some cases, such simple approaches usually introduce bias into the data, for instance, applying mean substitution leaves the mean unchanged (which is desirable) but decreases variance, which may be undesirable.
The mice package in R, helps you imputing missing values
with plausible data values. These plausible values are drawn from a
distribution specifically designed for each missing datapoint.
In this rmarkdown we are going to impute missing values using the
airquality dataset (available in R). For the purpose of the
demonstration I am going to remove some datapoints from the dataset.
data <- airquality
# Examine the data
head(data)## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6# Remove some datapoints
data[4:10,3] <- rep(NA,7)
data[1:5,4] <- NAAs far as categorical variables are concerned, replacing categorical
variables is usually not advisable. Some common practice include
replacing missing categorical variables with the mode of the observed
ones, however, it is questionable whether it is a good choice. Even
though in this case no datapoints are missing from the categorical
variables, we remove them from our dataset (we can add them back later
if needed) and take a look at the data using summary().
data <- data[-c(5,6)]
summary(data)## Ozone Solar.R Wind Temp
## Min. : 1.00 Min. : 7.0 Min. : 1.700 Min. :57.00
## 1st Qu.: 18.00 1st Qu.:115.8 1st Qu.: 7.400 1st Qu.:73.00
## Median : 31.50 Median :205.0 Median : 9.700 Median :79.00
## Mean : 42.13 Mean :185.9 Mean : 9.806 Mean :78.28
## 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 NA's :7 NA's :5Apparently Ozone is the variable with the most missing datapoints. Below we are going to dig deeper into the missing data patterns.
Quick classification of missing data
As we learned in class lectures, there are three types of missing data:
- MCAR (missing completely at random): The desirable scenario although often not the case for our data.
- MAR (missing at random):
- MNAR (missing not at random): This is a more serious issue and in this case it might be wise to check the data gathering process further and try to understand why the information is missing. For instance, if most of the people in a survey did not answer a certain question, why did they do that? Was the question unclear?
Assuming data is MCAR, too much missing data can be a problem too. Usually a safe maximum threshold is 5% of the total for large datasets. If missing data for a certain feature or sample is more than 5% then you probably should leave that feature or sample out. We therefore check for features (columns) and samples (rows) where more than 5% of the data is missing using a simple function.
pMiss <- function(x){sum(is.na(x))/length(x)*100}
apply(data,2,pMiss)## Ozone Solar.R Wind Temp
## 24.183007 4.575163 4.575163 3.267974apply(data,1,pMiss)## [1] 25 25 25 50 100 50 25 25 25 50 25 0 0 0 0 0 0 0
## [19] 0 0 0 0 0 0 25 25 50 0 0 0 0 25 25 25 25 25
## [37] 25 0 25 0 0 25 25 0 25 25 0 0 0 0 0 25 25 25
## [55] 25 25 25 25 25 25 25 0 0 0 25 0 0 0 0 0 0 25
## [73] 0 0 25 0 0 0 0 0 0 0 25 25 0 0 0 0 0 0
## [91] 0 0 0 0 0 25 25 25 0 0 0 25 25 0 0 0 25 0
## [109] 0 0 0 0 0 0 25 0 0 0 25 0 0 0 0 0 0 0
## [127] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [145] 0 0 0 0 0 25 0 0 0We see that Ozone is missing almost 25% of the datapoints. The other variables are below the 5% threshold.
Using mice for looking at missing data pattern
The mice package provides a nice function
md.pattern() to get a better understanding of the pattern
of missing data
library(mice)##
## Attaching package: 'mice'## The following object is masked from 'package:stats':
##
## filter## The following objects are masked from 'package:base':
##
## cbind, rbindmd.pattern(data)
## Temp Solar.R Wind Ozone
## 104 1 1 1 1 0
## 34 1 1 1 0 1
## 3 1 1 0 1 1
## 1 1 1 0 0 2
## 4 1 0 1 1 1
## 1 1 0 1 0 2
## 1 1 0 0 1 2
## 3 0 1 1 1 1
## 1 0 1 0 1 2
## 1 0 0 0 0 4
## 5 7 7 37 56The output tells us that 104 samples are complete, 34 samples miss
only the Ozone measurement, 4 samples miss only the Solar.R
value and so on.
The accompanied plot also contains some useful information:
- Each column represents a variable in your dataset (Temp, Solar.R, Wind, Ozone).
- Each row represents a unique pattern of missingness, where the blue squares indicate observed (non-missing) values and the red squares indicate missing values.
- The numbers on the left side show how many cases (rows in your dataset) have the corresponding pattern of missingness.
- The numbers at the bottom show how many missing values there are for each variable.
A perhaps more helpful visual representation can be obtained using
the VIM package as follows
library(VIM)## Loading required package: colorspace## Loading required package: grid## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleepaggr_plot <- aggr(data, col=c('navyblue','red'), numbers=TRUE, sortVars=TRUE, labels=names(data), cex.axis=.7, gap=3, ylab=c("Histogram of missing data","Pattern"))
##
## Variables sorted by number of missings:
## Variable Count
## Ozone 0.24183007
## Solar.R 0.04575163
## Wind 0.04575163
## Temp 0.03267974The plot helps us understanding that almost 70% of the samples are not missing any information, 22% are missing the Ozone value, and the remaining ones show other missing patterns. Through this approach the situation looks a bit clearer in my opinion.
Another (hopefully) helpful visual approach is a special box plot.
marginplot(data[c(1,2)])
Obviously here we are constrained at plotting 2 variables at a time only, but nevertheless we can gather some interesting insights.
The red box plot on the left shows the distribution of Solar.R with Ozone missing while the blue box plot shows the distribution of the remaining datapoints. Likewhise for the Ozone box plots at the bottom of the graph.
If our assumption of MCAR data is correct, then we expect the red and blue box plots to be very similar.
Imputing the missing data
The mice() function takes care of the imputing
process
tempData <- mice(data,m=5,maxit=50,meth='pmm',seed=500)##
## iter imp variable
## 1 1 Ozone Solar.R Wind Temp
## 1 2 Ozone Solar.R Wind Temp
## 1 3 Ozone Solar.R Wind Temp
## 1 4 Ozone Solar.R Wind Temp
## 1 5 Ozone Solar.R Wind Temp
## 2 1 Ozone Solar.R Wind Temp
## 2 2 Ozone Solar.R Wind Temp
## 2 3 Ozone Solar.R Wind Temp
## 2 4 Ozone Solar.R Wind Temp
## 2 5 Ozone Solar.R Wind Temp
## 3 1 Ozone Solar.R Wind Temp
## 3 2 Ozone Solar.R Wind Temp
## 3 3 Ozone Solar.R Wind Temp
## 3 4 Ozone Solar.R Wind Temp
## 3 5 Ozone Solar.R Wind Temp
## 4 1 Ozone Solar.R Wind Temp
## 4 2 Ozone Solar.R Wind Temp
## 4 3 Ozone Solar.R Wind Temp
## 4 4 Ozone Solar.R Wind Temp
## 4 5 Ozone Solar.R Wind Temp
## 5 1 Ozone Solar.R Wind Temp
## 5 2 Ozone Solar.R Wind Temp
## 5 3 Ozone Solar.R Wind Temp
## 5 4 Ozone Solar.R Wind Temp
## 5 5 Ozone Solar.R Wind Temp
## 6 1 Ozone Solar.R Wind Temp
## 6 2 Ozone Solar.R Wind Temp
## 6 3 Ozone Solar.R Wind Temp
## 6 4 Ozone Solar.R Wind Temp
## 6 5 Ozone Solar.R Wind Temp
## 7 1 Ozone Solar.R Wind Temp
## 7 2 Ozone Solar.R Wind Temp
## 7 3 Ozone Solar.R Wind Temp
## 7 4 Ozone Solar.R Wind Temp
## 7 5 Ozone Solar.R Wind Temp
## 8 1 Ozone Solar.R Wind Temp
## 8 2 Ozone Solar.R Wind Temp
## 8 3 Ozone Solar.R Wind Temp
## 8 4 Ozone Solar.R Wind Temp
## 8 5 Ozone Solar.R Wind Temp
## 9 1 Ozone Solar.R Wind Temp
## 9 2 Ozone Solar.R Wind Temp
## 9 3 Ozone Solar.R Wind Temp
## 9 4 Ozone Solar.R Wind Temp
## 9 5 Ozone Solar.R Wind Temp
## 10 1 Ozone Solar.R Wind Temp
## 10 2 Ozone Solar.R Wind Temp
## 10 3 Ozone Solar.R Wind Temp
## 10 4 Ozone Solar.R Wind Temp
## 10 5 Ozone Solar.R Wind Temp
## 11 1 Ozone Solar.R Wind Temp
## 11 2 Ozone Solar.R Wind Temp
## 11 3 Ozone Solar.R Wind Temp
## 11 4 Ozone Solar.R Wind Temp
## 11 5 Ozone Solar.R Wind Temp
## 12 1 Ozone Solar.R Wind Temp
## 12 2 Ozone Solar.R Wind Temp
## 12 3 Ozone Solar.R Wind Temp
## 12 4 Ozone Solar.R Wind Temp
## 12 5 Ozone Solar.R Wind Temp
## 13 1 Ozone Solar.R Wind Temp
## 13 2 Ozone Solar.R Wind Temp
## 13 3 Ozone Solar.R Wind Temp
## 13 4 Ozone Solar.R Wind Temp
## 13 5 Ozone Solar.R Wind Temp
## 14 1 Ozone Solar.R Wind Temp
## 14 2 Ozone Solar.R Wind Temp
## 14 3 Ozone Solar.R Wind Temp
## 14 4 Ozone Solar.R Wind Temp
## 14 5 Ozone Solar.R Wind Temp
## 15 1 Ozone Solar.R Wind Temp
## 15 2 Ozone Solar.R Wind Temp
## 15 3 Ozone Solar.R Wind Temp
## 15 4 Ozone Solar.R Wind Temp
## 15 5 Ozone Solar.R Wind Temp
## 16 1 Ozone Solar.R Wind Temp
## 16 2 Ozone Solar.R Wind Temp
## 16 3 Ozone Solar.R Wind Temp
## 16 4 Ozone Solar.R Wind Temp
## 16 5 Ozone Solar.R Wind Temp
## 17 1 Ozone Solar.R Wind Temp
## 17 2 Ozone Solar.R Wind Temp
## 17 3 Ozone Solar.R Wind Temp
## 17 4 Ozone Solar.R Wind Temp
## 17 5 Ozone Solar.R Wind Temp
## 18 1 Ozone Solar.R Wind Temp
## 18 2 Ozone Solar.R Wind Temp
## 18 3 Ozone Solar.R Wind Temp
## 18 4 Ozone Solar.R Wind Temp
## 18 5 Ozone Solar.R Wind Temp
## 19 1 Ozone Solar.R Wind Temp
## 19 2 Ozone Solar.R Wind Temp
## 19 3 Ozone Solar.R Wind Temp
## 19 4 Ozone Solar.R Wind Temp
## 19 5 Ozone Solar.R Wind Temp
## 20 1 Ozone Solar.R Wind Temp
## 20 2 Ozone Solar.R Wind Temp
## 20 3 Ozone Solar.R Wind Temp
## 20 4 Ozone Solar.R Wind Temp
## 20 5 Ozone Solar.R Wind Temp
## 21 1 Ozone Solar.R Wind Temp
## 21 2 Ozone Solar.R Wind Temp
## 21 3 Ozone Solar.R Wind Temp
## 21 4 Ozone Solar.R Wind Temp
## 21 5 Ozone Solar.R Wind Temp
## 22 1 Ozone Solar.R Wind Temp
