Checks after Multiple Imputation
Preface
R packages
In this practical, a number of R packages are used. If any of them are not installed you may be able to follow the practical but will not be able to run all of the code. The packages used (with versions that were used to generate the solutions) are:
- R version 4.3.0 (2023-04-21 ucrt)
mice(version: 3.15.0)RColorBrewer(version: 1.1.3)reshape2(version: 1.4.4)ggplot2(version: 3.4.2)
Help files
You can find help files for any function by adding a ?
before the name of the function.
Alternatively, you can look up the help pages online at https://www.rdocumentation.org/ or find the whole manual for a package at https://cran.r-project.org/web/packages/available_packages_by_name.html
Dataset
For this practical, we will use the EP16dat1 dataset, which is a subset of the NHANES (National Health and Nutrition Examination Survey) data.
To get the EP16dat1 dataset, load the file
EP16dat1.RData. You can download it here.
To load this dataset into R, you can use the command
file.choose() which opens the explorer and allows you to
navigate to the location of the file on your computer.
If you know the path to the file, you can also use
load("<path>/EP16dat1.RData").
If you have not followed the first practical or if you re-loaded the
EP16dat1 data, you need to re-code the variable
educ again:
EP16dat1$educ <- as.ordered(EP16dat1$educ)Imputed data
The imputed data are stored in a mids object called
imp that we created in the previous practical.
You can load it into your workspace by clicking the object
imps.RData if you are using RStudio. Alternatively, you can
load this workspace using
load("<path>/imps.RData").
The help
file tells us that a mids object is a list with several
elements:
data:
|
Original (incomplete) data set. |
imp:
|
The imputed values: A list of ncol(data) components, each
list component is a matrix with nmis[j] rows and
m columns.
|
m:
|
The number of imputations. |
where:
|
The missingness indicator matrix. |
blocks
|
The blocks argument of the mice() function.
|
call:
|
The call that created the mids object.
|
nmis:
|
The number of missing observations per variable. |
method:
|
The vector imputation methods. |
predictorMatrix:
|
The predictor matrix. |
visitSequence:
|
The sequence in which columns are visited during imputation. |
formulas
|
A named list of formulas corresponding the the imputed variables (blocks). |
post:
|
A vector of strings of length length(blocks) with commands
for post-processing.
|
seed:
|
The seed value of the solution. |
iteration:
|
The number of iterations. |
lastSeedValue:
|
The most recent seed value. |
chainMean:
|
The mean of imputed values per variable and iteration: a list of
m components. Each component is a matrix with
maxitcolumns and length(visitSequence) rows.
|
chainVar:
|
The variances of imputed values per variable and iteration(same
structure as chainMean).
|
loggedEvents:
|
A data.frame with the record of automatic corrective
actions and warnings; (NULL if no action was made).
|
version
|
Version number of the mice package that created the object. |
date
|
Date at which the object was created. |
Details of the loggedEvents:
mice() does some pre-processing of the data:
- variables containing missing values, that are not imputed but used as predictor are removed
- constant variables are removed
- collinear variables are removed
Furthermore, during each iteration
- variables (or dummy variables) that are linearly dependent are removed
polrimputation that does not converge is replaced bypolyreg.
data.frame in loggedEvents has the
following columns:
it
|
iteration number |
im
|
imputation number |
dep
|
name of the name of the variable being imputed |
meth
|
imputation method used |
out
|
character vector with names of altered/removed predictors |
Evaluate the imputation
Checking the settings
It is good practice to make sure that mice() has not
done any processing of the data that was not planned or that you are not
aware of. This means checking that the correct method,
predictorMatrix and visitSequence were
used.
Task
Do these checks for imp.
Solution
imp$method## HDL race DBP bili smoke DM
## "norm" "" "norm" "norm" "polr" ""
## gender WC chol HyperMed alc SBP
## "" "norm" "norm" "" "polr" "norm"
## wgt hypten cohort occup age educ
## "norm" "logreg" "" "polyreg" "" "polr"
## albu creat uricacid BMI hypchol hgt
## "norm" "pmm" "norm" "~I(wgt/hgt^2)" "logreg" "norm"imp$predictorMatrix## HDL race DBP bili smoke DM gender WC chol HyperMed alc SBP wgt hypten cohort occup age
## HDL 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## race 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## DBP 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## bili 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1
## smoke 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1
## DM 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1
## gender 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1
## WC 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1
## chol 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1
## HyperMed 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## alc 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1
## SBP 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1
## wgt 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1
## hypten 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1
## cohort 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## occup 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1
## age 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0
## educ 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## albu 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## creat 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## uricacid 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## BMI 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## hypchol 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1
## hgt 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1
## educ albu creat uricacid BMI hypchol hgt
## HDL 1 1 1 1 1 1 0
## race 1 1 1 1 1 1 0
## DBP 1 1 1 1 1 1 0
## bili 1 1 1 1 1 1 0
## smoke 1 1 1 1 1 1 0
## DM 1 1 1 1 1 1 0
## gender 1 1 1 1 1 1 0
## WC 1 1 1 1 1 1 0
## chol 1 1 1 1 1 0 0
## HyperMed 1 1 1 1 1 1 0
## alc 1 1 1 1 1 1 0
## SBP 1 1 1 1 1 1 0
## wgt 1 1 1 1 0 1 1
## hypten 1 1 1 1 1 1 0
## cohort 1 1 1 1 1 1 0
## occup 1 1 1 1 1 1 0
## age 1 1 1 1 1 1 0
## educ 0 1 1 1 1 1 0
## albu 1 0 1 1 1 1 0
## creat 1 1 0 1 1 1 0
## uricacid 1 1 1 0 1 1 0
## BMI 1 1 1 1 0 1 0
## hypchol 1 1 1 1 1 0 0
## hgt 1 1 1 1 0 1 0imp$visitSequence## [1] "HDL" "race" "DBP" "bili" "smoke" "DM" "gender" "WC"
## [9] "chol" "HyperMed" "alc" "SBP" "wgt" "hypten" "cohort" "occup"
## [17] "age" "educ" "albu" "creat" "uricacid" "hypchol" "hgt" "BMI"# you can also try
# identical(imp$method, meth)
# identical(imp$predictorMatrix, pred)
# identical(imp$visitSequence, visSeq)Logged events
Checking the loggedEvent shows us if mice()
detected any problems during the imputation.
Task 1
Check the loggedEvents for imp.
Solution 1
imp$loggedEvents## NULLThere are no logged events, great!
Task 2
Let’s see what would have happened if we had not prepared the
predictorMatrix, method and
visitSequence before imputation.
Run the imputation without setting any additional arguments:
impnaive <- mice(EP16dat1, m = 5, maxit = 30)
Take a look at the loggedEvents of
impnaive.
Solution 2
impnaive$loggedEvents## it im dep meth out
## 1 0 0 constant cohort
## 2 1 1 HyperMed polr hyptenyes
## 3 1 2 HyperMed polr hyptenyes
## 4 1 3 HyperMed polr hyptenyes
## 5 1 4 HyperMed polr hyptenyes
## 6 1 5 HyperMed polr hyptenyes
## 7 2 1 HyperMed polr