## 22 2 Ozone Solar.R Wind Temp
## 22 3 Ozone Solar.R Wind Temp
## 22 4 Ozone Solar.R Wind Temp
## 22 5 Ozone Solar.R Wind Temp
## 23 1 Ozone Solar.R Wind Temp
## 23 2 Ozone Solar.R Wind Temp
## 23 3 Ozone Solar.R Wind Temp
## 23 4 Ozone Solar.R Wind Temp
## 23 5 Ozone Solar.R Wind Temp
## 24 1 Ozone Solar.R Wind Temp
## 24 2 Ozone Solar.R Wind Temp
## 24 3 Ozone Solar.R Wind Temp
## 24 4 Ozone Solar.R Wind Temp
## 24 5 Ozone Solar.R Wind Temp
## 25 1 Ozone Solar.R Wind Temp
## 25 2 Ozone Solar.R Wind Temp
## 25 3 Ozone Solar.R Wind Temp
## 25 4 Ozone Solar.R Wind Temp
## 25 5 Ozone Solar.R Wind Temp
## 26 1 Ozone Solar.R Wind Temp
## 26 2 Ozone Solar.R Wind Temp
## 26 3 Ozone Solar.R Wind Temp
## 26 4 Ozone Solar.R Wind Temp
## 26 5 Ozone Solar.R Wind Temp
## 27 1 Ozone Solar.R Wind Temp
## 27 2 Ozone Solar.R Wind Temp
## 27 3 Ozone Solar.R Wind Temp
## 27 4 Ozone Solar.R Wind Temp
## 27 5 Ozone Solar.R Wind Temp
## 28 1 Ozone Solar.R Wind Temp
## 28 2 Ozone Solar.R Wind Temp
## 28 3 Ozone Solar.R Wind Temp
## 28 4 Ozone Solar.R Wind Temp
## 28 5 Ozone Solar.R Wind Temp
## 29 1 Ozone Solar.R Wind Temp
## 29 2 Ozone Solar.R Wind Temp
## 29 3 Ozone Solar.R Wind Temp
## 29 4 Ozone Solar.R Wind Temp
## 29 5 Ozone Solar.R Wind Temp
## 30 1 Ozone Solar.R Wind Temp
## 30 2 Ozone Solar.R Wind Temp
## 30 3 Ozone Solar.R Wind Temp
## 30 4 Ozone Solar.R Wind Temp
## 30 5 Ozone Solar.R Wind Temp
## 31 1 Ozone Solar.R Wind Temp
## 31 2 Ozone Solar.R Wind Temp
## 31 3 Ozone Solar.R Wind Temp
## 31 4 Ozone Solar.R Wind Temp
## 31 5 Ozone Solar.R Wind Temp
## 32 1 Ozone Solar.R Wind Temp
## 32 2 Ozone Solar.R Wind Temp
## 32 3 Ozone Solar.R Wind Temp
## 32 4 Ozone Solar.R Wind Temp
## 32 5 Ozone Solar.R Wind Temp
## 33 1 Ozone Solar.R Wind Temp
## 33 2 Ozone Solar.R Wind Temp
## 33 3 Ozone Solar.R Wind Temp
## 33 4 Ozone Solar.R Wind Temp
## 33 5 Ozone Solar.R Wind Temp
## 34 1 Ozone Solar.R Wind Temp
## 34 2 Ozone Solar.R Wind Temp
## 34 3 Ozone Solar.R Wind Temp
## 34 4 Ozone Solar.R Wind Temp
## 34 5 Ozone Solar.R Wind Temp
## 35 1 Ozone Solar.R Wind Temp
## 35 2 Ozone Solar.R Wind Temp
## 35 3 Ozone Solar.R Wind Temp
## 35 4 Ozone Solar.R Wind Temp
## 35 5 Ozone Solar.R Wind Temp
## 36 1 Ozone Solar.R Wind Temp
## 36 2 Ozone Solar.R Wind Temp
## 36 3 Ozone Solar.R Wind Temp
## 36 4 Ozone Solar.R Wind Temp
## 36 5 Ozone Solar.R Wind Temp
## 37 1 Ozone Solar.R Wind Temp
## 37 2 Ozone Solar.R Wind Temp
## 37 3 Ozone Solar.R Wind Temp
## 37 4 Ozone Solar.R Wind Temp
## 37 5 Ozone Solar.R Wind Temp
## 38 1 Ozone Solar.R Wind Temp
## 38 2 Ozone Solar.R Wind Temp
## 38 3 Ozone Solar.R Wind Temp
## 38 4 Ozone Solar.R Wind Temp
## 38 5 Ozone Solar.R Wind Temp
## 39 1 Ozone Solar.R Wind Temp
## 39 2 Ozone Solar.R Wind Temp
## 39 3 Ozone Solar.R Wind Temp
## 39 4 Ozone Solar.R Wind Temp
## 39 5 Ozone Solar.R Wind Temp
## 40 1 Ozone Solar.R Wind Temp
## 40 2 Ozone Solar.R Wind Temp
## 40 3 Ozone Solar.R Wind Temp
## 40 4 Ozone Solar.R Wind Temp
## 40 5 Ozone Solar.R Wind Temp
## 41 1 Ozone Solar.R Wind Temp
## 41 2 Ozone Solar.R Wind Temp
## 41 3 Ozone Solar.R Wind Temp
## 41 4 Ozone Solar.R Wind Temp
## 41 5 Ozone Solar.R Wind Temp
## 42 1 Ozone Solar.R Wind Temp
## 42 2 Ozone Solar.R Wind Temp
## 42 3 Ozone Solar.R Wind Temp
## 42 4 Ozone Solar.R Wind Temp
## 42 5 Ozone Solar.R Wind Temp
## 43 1 Ozone Solar.R Wind Temp
## 43 2 Ozone Solar.R Wind Temp
## 43 3 Ozone Solar.R Wind Temp
## 43 4 Ozone Solar.R Wind Temp
## 43 5 Ozone Solar.R Wind Temp
## 44 1 Ozone Solar.R Wind Temp
## 44 2 Ozone Solar.R Wind Temp
## 44 3 Ozone Solar.R Wind Temp
## 44 4 Ozone Solar.R Wind Temp
## 44 5 Ozone Solar.R Wind Temp
## 45 1 Ozone Solar.R Wind Temp
## 45 2 Ozone Solar.R Wind Temp
## 45 3 Ozone Solar.R Wind Temp
## 45 4 Ozone Solar.R Wind Temp
## 45 5 Ozone Solar.R Wind Temp
## 46 1 Ozone Solar.R Wind Temp
## 46 2 Ozone Solar.R Wind Temp
## 46 3 Ozone Solar.R Wind Temp
## 46 4 Ozone Solar.R Wind Temp
## 46 5 Ozone Solar.R Wind Temp
## 47 1 Ozone Solar.R Wind Temp
## 47 2 Ozone Solar.R Wind Temp
## 47 3 Ozone Solar.R Wind Temp
## 47 4 Ozone Solar.R Wind Temp
## 47 5 Ozone Solar.R Wind Temp
## 48 1 Ozone Solar.R Wind Temp
## 48 2 Ozone Solar.R Wind Temp
## 48 3 Ozone Solar.R Wind Temp
## 48 4 Ozone Solar.R Wind Temp
## 48 5 Ozone Solar.R Wind Temp
## 49 1 Ozone Solar.R Wind Temp
## 49 2 Ozone Solar.R Wind Temp
## 49 3 Ozone Solar.R Wind Temp
## 49 4 Ozone Solar.R Wind Temp
## 49 5 Ozone Solar.R Wind Temp
## 50 1 Ozone Solar.R Wind Temp
## 50 2 Ozone Solar.R Wind Temp
## 50 3 Ozone Solar.R Wind Temp
## 50 4 Ozone Solar.R Wind Temp
## 50 5 Ozone Solar.R Wind Tempsummary(tempData)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## Ozone Solar.R Wind Temp
## "pmm" "pmm" "pmm" "pmm"
## PredictorMatrix:
## Ozone Solar.R Wind Temp
## Ozone 0 1 1 1
## Solar.R 1 0 1 1
## Wind 1 1 0 1
## Temp 1 1 1 0A couple of notes on the parameters:
m=5refers to the number of imputed datasets. Five is the default value.meth='pmm'refers to the imputation method. In this case we are using predictive mean matching as imputation method. Other imputation methods can be used, typemethods(mice)for a list of the available imputation methods.
If you would like to check the imputed data, for instance for the variable Ozone, you need to enter the following line of code
tempData$imp$Ozone## 1 2 3 4 5
## 5 13 19 12 115 63
## 10 30 12 13 21 7
## 25 8 28 6 18 28
## 26 9 32 4 18 37
## 27 37 21 4 32 32
## 32 40 39 35 32 47
## 33 44 28 36 52 20
## 34 20 23 37 37 19
## 35 32 28 16 32 35
## 36 89 80 48 49 115
## 37 18 7 16 30 22
## 39 96 77 135 76 85
## 42 50 168 64 50 41
## 43 96 78 96 96 78
## 45 63 20 18 24 31
## 46 71 37 20 20 28
## 52 20 35 37 63 63
## 53 16 78 73 48 115
## 54 59 35 46 44 23
## 55 16 39 28 40 49
## 56 24 36 52 21 44
## 57 36 20 20 18 23
## 58 11 11 24 7 23
## 59 44 13 23 23 27
## 60 23 4 19 4 32
## 61 44 16 46 37 35
## 65 30 23 65 30 30
## 72 45 37 63 63 44
## 75 39 46 32 39 28
## 83 37 40 59 32 35
## 84 40 59 28 28 35
## 102 61 85 96 79 78
## 103 31 59 20 31 36
## 107 32 24 11 21 21
## 115 52 16 11 14 13
## 119 78 96 168 76 50
## 150 14 12 13 23 11The output shows the imputed data for each observation (first column left) within each imputed dataset (first row at the top).
If you need to check the imputation method used for each variable,
mice makes it very easy to do.
tempData$meth## Ozone Solar.R Wind Temp
## "pmm" "pmm" "pmm" "pmm"Now we can get back the completed dataset using the
complete() function. It is almost plain English:
completedData <- complete(tempData,1)The missing values have been replaced with the imputed values in the
first of the five datasets. If you wish to use another one, just change
the second parameter in the complete() function.
Inspecting the distribution of original and imputed data
Let’s compare the distributions of original and imputed data using a some useful plots.
First of all we can use a scatterplot and plot Ozone against all the other variables
xyplot(tempData,Ozone ~ Wind+Temp+Solar.R,pch=18,cex=1)
What we would like to see is that the shape of the magenta points (imputed) matches the shape of the blue ones (observed). The matching shape tells us that the imputed values are indeed “plausible values”.
Another helpful plot is the density plot:
densityplot(tempData)
The density of the imputed data for each imputed dataset is showed in pink while the density of the observed data is showed in blue. Again, under our previous assumptions we expect the distributions to be similar.
Another useful visual take on the distributions can be obtained using
the stripplot() function that shows the distributions of
the variables as individual points.
stripplot(tempData, pch = 20, cex = 1.2)
Suppose that the next step in our analysis is to fit a linear model
to the data. You may ask what imputed dataset to choose. The
mice package makes it again very easy to fit a a model to
each of the imputed dataset and then pool the results together.
modelFit1 <- with(tempData,lm(Temp~ Ozone+Solar.R+Wind))
pool(modelFit1)## Class: mipo m = 5
## term m estimate ubar b t dfcom
## 1 (Intercept) 5 72.70719792 7.093339e+00 4.431440e-01 7.625111e+00 149
## 2 Ozone 5 0.15924872 5.268255e-04 1.206098e-04 6.715573e-04 149
## 3 Solar.R 5 0.01252384 4.396201e-05 2.612657e-05 7.531389e-05 149
## 4 Wind 5 -0.34547006 4.067195e-02 2.113942e-03 4.320868e-02 149
## df riv lambda fmi
## 1 117.27936 0.07496792 0.06973968 0.08520801
## 2 49.30693 0.27472436 0.21551668 0.24551207
## 3 18.19046 0.71315866 0.41628290 0.47137535
## 4 123.65905 0.06237052 0.05870882 0.07357220# Get the summary
summary(pool(modelFit1))## term estimate std.error statistic df p.value
## 1 (Intercept) 72.70719792 2.761360433 26.330209 117.27936 4.655973e-51
## 2 Ozone 0.15924872 0.025914423 6.145177 49.30693 1.367056e-07
## 3 Solar.R 0.01252384 0.008678358 1.443112 18.19046 1.659893e-01
## 4 Wind -0.34547006 0.207866970 -1.661977 123.65905 9.905045e-02The variable modelFit1 contains the results of the
fitting performed over the imputed datasets, while the
pool() function pools them all together. Apparently, only
the Ozone variable is statistically significant.
Note that there are other columns aside from those typical of the
lm() model: fmi contains the fraction of
missing information while lambda is the proportion of total
variance that is attributable to the missing data. For more information
I suggest to check out the paper by Stef van Buuren: link to the
paper.
Remember that we initialized the mice function with a
specific seed (seed = 500), therefore the results are somewhat dependent
on our initial choice. To reduce this effect, we can impute a higher
number of dataset, by changing the default m=5 parameter in
the mice() function as follows.
tempData2 <- mice(data,m=50,seed=245435)##
## iter imp variable
## 1 1 Ozone Solar.R Wind Temp
## 1 2 Ozone Solar.R Wind Temp
## 1 3 Ozone Solar.R Wind Temp
## 1 4 Ozone Solar.R Wind Temp
## 1 5 Ozone Solar.R Wind Temp
## 1 6 Ozone Solar.R Wind Temp
## 1 7 Ozone Solar.R Wind Temp
## 1 8 Ozone Solar.R Wind Temp
## 1 9 Ozone Solar.R Wind Temp
## 1 10 Ozone Solar.R Wind Temp
## 1 11 Ozone Solar.R Wind Temp
## 1 12 Ozone Solar.R Wind Temp
## 1 13 Ozone Solar.R Wind Temp
## 1 14 Ozone Solar.R Wind Temp
## 1 15 Ozone Solar.R Wind Temp
## 1 16 Ozone Solar.R Wind Temp
## 1 17 Ozone Solar.R Wind Temp
## 1 18 Ozone Solar.R Wind Temp
## 1 19 Ozone Solar.R Wind Temp
## 1 20 Ozone Solar.R Wind Temp
## 1 21 Ozone Solar.R Wind Temp
## 1 22 Ozone Solar.R Wind Temp
## 1 23 Ozone Solar.R Wind Temp
## 1 24 Ozone Solar.R Wind Temp
## 1 25 Ozone Solar.R Wind Temp
## 1 26 Ozone Solar.R Wind Temp
## 1 27 Ozone Solar.R Wind Temp
## 1 28 Ozone Solar.R Wind Temp
## 1 29 Ozone Solar.R Wind Temp
## 1 30 Ozone Solar.R Wind Temp
## 1 31 Ozone Solar.R Wind Temp
## 1 32 Ozone Solar.R Wind Temp
## 1 33 Ozone Solar.R Wind Temp
## 1 34 Ozone Solar.R Wind Temp
## 1 35 Ozone Solar.R Wind Temp
## 1 36 Ozone Solar.R Wind Temp
## 1 37 Ozone Solar.R Wind Temp
## 1 38 Ozone Solar.R Wind Temp
## 1 39 Ozone Solar.R Wind Temp
## 1 40 Ozone Solar.R Wind Temp
## 1 41 Ozone Solar.R Wind Temp
## 1 42 Ozone Solar.R Wind Temp
## 1 43 Ozone Solar.R Wind Temp
## 1 44 Ozone Solar.R Wind Temp
## 1 45 Ozone Solar.R Wind Temp
## 1 46 Ozone Solar.R Wind Temp
## 1 47 Ozone Solar.R Wind Temp
## 1 48 Ozone Solar.R Wind Temp
## 1 49 Ozone Solar.R Wind Temp
## 1 50 Ozone Solar.R Wind Temp
## 2 1 Ozone Solar.R Wind Temp
## 2 2 Ozone Solar.R Wind Temp
## 2 3 Ozone Solar.R Wind Temp
## 2 4 Ozone Solar.R Wind Temp
## 2 5 Ozone Solar.R Wind Temp
## 2 6 Ozone Solar.R Wind Temp
## 2 7 Ozone Solar.R Wind Temp
## 2 8 Ozone Solar.R Wind Temp
## 2 9 Ozone Solar.R Wind Temp
## 2 10 Ozone Solar.R Wind Temp
## 2 11 Ozone Solar.R Wind Temp
## 2 12 Ozone Solar.R Wind Temp
## 2 13 Ozone Solar.R Wind Temp
## 2 14 Ozone Solar.R Wind Temp
## 2 15 Ozone Solar.R Wind Temp
## 2 16 Ozone Solar.R Wind Temp
## 2 17 Ozone Solar.R Wind Temp
## 2 18 Ozone Solar.R Wind Temp
## 2 19 Ozone Solar.R Wind Temp
## 2 20 Ozone Solar.R Wind Temp
## 2 21 Ozone Solar.R Wind Temp
## 2 22 Ozone Solar.R Wind Temp
## 2 23 Ozone Solar.R Wind Temp
## 2 24 Ozone Solar.R Wind Temp
## 2 25 Ozone Solar.R Wind Temp
## 2 26 Ozone Solar.R Wind Temp
## 2 27 Ozone Solar.R Wind Temp
## 2 28 Ozone Solar.R Wind Temp
## 2 29 Ozone Solar.R Wind Temp
## 2 30 Ozone Solar.R Wind Temp
## 2 31 Ozone Solar.R Wind Temp
## 2 32 Ozone Solar.R Wind Temp
## 2 33 Ozone Solar.R Wind Temp
## 2 34 Ozone Solar.R Wind Temp
## 2 35 Ozone Solar.R Wind Temp
## 2 36 Ozone Solar.R Wind Temp
## 2 37 Ozone Solar.R Wind Temp
## 2 38 Ozone Solar.R Wind Temp
## 2 39 Ozone Solar.R Wind Temp
## 2 40 Ozone Solar.R Wind Temp
## 2 41 Ozone Solar.R Wind Temp
## 2 42 Ozone Solar.R Wind Temp
## 2 43 Ozone Solar.R Wind Temp
## 2 44 Ozone Solar.R Wind Temp
## 2 45 Ozone Solar.R Wind Temp
## 2 46 Ozone Solar.R Wind Temp
## 2 47 Ozone Solar.R Wind Temp
## 2 48 Ozone Solar.R Wind Temp
## 2 49 Ozone Solar.R Wind Temp
## 2 50 Ozone Solar.R Wind Temp
## 3 1 Ozone Solar.R Wind Temp
## 3 2 Ozone Solar.R Wind Temp
## 3 3 Ozone Solar.R Wind Temp
## 3 4 Ozone Solar.R Wind Temp
## 3 5 Ozone Solar.R Wind Temp
## 3 6 Ozone Solar.R Wind Temp
## 3 7 Ozone Solar.R Wind Temp
## 3 8 Ozone Solar.R Wind Temp
## 3 9 Ozone Solar.R Wind Temp
## 3 10 Ozone Solar.R Wind Temp
## 3 11 Ozone Solar.R Wind Temp
## 3 12 Ozone Solar.R Wind Temp
## 3 13 Ozone Solar.R Wind Temp
## 3 14 Ozone Solar.R Wind Temp
## 3 15 Ozone Solar.R Wind Temp
## 3 16 Ozone Solar.R Wind Temp
## 3 17 Ozone Solar.R Wind Temp
## 3 18 Ozone Solar.R Wind Temp
## 3 19 Ozone Solar.R Wind Temp
## 3 20 Ozone Solar.R Wind Temp
## 3 21 Ozone Solar.R Wind Temp
## 3 22 Ozone Solar.R Wind Temp
## 3 23 Ozone Solar.R Wind Temp
## 3 24 Ozone Solar.R Wind Temp
## 3 25 Ozone Solar.R Wind Temp
## 3 26 Ozone Solar.R Wind Temp
## 3 27 Ozone Solar.R Wind Temp
## 3 28 Ozone Solar.R Wind Temp
## 3 29 Ozone Solar.R Wind Temp
## 3 30 Ozone Solar.R Wind Temp
## 3 31 Ozone Solar.R Wind Temp
## 3 32 Ozone Solar.R Wind Temp
## 3 33 Ozone Solar.R Wind Temp
## 3 34 Ozone Solar.R Wind Temp
## 3 35 Ozone Solar.R Wind Temp
## 3 36 Ozone Solar.R Wind Temp
## 3 37 Ozone Solar.R Wind Temp
## 3 38 Ozone Solar.R Wind Temp
## 3 39 Ozone Solar.R Wind Temp
## 3 40 Ozone Solar.R Wind Temp
## 3 41 Ozone Solar.R Wind Temp
## 3 42 Ozone Solar.R Wind Temp
## 3 43 Ozone Solar.R Wind Temp
## 3 44 Ozone Solar.R Wind Temp
## 3 45 Ozone Solar.R Wind Temp
## 3 46 Ozone Solar.R Wind Temp
## 3 47 Ozone Solar.R Wind Temp
## 3 48 Ozone Solar.R Wind Temp
## 3 49 Ozone Solar.R Wind Temp
## 3 50 Ozone Solar.R Wind Temp
## 4 1 Ozone Solar.R Wind Temp
## 4 2 Ozone Solar.R Wind Temp
## 4 3 Ozone Solar.R Wind Temp
## 4 4 Ozone Solar.R Wind Temp
## 4 5 Ozone Solar.R Wind Temp
## 4 6 Ozone Solar.R Wind Temp
## 4 7 Ozone Solar.R Wind Temp
## 4 8 Ozone Solar.R Wind Temp
## 4 9 Ozone Solar.R Wind Temp
## 4 10 Ozone Solar.R Wind Temp
## 4 11 Ozone Solar.R Wind Temp
## 4 12 Ozone Solar.R Wind Temp
## 4 13 Ozone Solar.R Wind Temp
## 4 14 Ozone Solar.R Wind Temp
## 4 15 Ozone Solar.R Wind Temp
## 4 16 Ozone Solar.R Wind Temp
## 4 17 Ozone Solar.R Wind Temp
## 4 18 Ozone Solar.R Wind Temp
## 4 19 Ozone Solar.R Wind Temp
## 4 20 Ozone Solar.R Wind Temp
## 4 21 Ozone Solar.R Wind Temp
## 4 22 Ozone Solar.R Wind Temp
## 4 23 Ozone Solar.R Wind Temp
## 4 24 Ozone Solar.R Wind Temp
## 4 25 Ozone Solar.R Wind Temp
## 4 26 Ozone Solar.R Wind Temp
## 4 27 Ozone Solar.R Wind Temp
## 4 28 Ozone Solar.R Wind Temp
## 4 29 Ozone Solar.R Wind Temp
## 4 30 Ozone Solar.R Wind Temp
## 4 31 Ozone Solar.R Wind Temp
## 4 32 Ozone Solar.R Wind Temp
## 4 33 Ozone Solar.R Wind Temp
## 4 34 Ozone Solar.R Wind Temp
## 4 35 Ozone Solar.R Wind Temp
## 4 36 Ozone Solar.R Wind Temp
## 4 37 Ozone Solar.R Wind Temp
## 4 38 Ozone Solar.R Wind Temp
## 4 39 Ozone Solar.R Wind Temp
## 4 40 Ozone Solar.R Wind Temp
## 4 41 Ozone Solar.R Wind Temp
## 4 42 Ozone Solar.R Wind Temp
## 4 43 Ozone Solar.R Wind Temp
## 4 44 Ozone Solar.R Wind Temp
## 4 45 Ozone Solar.R Wind Temp
## 4 46 Ozone Solar.R Wind Temp
## 4 47 Ozone Solar.R Wind Temp
## 4 48 Ozone Solar.R Wind Temp
## 4 49 Ozone Solar.R Wind Temp
## 4 50 Ozone Solar.R Wind Temp
## 5 1 Ozone Solar.R Wind Temp
## 5 2 Ozone Solar.R Wind Temp
## 5 3 Ozone Solar.R Wind Temp
## 5 4 Ozone Solar.R Wind Temp
## 5 5 Ozone Solar.R Wind Temp
## 5 6 Ozone Solar.R Wind Temp
## 5 7 Ozone Solar.R Wind Temp
## 5 8 Ozone Solar.R Wind Temp
## 5 9 Ozone Solar.R Wind Temp
## 5 10 Ozone Solar.R Wind Temp
## 5 11 Ozone Solar.R Wind Temp
## 5 12 Ozone Solar.R Wind Temp
## 5 13 Ozone Solar.R Wind Temp
## 5 14 Ozone Solar.R Wind Temp
## 5 15 Ozone Solar.R Wind Temp
## 5 16 Ozone Solar.R Wind Temp
## 5 17 Ozone Solar.R Wind Temp
## 5 18 Ozone Solar.R Wind Temp
## 5 19 Ozone Solar.R Wind Temp
## 5 20 Ozone Solar.R Wind Temp
## 5 21 Ozone Solar.R Wind Temp
## 5 22 Ozone Solar.R Wind Temp
## 5 23 Ozone Solar.R Wind Temp
## 5 24 Ozone Solar.R Wind Temp
## 5 25 Ozone Solar.R Wind Temp
## 5 26 Ozone Solar.R Wind Temp
## 5 27 Ozone Solar.R Wind Temp
## 5 28 Ozone Solar.R Wind Temp
## 5 29 Ozone Solar.R Wind Temp
## 5 30 Ozone Solar.R Wind Temp
## 5 31 Ozone Solar.R Wind Temp
## 5 32 Ozone Solar.R Wind Temp
## 5 33 Ozone Solar.R Wind Temp
## 5 34 Ozone Solar.R Wind Temp
## 5 35 Ozone Solar.R Wind Temp
## 5 36 Ozone Solar.R Wind Temp
## 5 37 Ozone Solar.R Wind Temp
## 5 38 Ozone Solar.R Wind Temp
## 5 39 Ozone Solar.R Wind Temp
## 5 40 Ozone Solar.R Wind Temp
## 5 41 Ozone Solar.R Wind Temp
## 5 42 Ozone Solar.R Wind Temp
## 5 43 Ozone Solar.R Wind Temp
## 5 44 Ozone Solar.R Wind Temp
## 5 45 Ozone Solar.R Wind Temp
## 5 46 Ozone Solar.R Wind Temp
## 5 47 Ozone Solar.R Wind Temp
## 5 48 Ozone Solar.R Wind Temp
## 5 49 Ozone Solar.R Wind Temp
## 5 50 Ozone Solar.R Wind TempmodelFit2 <- with(tempData2,lm(Temp~ Ozone+Solar.R+Wind))
summary(pool(modelFit2))## term estimate std.error statistic df p.value
## 1 (Intercept) 72.60178955 2.915916315 24.898448 105.59368 5.380239e-46
## 2 Ozone 0.16345639 0.026054628 6.273603 99.86352 9.122568e-09
## 3 Solar.R 0.01193645 0.007134344 1.673097 120.41496 9.690433e-02
## 4 Wind -0.33592048 0.222350762 -1.510768 107.41496 1.337838e-01After having taken into account the random seed initialization, we obtain (in this case) more or less the same results as before with only Ozone showing statistical significance.
Comparing the results
Let’s compare the results.
Let’s use a different dataset. We’ll use the training portion of the
Titanic dataset and try to impute missing values for the
Age column:
library(titanic)
titanic_train$Age## [1] 22.00 38.00 26.00 35.00 35.00 NA 54.00 2.00 27.00 14.00 4.00 58.00
## [13] 20.00 39.00 14.00 55.00 2.00 NA 31.00 NA 35.00 34.00 15.00 28.00
## [25] 8.00 38.00 NA 19.00 NA NA 40.00 NA NA 66.00 28.00 42.00
## [37] NA 21.00 18.00 14.00 40.00 27.00 NA 3.00 19.00 NA NA NA
## [49] NA 18.00 7.00 21.00 49.00 29.00 65.00 NA 21.00 28.50 5.00 11.00
## [61] 22.00 38.00 45.00 4.00 NA NA 29.00 19.00 17.00 26.00 32.00 16.00
## [73] 21.00 26.00 32.00 25.00 NA NA 0.83 30.00 22.00 29.00 NA 28.00
## [85] 17.00 33.00 16.00 NA 23.00 24.00 29.00 20.00 46.00 26.00 59.00 NA
## [97] 71.00 23.00 34.00 34.00 28.00 NA 21.00 33.00 37.00 28.00 21.00 NA
## [109] 38.00 NA 47.00 14.50 22.00 20.00 17.00 21.00 70.50 29.00 24.00 2.00
## [121] 21.00 NA 32.50 32.50 54.00 12.00 NA 24.00 NA 45.00 33.00 20.00
## [133] 47.00 29.00 25.00 23.00 19.00 37.00 16.00 24.00 NA 22.00 24.00 19.00
## [145] 18.00 19.00 27.00 9.00 36.50 42.00 51.00 22.00 55.50 40.50 NA 51.00
## [157] 16.00 30.00 NA NA 44.00 40.00 26.00 17.00 1.00 9.00 NA 45.00
## [169] NA 28.00 61.00 4.00 1.00 21.00 56.00 18.00 NA 50.00 30.00 36.00
## [181] NA NA 9.00 1.00 4.00 NA NA 45.00 40.00 36.00 32.00 19.00
## [193] 19.00 3.00 44.00 58.00 NA 42.00 NA 24.00 28.00 NA 34.00 45.50
## [205] 18.00 2.00 32.00 26.00 16.00 40.00 24.00 35.00 22.00 30.00 NA 31.00
## [217] 27.00 42.00 32.00 30.00 16.00 27.00 51.00 NA 38.00 22.00 19.00 20.50
## [229] 18.00 NA 35.00 29.00 59.00 5.00 24.00 NA 44.00 8.00 19.00 33.00
## [241] NA NA 29.00 22.00 30.00 44.00 25.00 24.00 37.00 54.00 NA 29.00
## [253] 62.00 30.00 41.00 29.00 NA 30.00 35.00 50.00 NA 3.00 52.00 40.00
## [265] NA 36.00 16.00 25.00 58.00 35.00 NA 25.00 41.00 37.00 NA 63.00
## [277] 45.00 NA 7.00 35.00 65.00 28.00 16.00 19.00 NA 33.00 30.00 22.00
## [289] 42.00 22.00 26.00 19.00 36.00 24.00 24.00 NA 23.50 2.00 NA 50.00
## [301] NA NA 19.00 NA NA 0.92 NA 17.00 30.00 30.00 24.00 18.00
## [313] 26.00 28.00 43.00 26.00 24.00 54.00 31.00 40.00 22.00 27.00 30.00 22.00
## [325] NA 36.00 61.00 36.00 31.00 16.00 NA 45.50 38.00 16.00 NA NA
## [337] 29.00 41.00 45.00 45.00 2.00 24.00 28.00 25.00 36.00 24.00 40.00 NA
## [349] 3.00 42.00 23.00 NA 15.00 25.00 NA 28.00 22.00 38.00 NA NA
## [361] 40.00 29.00 45.00 35.00 NA 30.00 60.00 NA NA 24.00 25.00 18.00
## [373] 19.00 22.00 3.00 NA 22.00 27.00 20.00 19.00 42.00 1.00 32.00 35.00
## [385] NA 18.00 1.00 36.00 NA 17.00 36.00 21.00 28.00 23.00 24.00 22.00
## [397] 31.00 46.00 23.00 28.00 39.00 26.00 21.00 28.00 20.00 34.00 51.00 3.00
## [409] 21.00 NA NA NA 33.00 NA 44.00 NA 34.00 18.00 30.00 10.00
## [421] NA 21.00 29.00 28.00 18.00 NA 28.00 19.00 NA 32.00 28.00 NA
## [433] 42.00 17.00 50.00 14.00 21.00 24.00 64.00 31.00 45.00 20.00 25.00 28.00
## [445] NA 4.00 13.00 34.00 5.00 52.00 36.00 NA 30.00 49.00 NA 29.00
## [457] 65.00 NA 50.00 NA 48.00 34.00 47.00 48.00 NA 38.00 NA 56.00
## [469] NA 0.75 NA 38.00 33.00 23.00 22.00 NA 34.00 29.00 22.00 2.00
## [481] 9.00 NA 50.00 63.00 25.00 NA 35.00 58.00 30.00 9.00 NA 21.00
## [493] 55.00 71.00 21.00 NA 54.00 NA 25.00 24.00 17.00 21.00 NA 37.00
## [505] 16.00 18.00 33.00 NA 28.00 26.00 29.00 NA 36.00 54.00 24.00 47.00
## [517] 34.00 NA 36.00 32.00 30.00 22.00 NA 44.00 NA 40.50 50.00 NA
## [529] 39.00 23.00 2.00 NA 17.00 NA 30.00 7.00 45.00 30.00 NA 22.00
## [541] 36.00 9.00 11.00 32.00 50.00 64.00 19.00 NA 33.00 8.00 17.00 27.00
## [553] NA 22.00 22.00 62.00 48.00 NA 39.00 36.00 NA 40.00 28.00 NA
## [565] NA 24.00 19.00 29.00 NA 32.00 62.00 53.00 36.00 NA 16.00 19.00
## [577] 34.00 39.00 NA 32.00 25.00 39.00 54.00 36.00 NA 18.00 47.00 60.00
## [589] 22.00 NA 35.00 52.00 47.00 NA 37.00 36.00 NA 49.00 NA 49.00
## [601] 24.00 NA NA 44.00 35.00 36.00 30.00 27.00 22.00 40.00 39.00 NA
## [613] NA NA 35.00 24.00 34.00 26.00 4.00 26.00 27.00 42.00 20.00 21.00
## [625] 21.00 61.00 57.00 21.00 26.00 NA 80.00 51.00 32.00 NA 9.00 28.00
## [637] 32.00 31.00 41.00 NA 20.00 24.00 2.00 NA 0.75 48.00 19.00 56.00
## [649] NA 23.00 NA 18.00 21.00 NA 18.00 24.00 NA 32.00 23.00 58.00
## [661] 50.00 40.00 47.00 36.00 20.00 32.00 25.00 NA 43.00 NA 40.00 31.00
## [673] 70.00 31.00 NA 18.00 24.50 18.00 43.00 36.00 NA 27.00 20.00 14.00
## [685] 60.00 25.00 14.00 19.00 18.00 15.00 31.00 4.00 NA 25.00 60.00 52.00
## [697] 44.00 NA 49.00 42.00 18.00 35.00 18.00 25.00 26.00 39.00 45.00 42.00
## [709] 22.00 NA 24.00 NA 48.00 29.00 52.00 19.00 38.00 27.00 NA 33.00
## [721] 6.00 17.00 34.00 50.00 27.00 20.00 30.00 NA 25.00 25.00 29.00 11.00
## [733] NA 23.00 23.00 28.50 48.00 35.00 NA NA NA 36.00 21.00 24.00
## [745] 31.00 70.00 16.00 30.00 19.00 31.00 4.00 6.00 33.00 23.00 48.00 0.67
## [757] 28.00 18.00 34.00 33.00 NA 41.00 20.00 36.00 16.00 51.00 NA 30.50
## [769] NA 32.00 24.00 48.00 57.00 NA 54.00 18.00 NA 5.00 NA 43.00
## [781] 13.00 17.00 29.00 NA 25.00 25.00 18.00 8.00 1.00 46.00 NA 16.00
## [793] NA NA 25.00 39.00 49.00 31.00 30.00 30.00 34.00 31.00 11.00 0.42
## [805] 27.00 31.00 39.00 18.00 39.00 33.00 26.00 39.00 35.00 6.00 30.50 NA
## [817] 23.00 31.00 43.00 10.00 52.00 27.00 38.00 27.00 2.00 NA NA 1.00
## [829] NA 62.00 15.00 0.83 NA 23.00 18.00 39.00 21.00 NA 32.00 NA
## [841] 20.00 16.00 30.00 34.50 17.00 42.00 NA 35.00 28.00 NA 4.00 74.00
## [853] 9.00 16.00 44.00 18.00 45.00 51.00 24.00 NA 41.00 21.00 48.00 NA
## [865] 24.00 42.00 27.00 31.00 NA 4.00 26.00 47.00 33.00 47.00 28.00 15.00
## [877] 20.00 19.00 NA 56.00 25.00 33.00 22.00 28.00 25.00 39.00 27.00 19.00
## [889] NA 26.00 32.00There’s a fair amount of NA values, and it’s our job to
impute them. They’re most likely missing because the creator of the
dataset had no information on the person’s age. If you were to build a,
say machine learning model, on this dataset, the best way to evaluate
the imputation technique would be to measure classification metrics
(accuracy, precision, recall, f1) after training the model (we will talk
more about this when we discuss logistic regression).
Simple Value Imputation in R with Built-in Functions
The value_imputed variable will store a data.frame of
the imputed ages The imputation itself boils down to replacing a column
subset that has a value of NA with the value of our choice.
We now have a dataset with four columns representing the ages.
- Zero: constant imputation, feel free to change the value.
- Mean (average): average age after when all NAs are removed.
- Median: median age after when all NAs are removed.
value_imputed <- data.frame(original = titanic_train$Age,
imputed_zero = replace(titanic_train$Age, is.na(titanic_train$Age), 0),
imputed_mean = replace(titanic_train$Age,
is.na(titanic_train$Age),
mean(titanic_train$Age, na.rm = TRUE)),
imputed_median = replace(titanic_train$Age,
is.na(titanic_train$Age),
median(titanic_train$Age, na.rm = TRUE)))
value_imputed## original imputed_zero imputed_mean imputed_median
## 1 22.00 22.00 22.00000 22.00
## 2 38.00 38.00 38.00000 38.00
## 3 26.00 26.00 26.00000 26.00
## 4 35.00 35.00 35.00000 35.00
## 5 35.00 35.00 35.00000 35.00
## 6 NA 0.00 29.69912 28.00
## 7 54.00 54.00 54.00000 54.00
## 8 2.00 2.00 2.00000 2.00
## 9 27.00 27.00 27.00000 27.00
## 10 14.00 14.00 14.00000 14.00
## 11 4.00 4.00 4.00000 4.00
## 12 58.00 58.00 58.00000 58.00
## 13 20.00 20.00 20.00000 20.00
## 14 39.00 39.00 39.00000 39.00
## 15 14.00 14.00 14.00000 14.00
## 16 55.00 55.00 55.00000 55.00
## 17 2.00 2.00 2.00000 2.00
## 18 NA 0.00 29.69912 28.00
## 19 31.00 31.00 31.00000 31.00
## 20 NA 0.00 29.69912 28.00
## 21 35.00 35.00 35.00000 35.00
## 22 34.00 34.00 34.00000 34.00
## 23 15.00 15.00 15.00000 15.00
## 24 28.00 28.00 28.00000 28.00
## 25 8.00 8.00 8.00000 8.00
## 26 38.00 38.00 38.00000 38.00
## 27 NA 0.00 29.69912 28.00
## 28 19.00 19.00 19.00000 19.00
## 29 NA 0.00 29.69912 28.00
## 30 NA 0.00 29.69912 28.00
## 31 40.00 40.00 40.00000 40.00
## 32 NA 0.00 29.69912 28.00
## 33 NA 0.00 29.69912 28.00
## 34 66.00 66.00 66.00000 66.00
## 35 28.00 28.00 28.00000 28.00
## 36 42.00 42.00 42.00000 42.00
## 37 NA 0.00 29.69912 28.00
## 38 21.00 21.00 21.00000 21.00
## 39 18.00 18.00 18.00000 18.00
## 40 14.00 14.00 14.00000 14.00
## 41 40.00 40.00 40.00000 40.00
## 42 27.00 27.00 27.00000 27.00
## 43 NA 0.00 29.69912 28.00
## 44 3.00 3.00 3.00000 3.00
## 45 19.00 19.00 19.00000 19.00
## 46 NA 0.00 29.69912 28.00
## 47 NA 0.00 29.69912 28.00
## 48 NA 0.00 29.69912 28.00
## 49 NA 0.00 29.69912 28.00
## 50 18.00 18.00 18.00000 18.00
## 51 7.00 7.00 7.00000 7.00
## 52 21.00 21.00 21.00000 21.00
## 53 49.00 49.00 49.00000 49.00
## 54 29.00 29.00 29.00000 29.00
## 55 65.00 65.00 65.00000 65.00
## 56 NA 0.00 29.69912 28.00
## 57 21.00 21.00 21.00000 21.00
## 58 28.50 28.50 28.50000 28.50
## 59 5.00 5.00 5.00000 5.00
## 60 11.00 11.00 11.00000 11.00
## 61 22.00 22.00 22.00000 22.00
## 62 38.00 38.00 38.00000 38.00
## 63 45.00 45.00 45.00000 45.00
## 64 4.00 4.00 4.00000 4.00
## 65 NA 0.00 29.69912 28.00
## 66 NA 0.00 29.69912 28.00
## 67 29.00 29.00 29.00000 29.00
## 68 19.00 19.00 19.00000 19.00
## 69 17.00 17.00 17.00000 17.00
## 70 26.00 26.00 26.00000 26.00
## 71 32.00 32.00 32.00000 32.00
## 72 16.00 16.00 16.00000 16.00
## 73 21.00 21.00 21.00000 21.00
## 74 26.00 26.00 26.00000 26.00
## 75 32.00 32.00 32.00000 32.00
## 76 25.00 25.00 25.00000 25.00
## 77 NA 0.00 29.69912 28.00
## 78 NA 0.00 29.69912 28.00
## 79 0.83 0.83 0.83000 0.83
## 80 30.00 30.00 30.00000 30.00
## 81 22.00 22.00 22.00000 22.00
## 82 29.00 29.00 29.00000 29.00
## 83 NA 0.00 29.69912 28.00
## 84 28.00 28.00 28.00000 28.00
## 85 17.00 17.00 17.00000 17.00
## 86 33.00 33.00 33.00000 33.00
## 87 16.00 16.00 16.00000 16.00
## 88 NA 0.00 29.69912 28.00
## 89 23.00 23.00 23.00000 23.00
## 90 24.00 24.00 24.00000 24.00
## 91 29.00 29.00 29.00000 29.00
## 92 20.00 20.00 20.00000 20.00
## 93 46.00 46.00 46.00000 46.00
## 94 26.00 26.00 26.00000 26.00
## 95 59.00 59.00 59.00000 59.00
## 96 NA 0.00 29.69912 28.00
## 97 71.00 71.00 71.00000 71.00
## 98 23.00 23.00 23.00000 23.00
## 99 34.00 34.00 34.00000 34.00
## 100 34.00 34.00 34.00000 34.00
## 101 28.00 28.00 28.00000 28.00
## 102 NA 0.00 29.69912 28.00
## 103 21.00 21.00 21.00000 21.00
## 104 33.00 33.00 33.00000 33.00
## 105 37.00 37.00 37.00000 37.00
## 106 28.00 28.00 28.00000 28.00
## 107 21.00 21.00 21.00000 21.00
## 108 NA 0.00 29.69912 28.00
## 109 38.00 38.00 38.00000 38.00
## 110 NA 0.00 29.69912 28.00
## 111 47.00 47.00 47.00000 47.00
## 112 14.50 14.50 14.50000 14.50
## 113 22.00 22.00 22.00000 22.00
## 114 20.00 20.00 20.00000 20.00
## 115 17.00 17.00 17.00000 17.00
## 116 21.00 21.00 21.00000 21.00
## 117 70.50 70.50 70.50000 70.50
## 118 29.00 29.00 29.00000 29.00
## 119 24.00 24.00 24.00000 24.00
## 120 2.00 2.00 2.00000 2.00
## 121 21.00 21.00 21.00000 21.00
## 122 NA 0.00 29.69912 28.00
## 123 32.50 32.50 32.50000 32.50
## 124 32.50 32.50 32.50000 32.50
## 125 54.00 54.00 54.00000 54.00
## 126 12.00 12.00 12.00000 12.00
## 127 NA 0.00 29.69912 28.00
## 128 24.00 24.00 24.00000 24.00
## 129 NA 0.00 29.69912 28.00
## 130 45.00 45.00 45.00000 45.00
## 131 33.00 33.00 33.00000 33.00
## 132 20.00 20.00 20.00000 20.00
## 133 47.00 47.00 47.00000 47.00
## 134 29.00 29.00 29.00000 29.00
## 135 25.00 25.00 25.00000 25.00
## 136 23.00 23.00 23.00000 23.00
## 137 19.00 19.00 19.00000 19.00
## 138 37.00 37.00 37.00000 37.00
## 139 16.00 16.00 16.00000 16.00
## 140 24.00 24.00 24.00000 24.00
## 141 NA 0.00 29.69912 28.00
## 142 22.00 22.00 22.00000 22.00
## 143 24.00 24.00 24.00000 24.00
## 144 19.00 19.00 19.00000 19.00
## 145 18.00 18.00 18.00000 18.00
## 146 19.00 19.00 19.00000 19.00
## 147 27.00 27.00 27.00000 27.00
## 148 9.00 9.00 9.00000 9.00
## 149 36.50 36.50 36.50000 36.50
## 150 42.00 42.00 42.00000 42.00
## 151 51.00 51.00 51.00000 51.00
## 152 22.00 22.00 22.00000 22.00
## 153 55.50 55.50 55.50000 55.50
## 154 40.50 40.50 40.50000 40.50
## 155 NA 0.00 29.69912 28.00
## 156 51.00 51.00 51.00000 51.00
## 157 16.00 16.00 16.00000 16.00
## 158 30.00 30.00 30.00000 30.00
## 159 NA 0.00 29.69912 28.00
## 160 NA 0.00 29.69912 28.00
## 161 44.00 44.00 44.00000 44.00
## 162 40.00 40.00 40.00000 40.00
## 163 26.00 26.00 26.00000 26.00
## 164 17.00 17.00 17.00000 17.00
## 165 1.00 1.00 1.00000 1.00
## 166 9.00 9.00 9.00000 9.00
## 167 NA 0.00 29.69912 28.00
## 168 45.00 45.00 45.00000 45.00
## 169 NA 0.00 29.69912 28.00
## 170 28.00 28.00 28.00000 28.00
## 171 61.00 61.00 61.00000 61.00
## 172 4.00 4.00 4.00000 4.00
## 173 1.00 1.00 1.00000 1.00
## 174 21.00 21.00 21.00000 21.00
## 175 56.00 56.00 56.00000 56.00
## 176 18.00 18.00 18.00000 18.00
## 177 NA 0.00 29.69912 28.00
## 178 50.00 50.00 50.00000 50.00
## 179 30.00 30.00 30.00000 30.00
## 180 36.00 36.00 36.00000 36.00
## 181 NA 0.00 29.69912 28.00
## 182 NA 0.00 29.69912 28.00
## 183 9.00 9.00 9.00000 9.00
## 184 1.00 1.00 1.00000 1.00
## 185 4.00 4.00 4.00000 4.00
## 186 NA 0.00 29.69912 28.00
## 187 NA 0.00 29.69912 28.00
## 188 45.00 45.00 45.00000 45.00
## 189 40.00 40.00 40.00000 40.00
## 190 36.00 36.00 36.00000 36.00
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## 703 18.00 18.00 18.00000 18.00
## 704 25.00 25.00 25.00000 25.00
## 705 26.00 26.00 26.00000 26.00
## 706 39.00 39.00 39.00000 39.00
## 707 45.00 45.00 45.00000 45.00
## 708 42.00 42.00 42.00000 42.00
## 709 22.00 22.00 22.00000 22.00
## 710 NA 0.00 29.69912 28.00
## 711 24.00 24.00 24.00000 24.00
## 712 NA 0.00 29.69912 28.00
## 713 48.00 48.00 48.00000 48.00
## 714 29.00 29.00 29.00000 29.00
## 715 52.00 52.00 52.00000 52.00
## 716 19.00 19.00 19.00000 19.00
## 717 38.00 38.00 38.00000 38.00
## 718 27.00 27.00 27.00000 27.00
## 719 NA 0.00 29.69912 28.00
## 720 33.00 33.00 33.00000 33.00
## 721 6.00 6.00 6.00000 6.00
## 722 17.00 17.00 17.00000 17.00
## 723 34.00 34.00 34.00000 34.00
## 724 50.00 50.00 50.00000 50.00
## 725 27.00 27.00 27.00000 27.00
## 726 20.00 20.00 20.00000 20.00
## 727 30.00 30.00 30.00000 30.00
## 728 NA 0.00 29.69912 28.00
## 729 25.00 25.00 25.00000 25.00
## 730 25.00 25.00 25.00000 25.00
## 731 29.00 29.00 29.00000 29.00
## 732 11.00 11.00 11.00000 11.00
## 733 NA 0.00 29.69912 28.00
## 734 23.00 23.00 23.00000 23.00
## 735 23.00 23.00 23.00000 23.00
## 736 28.50 28.50 28.50000 28.50
## 737 48.00 48.00 48.00000 48.00
## 738 35.00 35.00 35.00000 35.00
## 739 NA 0.00 29.69912 28.00
## 740 NA 0.00 29.69912 28.00
## 741 NA 0.00 29.69912 28.00
## 742 36.00 36.00 36.00000 36.00
## 743 21.00 21.00 21.00000 21.00
## 744 24.00 24.00 24.00000 24.00
## 745 31.00 31.00 31.00000 31.00
## 746 70.00 70.00 70.00000 70.00
## 747 16.00 16.00 16.00000 16.00
## 748 30.00 30.00 30.00000 30.00
## 749 19.00 19.00 19.00000 19.00
## 750 31.00 31.00 31.00000 31.00
## 751 4.00 4.00 4.00000 4.00
## 752 6.00 6.00 6.00000 6.00
## 753 33.00 33.00 33.00000 33.00
## 754 23.00 23.00 23.00000 23.00
## 755 48.00 48.00 48.00000 48.00
## 756 0.67 0.67 0.67000 0.67
## 757 28.00 28.00 28.00000 28.00
## 758 18.00 18.00 18.00000 18.00
## 759 34.00 34.00 34.00000 34.00
## 760 33.00 33.00 33.00000 33.00
## 761 NA 0.00 29.69912 28.00
## 762 41.00 41.00 41.00000 41.00
## 763 20.00 20.00 20.00000 20.00
## 764 36.00 36.00 36.00000 36.00
## 765 16.00 16.00 16.00000 16.00
## 766 51.00 51.00 51.00000 51.00
## 767 NA 0.00 29.69912 28.00
## 768 30.50 30.50 30.50000 30.50
## 769 NA 0.00 29.69912 28.00
## 770 32.00 32.00 32.00000 32.00
## 771 24.00 24.00 24.00000 24.00
## 772 48.00 48.00 48.00000 48.00
## 773 57.00 57.00 57.00000 57.00
## 774 NA 0.00 29.69912 28.00
## 775 54.00 54.00 54.00000 54.00
## 776 18.00 18.00 18.00000 18.00
## 777 NA 0.00 29.69912 28.00
## 778 5.00 5.00 5.00000 5.00
## 779 NA 0.00 29.69912 28.00
## 780 43.00 43.00 43.00000 43.00
## 781 13.00 13.00 13.00000 13.00
## 782 17.00 17.00 17.00000 17.00
## 783 29.00 29.00 29.00000 29.00
## 784 NA 0.00 29.69912 28.00
## 785 25.00 25.00 25.00000 25.00
## 786 25.00 25.00 25.00000 25.00
## 787 18.00 18.00 18.00000 18.00
## 788 8.00 8.00 8.00000 8.00
## 789 1.00 1.00 1.00000 1.00
## 790 46.00 46.00 46.00000 46.00
## 791 NA 0.00 29.69912 28.00
## 792 16.00 16.00 16.00000 16.00
## 793 NA 0.00 29.69912 28.00
## 794 NA 0.00 29.69912 28.00
## 795 25.00 25.00 25.00000 25.00
## 796 39.00 39.00 39.00000 39.00
## 797 49.00 49.00 49.00000 49.00
## 798 31.00 31.00 31.00000 31.00
## 799 30.00 30.00 30.00000 30.00
## 800 30.00 30.00 30.00000 30.00
## 801 34.00 34.00 34.00000 34.00
## 802 31.00 31.00 31.00000 31.00
## 803 11.00 11.00 11.00000 11.00
## 804 0.42 0.42 0.42000 0.42
## 805 27.00 27.00 27.00000 27.00
## 806 31.00 31.00 31.00000 31.00
## 807 39.00 39.00 39.00000 39.00
## 808 18.00 18.00 18.00000 18.00
## 809 39.00 39.00 39.00000 39.00
## 810 33.00 33.00 33.00000 33.00
## 811 26.00 26.00 26.00000 26.00
## 812 39.00 39.00 39.00000 39.00
## 813 35.00 35.00 35.00000 35.00
## 814 6.00 6.00 6.00000 6.00
## 815 30.50 30.50 30.50000 30.50
## 816 NA 0.00 29.69912 28.00
## 817 23.00 23.00 23.00000 23.00
## 818 31.00 31.00 31.00000 31.00
## 819 43.00 43.00 43.00000 43.00
## 820 10.00 10.00 10.00000 10.00
## 821 52.00 52.00 52.00000 52.00
## 822 27.00 27.00 27.00000 27.00
## 823 38.00 38.00 38.00000 38.00
## 824 27.00 27.00 27.00000 27.00
## 825 2.00 2.00 2.00000 2.00
## 826 NA 0.00 29.69912 28.00
## 827 NA 0.00 29.69912 28.00
## 828 1.00 1.00 1.00000 1.00
## 829 NA 0.00 29.69912 28.00
## 830 62.00 62.00 62.00000 62.00
## 831 15.00 15.00 15.00000 15.00
## 832 0.83 0.83 0.83000 0.83
## 833 NA 0.00 29.69912 28.00
## 834 23.00 23.00 23.00000 23.00
## 835 18.00 18.00 18.00000 18.00
## 836 39.00 39.00 39.00000 39.00
## 837 21.00 21.00 21.00000 21.00
## 838 NA 0.00 29.69912 28.00
## 839 32.00 32.00 32.00000 32.00
## 840 NA 0.00 29.69912 28.00
## 841 20.00 20.00 20.00000 20.00
## 842 16.00 16.00 16.00000 16.00
## 843 30.00 30.00 30.00000 30.00
## 844 34.50 34.50 34.50000 34.50
## 845 17.00 17.00 17.00000 17.00
## 846 42.00 42.00 42.00000 42.00
## 847 NA 0.00 29.69912 28.00
## 848 35.00 35.00 35.00000 35.00
## 849 28.00 28.00 28.00000 28.00
## 850 NA 0.00 29.69912 28.00
## 851 4.00 4.00 4.00000 4.00
## 852 74.00 74.00 74.00000 74.00
## 853 9.00 9.00 9.00000 9.00
## 854 16.00 16.00 16.00000 16.00
## 855 44.00 44.00 44.00000 44.00
## 856 18.00 18.00 18.00000 18.00
## 857 45.00 45.00 45.00000 45.00
## 858 51.00 51.00 51.00000 51.00
## 859 24.00 24.00 24.00000 24.00
## 860 NA 0.00 29.69912 28.00
## 861 41.00 41.00 41.00000 41.00
## 862 21.00 21.00 21.00000 21.00
## 863 48.00 48.00 48.00000 48.00
## 864 NA 0.00 29.69912 28.00
## 865 24.00 24.00 24.00000 24.00
## 866 42.00 42.00 42.00000 42.00
## 867 27.00 27.00 27.00000 27.00
## 868 31.00 31.00 31.00000 31.00
## 869 NA 0.00 29.69912 28.00
## 870 4.00 4.00 4.00000 4.00
## 871 26.00 26.00 26.00000 26.00
## 872 47.00 47.00 47.00000 47.00
## 873 33.00 33.00 33.00000 33.00
## 874 47.00 47.00 47.00000 47.00
## 875 28.00 28.00 28.00000 28.00
## 876 15.00 15.00 15.00000 15.00
## 877 20.00 20.00 20.00000 20.00
## 878 19.00 19.00 19.00000 19.00
## 879 NA 0.00 29.69912 28.00
## 880 56.00 56.00 56.00000 56.00
## 881 25.00 25.00 25.00000 25.00
## 882 33.00 33.00 33.00000 33.00
## 883 22.00 22.00 22.00000 22.00
## 884 28.00 28.00 28.00000 28.00
## 885 25.00 25.00 25.00000 25.00
## 886 39.00 39.00 39.00000 39.00
## 887 27.00 27.00 27.00000 27.00
## 888 19.00 19.00 19.00000 19.00
## 889 NA 0.00 29.69912 28.00
## 890 26.00 26.00 26.00000 26.00
## 891 32.00 32.00 32.00000 32.00Let’s take a look at the variable distribution changes introduced by imputation on a 2×2 grid of histograms:
library(ggplot2)
library(cowplot) # for plot_grid()
h1 <- ggplot(value_imputed, aes(x = original)) +
geom_histogram(fill = "#ad1538", color = "#000000", position = "identity") +
ggtitle("Original distribution") +
theme_classic()
h2 <- ggplot(value_imputed, aes(x = imputed_zero)) +
geom_histogram(fill = "#15ad4f", color = "#000000", position = "identity") +
ggtitle("Zero-imputed distribution") +
theme_classic()
h3 <- ggplot(value_imputed, aes(x = imputed_mean)) +
geom_histogram(fill = "#1543ad", color = "#000000", position = "identity") +
ggtitle("Mean-imputed distribution") +
theme_classic()
h4 <- ggplot(value_imputed, aes(x = imputed_median)) +
geom_histogram(fill = "#ad8415", color = "#000000", position = "identity") +
ggtitle("Median-imputed distribution") +
theme_classic()
plot_grid(h1, h2, h3, h4, nrow = 2, ncol = 2)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 177 rows containing non-finite outside the scale range
## (`stat_bin()`).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
All imputation methods severely impact the distribution. There are a lot of missing values, so setting a single constant value doesn’t make much sense. Zero imputation is the worst, as it’s highly unlikely for close to 200 passengers to have the age of zero.
Maybe mode imputation would provide better results, but we’ll leave that up to you.
What about the results from the imputation methods from using MICE?
Here, we will need the information from the other variables in the dataset.
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniontitanic_numeric <- titanic_train %>%
select(Survived, Pclass, SibSp, Parch, Age)Here, we will use the following MICE imputation methods:
pmm: Predictive mean matching.cart: Classification and regression trees.laso.norm: Lasso linear regression.
Once again, the results will be stored in a data.frame:
mice_imputed <- data.frame(original = titanic_train$Age,
imputed_pmm = complete(mice(titanic_numeric, method = "pmm"))$Age,
imputed_cart = complete(mice(titanic_numeric, method = "cart"))$Age,
imputed_lasso = complete(mice(titanic_numeric, method = "lasso.norm"))$Age)##
## iter imp variable
## 1 1 Age
## 1 2 Age
## 1 3 Age
## 1 4 Age
## 1 5 Age
## 2 1 Age
## 2 2 Age
## 2 3 Age
## 2 4 Age
## 2 5 Age
## 3 1 Age
## 3 2 Age
## 3 3 Age
## 3 4 Age
## 3 5 Age
## 4 1 Age
## 4 2 Age
## 4 3 Age
## 4 4 Age
## 4 5 Age
## 5 1 Age
## 5 2 Age
## 5 3 Age
## 5 4 Age
## 5 5 Age
##
## iter imp variable
## 1 1 Age
## 1 2 Age
## 1 3 Age
## 1 4 Age
## 1 5 Age
## 2 1 Age
## 2 2 Age
## 2 3 Age
## 2 4 Age
## 2 5 Age
## 3 1 Age
## 3 2 Age
## 3 3 Age
## 3 4 Age
## 3 5 Age
## 4 1 Age
## 4 2 Age
## 4 3 Age
## 4 4 Age
## 4 5 Age
## 5 1 Age
## 5 2 Age
## 5 3 Age
## 5 4 Age
## 5 5 Age
##
## iter imp variable
## 1 1 Age
## 1 2 Age
## 1 3 Age
## 1 4 Age
## 1 5 Age
## 2 1 Age
## 2 2 Age
## 2 3 Age
## 2 4 Age
## 2 5 Age
## 3 1 Age
## 3 2 Age
## 3 3 Age
## 3 4 Age
## 3 5 Age
## 4 1 Age
## 4 2 Age
## 4 3 Age
## 4 4 Age
## 4 5 Age
## 5 1 Age
## 5 2 Age
## 5 3 Age
## 5 4 Age
## 5 5 Agemice_imputed## original imputed_pmm imputed_cart imputed_lasso
## 1 22.00 22.00 22.00 22.000000
## 2 38.00 38.00 38.00 38.000000
## 3 26.00 26.00 26.00 26.000000
## 4 35.00 35.00 35.00 35.000000
## 5 35.00 35.00 35.00 35.000000
## 6 NA 50.00 28.00 23.138597
## 7 54.00 54.00 54.00 54.000000
## 8 2.00 2.00 2.00 2.000000
## 9 27.00 27.00 27.00 27.000000
## 10 14.00 14.00 14.00 14.000000
## 11 4.00 4.00 4.00 4.000000
## 12 58.00 58.00 58.00 58.000000
## 13 20.00 20.00 20.00 20.000000
## 14 39.00 39.00 39.00 39.000000
## 15 14.00 14.00 14.00 14.000000
## 16 55.00 55.00 55.00 55.000000
## 17 2.00 2.00 2.00 2.000000
## 18 NA 19.00 34.00 29.699241
## 19 31.00 31.00 31.00 31.000000
## 20 NA 16.00 63.00 28.063402
## 21 35.00 35.00 35.00 35.000000
## 22 34.00 34.00 34.00 34.000000
## 23 15.00 15.00 15.00 15.000000
## 24 28.00 28.00 28.00 28.000000
## 25 8.00 8.00 8.00 8.000000
## 26 38.00 38.00 38.00 38.000000
## 27 NA 50.00 29.00 33.361442
## 28 19.00 19.00 19.00 19.000000
## 29 NA 27.00 45.00 49.407257
## 30 NA 13.00 45.50 44.382027
## 31 40.00 40.00 40.00 40.000000
## 32 NA 17.00 51.00 40.220626
## 33 NA 32.00 19.00 27.968374
## 34 66.00 66.00 66.00 66.000000
## 35 28.00 28.00 28.00 28.000000
## 36 42.00 42.00 42.00 42.000000
## 37 NA 24.00 13.00 18.964398
## 38 21.00 21.00 21.00 21.000000
## 39 18.00 18.00 18.00 18.000000
## 40 14.00 14.00 14.00 14.000000
## 41 40.00 40.00 40.00 40.000000
## 42 27.00 27.00 27.00 27.000000
## 43 NA 50.00 25.00 58.783021
## 44 3.00 3.00 3.00 3.000000
## 45 19.00 19.00 19.00 19.000000
## 46 NA 18.00 19.00 34.664493
## 47 NA 40.00 26.00 29.418582
## 48 NA 32.00 23.00 25.814748
## 49 NA 39.00 29.00 17.092353
## 50 18.00 18.00 18.00 18.000000
## 51 7.00 7.00 7.00 7.000000
## 52 21.00 21.00 21.00 21.000000
## 53 49.00 49.00 49.00 49.000000
## 54 29.00 29.00 29.00 29.000000
## 55 65.00 65.00 65.00 65.000000
## 56 NA 25.00 62.00 34.964772
## 57 21.00 21.00 21.00 21.000000
## 58 28.50 28.50 28.50 28.500000
## 59 5.00 5.00 5.00 5.000000
## 60 11.00 11.00 11.00 11.000000
## 61 22.00 22.00 22.00 22.000000
## 62 38.00 38.00 38.00 38.000000
## 63 45.00 45.00 45.00 45.000000
## 64 4.00 4.00 4.00 4.000000
## 65 NA 71.00 40.00 42.456328
## 66 NA 3.00 27.00 38.422024
## 67 29.00 29.00 29.00 29.000000
## 68 19.00 19.00 19.00 19.000000
## 69 17.00 17.00 17.00 17.000000
## 70 26.00 26.00 26.00 26.000000
## 71 32.00 32.00 32.00 32.000000
## 72 16.00 16.00 16.00 16.000000
## 73 21.00 21.00 21.00 21.000000
## 74 26.00 26.00 26.00 26.000000
## 75 32.00 32.00 32.00 32.000000
## 76 25.00 25.00 25.00 25.000000
## 77 NA 18.00 16.00 7.928571
## 78 NA 18.00 24.00 19.626921
## 79 0.83 0.83 0.83 0.830000
## 80 30.00 30.00 30.00 30.000000
## 81 22.00 22.00 22.00 22.000000
## 82 29.00 29.00 29.00 29.000000
## 83 NA 32.00 16.00 21.627360
## 84 28.00 28.00 28.00 28.000000
## 85 17.00 17.00 17.00 17.000000
## 86 33.00 33.00 33.00 33.000000
## 87 16.00 16.00 16.00 16.000000
## 88 NA 41.00 36.00 53.314791
## 89 23.00 23.00 23.00 23.000000
## 90 24.00 24.00 24.00 24.000000
## 91 29.00 29.00 29.00 29.000000
## 92 20.00 20.00 20.00 20.000000
## 93 46.00 46.00 46.00 46.000000
## 94 26.00 26.00 26.00 26.000000
## 95 59.00 59.00 59.00 59.000000
## 96 NA 25.00 19.00 25.431443
## 97 71.00 71.00 71.00 71.000000
## 98 23.00 23.00 23.00 23.000000
## 99 34.00 34.00 34.00 34.000000
## 100 34.00 34.00 34.00 34.000000
## 101 28.00 28.00 28.00 28.000000
## 102 NA 18.00 16.00 35.232305
## 103 21.00 21.00 21.00 21.000000
## 104 33.00 33.00 33.00 33.000000
## 105 37.00 37.00 37.00 37.000000
## 106 28.00 28.00 28.00 28.000000
## 107 21.00 21.00 21.00 21.000000
## 108 NA 45.00 30.00 25.935342
## 109 38.00 38.00 38.00 38.000000
## 110 NA 25.00 33.00 12.848847
## 111 47.00 47.00 47.00 47.000000
## 112 14.50 14.50 14.50 14.500000
## 113 22.00 22.00 22.00 22.000000
## 114 20.00 20.00 20.00 20.000000
## 115 17.00 17.00 17.00 17.000000
## 116 21.00 21.00 21.00 21.000000
## 117 70.50 70.50 70.50 70.500000
## 118 29.00 29.00 29.00 29.000000
## 119 24.00 24.00 24.00 24.000000
## 120 2.00 2.00 2.00 2.000000
## 121 21.00 21.00 21.00 21.000000
## 122 NA 25.00 23.00 28.661167
## 123 32.50 32.50 32.50 32.500000
## 124 32.50 32.50 32.50 32.500000
## 125 54.00 54.00 54.00 54.000000
## 126 12.00 12.00 12.00 12.000000
## 127 NA 13.00 29.00 30.054590
## 128 24.00 24.00 24.00 24.000000
## 129 NA 35.00 0.42 18.657682
## 130 45.00 45.00 45.00 45.000000
## 131 33.00 33.00 33.00 33.000000
## 132 20.00 20.00 20.00 20.000000
## 133 47.00 47.00 47.00 47.000000
## 134 29.00 29.00 29.00 29.000000
## 135 25.00 25.00 25.00 25.000000
## 136 23.00 23.00 23.00 23.000000
## 137 19.00 19.00 19.00 19.000000
## 138 37.00 37.00 37.00 37.000000
## 139 16.00 16.00 16.00 16.000000
## 140 24.00 24.00 24.00 24.000000
## 141 NA 28.00 44.00 20.391541
## 142 22.00 22.00 22.00 22.000000
## 143 24.00 24.00 24.00 24.000000
## 144 19.00 19.00 19.00 19.000000
## 145 18.00 18.00 18.00 18.000000
## 146 19.00 19.00 19.00 19.000000
## 147 27.00 27.00 27.00 27.000000
## 148 9.00 9.00 9.00 9.000000
## 149 36.50 36.50 36.50 36.500000
## 150 42.00 42.00 42.00 42.000000
## 151 51.00 51.00 51.00 51.000000
## 152 22.00 22.00 22.00 22.000000
## 153 55.50 55.50 55.50 55.500000
## 154 40.50 40.50 40.50 40.500000
## 155 NA 41.00 33.00 40.138689
## 156 51.00 51.00 51.00 51.000000
## 157 16.00 16.00 16.00 16.000000
## 158 30.00 30.00 30.00 30.000000
## 159 NA 41.00 41.00 20.403791
## 160 NA 5.00 11.00 -1.686867
## 161 44.00 44.00 44.00 44.000000
## 162 40.00 40.00 40.00 40.000000
## 163 26.00 26.00 26.00 26.000000
## 164 17.00 17.00 17.00 17.000000
## 165 1.00 1.00 1.00 1.000000
## 166 9.00 9.00 9.00 9.000000
## 167 NA 28.00 58.00 39.490353
## 168 45.00 45.00 45.00 45.000000
## 169 NA 45.50 62.00 42.199702
## 170 28.00 28.00 28.00 28.000000
## 171 61.00 61.00 61.00 61.000000
## 172 4.00 4.00 4.00 4.000000
## 173 1.00 1.00 1.00 1.000000
## 174 21.00 21.00 21.00 21.000000
## 175 56.00 56.00 56.00 56.000000
## 176 18.00 18.00 18.00 18.000000
## 177 NA 10.00 3.00 17.414502
## 178 50.00 50.00 50.00 50.000000
## 179 30.00 30.00 30.00 30.000000
## 180 36.00 36.00 36.00 36.000000
## 181 NA 16.00 16.00 -3.147851
## 182 NA 30.00 35.00 55.961696
## 183 9.00 9.00 9.00 9.000000
## 184 1.00 1.00 1.00 1.000000
## 185 4.00 4.00 4.00 4.000000
## 186 NA 38.00 45.00 36.839671
## 187 NA 20.00 25.00 22.049281
## 188 45.00 45.00 45.00 45.000000
## 189 40.00 40.00 40.00 40.000000
## 190 36.00 36.00 36.00 36.000000
## 191 32.00 32.00 32.00 32.000000
## 192 19.00 19.00 19.00 19.000000
## 193 19.00 19.00 19.00 19.000000
## 194 3.00 3.00 3.00 3.000000
## 195 44.00 44.00 44.00 44.000000
## 196 58.00 58.00 58.00 58.000000
## 197 NA 25.00 28.00 27.222496
## 198 42.00 42.00 42.00 42.000000
## 199 NA 24.00 16.00 12.997681
## 200 24.00 24.00 24.00 24.000000
## 201 28.00 28.00 28.00 28.000000
## 202 NA 5.00 1.00 14.523671
## 203 34.00 34.00 34.00 34.000000
## 204 45.50 45.50 45.50 45.500000
## 205 18.00 18.00 18.00 18.000000
## 206 2.00 2.00 2.00 2.000000
## 207 32.00 32.00 32.00 32.000000
## 208 26.00 26.00 26.00 26.000000
## 209 16.00 16.00 16.00 16.000000
## 210 40.00 40.00 40.00 40.000000
## 211 24.00 24.00 24.00 24.000000
## 212 35.00 35.00 35.00 35.000000
## 213 22.00 22.00 22.00 22.000000
## 214 30.00 30.00 30.00 30.000000
## 215 NA 3.00 47.00 20.278079
## 216 31.00 31.00 31.00 31.000000
## 217 27.00 27.00 27.00 27.000000
## 218 42.00 42.00 42.00 42.000000
## 219 32.00 32.00 32.00 32.000000
## 220 30.00 30.00 30.00 30.000000
## 221 16.00 16.00 16.00 16.000000
## 222 27.00 27.00 27.00 27.000000
## 223 51.00 51.00 51.00 51.000000
## 224 NA 25.00 19.00 37.804621
## 225 38.00 38.00 38.00 38.000000
## 226 22.00 22.00 22.00 22.000000
## 227 19.00 19.00 19.00 19.000000
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## 734 23.00 23.00 23.00 23.000000
## 735 23.00 23.00 23.00 23.000000
## 736 28.50 28.50 28.50 28.500000
## 737 48.00 48.00 48.00 48.000000
## 738 35.00 35.00 35.00 35.000000
## 739 NA 18.00 32.00 50.635961
## 740 NA 50.00 26.00 48.306316
## 741 NA 52.00 19.00 50.612894
## 742 36.00 36.00 36.00 36.000000
## 743 21.00 21.00 21.00 21.000000
## 744 24.00 24.00 24.00 24.000000
## 745 31.00 31.00 31.00 31.000000
## 746 70.00 70.00 70.00 70.000000
## 747 16.00 16.00 16.00 16.000000
## 748 30.00 30.00 30.00 30.000000
## 749 19.00 19.00 19.00 19.000000
## 750 31.00 31.00 31.00 31.000000
## 751 4.00 4.00 4.00 4.000000
## 752 6.00 6.00 6.00 6.000000
## 753 33.00 33.00 33.00 33.000000
## 754 23.00 23.00 23.00 23.000000
## 755 48.00 48.00 48.00 48.000000
## 756 0.67 0.67 0.67 0.670000
## 757 28.00 28.00 28.00 28.000000
## 758 18.00 18.00 18.00 18.000000
## 759 34.00 34.00 34.00 34.000000
## 760 33.00 33.00 33.00 33.000000
## 761 NA 13.00 16.00 31.803481
## 762 41.00 41.00 41.00 41.000000
## 763 20.00 20.00 20.00 20.000000
## 764 36.00 36.00 36.00 36.000000
## 765 16.00 16.00 16.00 16.000000
## 766 51.00 51.00 51.00 51.000000
## 767 NA 47.00 56.00 40.361236
## 768 30.50 30.50 30.50 30.500000
## 769 NA 3.00 25.00 15.651240
## 770 32.00 32.00 32.00 32.000000
## 771 24.00 24.00 24.00 24.000000
## 772 48.00 48.00 48.00 48.000000
## 773 57.00 57.00 57.00 57.000000
## 774 NA 13.00 24.00 36.102583
## 775 54.00 54.00 54.00 54.000000
## 776 18.00 18.00 18.00 18.000000
## 777 NA 50.00 24.00 12.751652
## 778 5.00 5.00 5.00 5.000000
## 779 NA 25.00 45.50 35.792110
## 780 43.00 43.00 43.00 43.000000
## 781 13.00 13.00 13.00 13.000000
## 782 17.00 17.00 17.00 17.000000
## 783 29.00 29.00 29.00 29.000000
## 784 NA 18.00 26.00 9.943468
## 785 25.00 25.00 25.00 25.000000
## 786 25.00 25.00 25.00 25.000000
## 787 18.00 18.00 18.00 18.000000
## 788 8.00 8.00 8.00 8.000000
## 789 1.00 1.00 1.00 1.000000
## 790 46.00 46.00 46.00 46.000000
## 791 NA 13.00 19.00 13.405442
## 792 16.00 16.00 16.00 16.000000
## 793 NA 16.00 11.00 -27.366029
## 794 NA 38.00 62.00 56.220349
## 795 25.00 25.00 25.00 25.000000
## 796 39.00 39.00 39.00 39.000000
## 797 49.00 49.00 49.00 49.000000
## 798 31.00 31.00 31.00 31.000000
## 799 30.00 30.00 30.00 30.000000
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## 804 0.42 0.42 0.42 0.420000
## 805 27.00 27.00 27.00 27.000000
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## 808 18.00 18.00 18.00 18.000000
## 809 39.00 39.00 39.00 39.000000
## 810 33.00 33.00 33.00 33.000000
## 811 26.00 26.00 26.00 26.000000
## 812 39.00 39.00 39.00 39.000000
## 813 35.00 35.00 35.00 35.000000
## 814 6.00 6.00 6.00 6.000000
## 815 30.50 30.50 30.50 30.500000
## 816 NA 71.00 62.00 37.351594
## 817 23.00 23.00 23.00 23.000000
## 818 31.00 31.00 31.00 31.000000
## 819 43.00 43.00 43.00 43.000000
## 820 10.00 10.00 10.00 10.000000
## 821 52.00 52.00 52.00 52.000000
## 822 27.00 27.00 27.00 27.000000
## 823 38.00 38.00 38.00 38.000000
## 824 27.00 27.00 27.00 27.000000
## 825 2.00 2.00 2.00 2.000000
## 826 NA 25.00 30.00 35.616908
## 827 NA 25.00 49.00 18.377707
## 828 1.00 1.00 1.00 1.000000
## 829 NA 45.00 26.00 15.378832
## 830 62.00 62.00 62.00 62.000000
## 831 15.00 15.00 15.00 15.000000
## 832 0.83 0.83 0.83 0.830000
## 833 NA 50.00 25.00 36.482607
## 834 23.00 23.00 23.00 23.000000
## 835 18.00 18.00 18.00 18.000000
## 836 39.00 39.00 39.00 39.000000
## 837 21.00 21.00 21.00 21.000000
## 838 NA 18.00 28.00 25.091181
## 839 32.00 32.00 32.00 32.000000
## 840 NA 35.00 44.00 40.287568
## 841 20.00 20.00 20.00 20.000000
## 842 16.00 16.00 16.00 16.000000
## 843 30.00 30.00 30.00 30.000000
## 844 34.50 34.50 34.50 34.500000
## 845 17.00 17.00 17.00 17.000000
## 846 42.00 42.00 42.00 42.000000
## 847 NA 5.00 11.00 -9.862554
## 848 35.00 35.00 35.00 35.000000
## 849 28.00 28.00 28.00 28.000000
## 850 NA 48.00 39.00 38.411686
## 851 4.00 4.00 4.00 4.000000
## 852 74.00 74.00 74.00 74.000000
## 853 9.00 9.00 9.00 9.000000
## 854 16.00 16.00 16.00 16.000000
## 855 44.00 44.00 44.00 44.000000
## 856 18.00 18.00 18.00 18.000000
## 857 45.00 45.00 45.00 45.000000
## 858 51.00 51.00 51.00 51.000000
## 859 24.00 24.00 24.00 24.000000
## 860 NA 13.00 28.00 58.146066
## 861 41.00 41.00 41.00 41.000000
## 862 21.00 21.00 21.00 21.000000
## 863 48.00 48.00 48.00 48.000000
## 864 NA 14.00 9.00 -3.237722
## 865 24.00 24.00 24.00 24.000000
## 866 42.00 42.00 42.00 42.000000
## 867 27.00 27.00 27.00 27.000000
## 868 31.00 31.00 31.00 31.000000
## 869 NA 25.00 28.00 14.966908
## 870 4.00 4.00 4.00 4.000000
## 871 26.00 26.00 26.00 26.000000
## 872 47.00 47.00 47.00 47.000000
## 873 33.00 33.00 33.00 33.000000
## 874 47.00 47.00 47.00 47.000000
## 875 28.00 28.00 28.00 28.000000
## 876 15.00 15.00 15.00 15.000000
## 877 20.00 20.00 20.00 20.000000
## 878 19.00 19.00 19.00 19.000000
## 879 NA 18.00 22.00 23.425275
## 880 56.00 56.00 56.00 56.000000
## 881 25.00 25.00 25.00 25.000000
## 882 33.00 33.00 33.00 33.000000
## 883 22.00 22.00 22.00 22.000000
## 884 28.00 28.00 28.00 28.000000
## 885 25.00 25.00 25.00 25.000000
## 886 39.00 39.00 39.00 39.000000
## 887 27.00 27.00 27.00 27.000000
## 888 19.00 19.00 19.00 19.000000
## 889 NA 4.00 32.00 13.016662
## 890 26.00 26.00 26.00 26.000000
## 891 32.00 32.00 32.00 32.000000It’s hard to judge from the table data alone, so we’ll draw a grid of histograms once again (copy and modify the code from the previous section):
h1 <- ggplot(mice_imputed, aes(x = original)) +
geom_histogram(fill = "#ad1538", color = "#000000", position = "identity") +
ggtitle("Original distribution") +
theme_classic()
h2 <- ggplot(mice_imputed, aes(x = imputed_pmm)) +
geom_histogram(fill = "#15ad4f", color = "#000000", position = "identity") +
ggtitle("MICE-pmm-imputed distribution") +
theme_classic()
h3 <- ggplot(mice_imputed, aes(x = imputed_cart)) +
geom_histogram(fill = "#1543ad", color = "#000000", position = "identity") +
ggtitle("MICE-cart-imputed distribution") +
theme_classic()
h4 <- ggplot(mice_imputed, aes(x = imputed_lasso)) +
geom_histogram(fill = "#ad8415", color = "#000000", position = "identity") +
ggtitle("MICE-lasso-imputed distribution") +
theme_classic()
plot_grid(h1, h2, h3, h4, nrow = 2, ncol = 2)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 177 rows containing non-finite outside the scale range
## (`stat_bin()`).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
The imputed distributions overall look much closer to the original one. The CART-imputed age distribution probably looks the closest. Also, take a look at the last histogram – the age values go below zero. This doesn’t make sense for a variable such as age, so you will need to correct the negative values manually if you opt for this imputation technique.
Imputation with R missForest Package
The Miss Forest imputation technique is based on the Random Forest algorithm. It’s a non-parametric imputation method, which means it doesn’t make explicit assumptions about the function form, but instead tries to estimate the function in a way that’s closest to the data points.
In other words, it builds a random forest model for each variable and then uses the model to predict missing values. You can learn more about it by reading the article by Oxford Academic.
Let’s see how it works for imputation in R. We’ll apply it to the entire numerical dataset and only extract the age:
library(missForest)##
## Attaching package: 'missForest'## The following object is masked from 'package:VIM':
##
## nrmsemissForest_imputed <- data.frame(
original = titanic_numeric$Age,
imputed_missForest = missForest(titanic_numeric)$ximp$Age
)
missForest_imputed## original imputed_missForest
## 1 22.00 22.000000
## 2 38.00 38.000000
## 3 26.00 26.000000
## 4 35.00 35.000000
## 5 35.00 35.000000
## 6 NA 28.935501
## 7 54.00 54.000000
## 8 2.00 2.000000
## 9 27.00 27.000000
## 10 14.00 14.000000
## 11 4.00 4.000000
## 12 58.00 58.000000
## 13 20.00 20.000000
## 14 39.00 39.000000
## 15 14.00 14.000000
## 16 55.00 55.000000
## 17 2.00 2.000000
## 18 NA 32.117919
## 19 31.00 31.000000
## 20 NA 27.099293
## 21 35.00 35.000000
## 22 34.00 34.000000
## 23 15.00 15.000000
## 24 28.00 28.000000
## 25 8.00 8.000000
## 26 38.00 38.000000
## 27 NA 28.935501
## 28 19.00 19.000000
## 29 NA 27.099293
## 30 NA 28.935501
## 31 40.00 40.000000
## 32 NA 37.533744
## 33 NA 27.099293
## 34 66.00 66.000000
## 35 28.00 28.000000
## 36 42.00 42.000000
## 37 NA 27.099293
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## 39 18.00 18.000000
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## 43 NA 28.935501
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## 48 NA 27.099293
## 49 NA 26.968359
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## 52 21.00 21.000000
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## 54 29.00 29.000000
## 55 65.00 65.000000
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## 58 28.50 28.500000
## 59 5.00 5.000000
## 60 11.00 11.000000
## 61 22.00 22.000000
## 62 38.00 38.000000
## 63 45.00 45.000000
## 64 4.00 4.000000
## 65 NA 45.034064
## 66 NA 14.045910
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## 68 19.00 19.000000
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## 71 32.00 32.000000
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## 78 NA 28.935501
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## 82 29.00 29.000000
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## 85 17.00 17.000000
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## 87 16.00 16.000000
## 88 NA 28.935501
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## 91 29.00 29.000000
## 92 20.00 20.000000
## 93 46.00 46.000000
## 94 26.00 26.000000
## 95 59.00 59.000000
## 96 NA 28.935501
## 97 71.00 71.000000
## 98 23.00 23.000000
## 99 34.00 34.000000
## 100 34.00 34.000000
## 101 28.00 28.000000
## 102 NA 28.935501
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## 104 33.00 33.000000
## 105 37.00 37.000000
## 106 28.00 28.000000
## 107 21.00 21.000000
## 108 NA 27.099293
## 109 38.00 38.000000
## 110 NA 23.695411
## 111 47.00 47.000000
## 112 14.50 14.500000
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## 118 29.00 29.000000
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## 121 21.00 21.000000
## 122 NA 28.935501
## 123 32.50 32.500000
## 124 32.50 32.500000
## 125 54.00 54.000000
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## 127 NA 28.935501
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## 141 NA 30.097261
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## 171 61.00 61.000000
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## 181 NA 9.825194
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## 183 9.00 9.000000
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## 197 NA 28.935501
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## 251 NA 28.935501
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## 296 NA 45.034064
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## 301 NA 27.099293
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## 305 NA 28.935501
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## 889 NA 25.821523
## 890 26.00 26.000000
## 891 32.00 32.000000There’s no option for different imputation techniques with Miss Forest, as it always uses the random forests algorithm:
Finally, let’s visualize the distributions:
h1 <- ggplot(missForest_imputed, aes(x = original)) +
geom_histogram(fill = "#ad1538", color = "#000000", position = "identity") +
ggtitle("Original distribution") +
theme_classic()
h2 <- ggplot(missForest_imputed, aes(x = imputed_missForest)) +
geom_histogram(fill = "#15ad4f", color = "#000000", position = "identity") +
ggtitle("random-forest-imputed distribution") +
theme_classic()
plot_grid(h1, h2, nrow = 1, ncol = 2)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 177 rows containing non-finite outside the scale range
## (`stat_bin()`).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
It looks like Miss Forest gravitated towards a constant value imputation since a large portion of values is around 35. The distribution is quite different from the original one, which means Miss Forest isn’t the best imputation technique we’ve seen today.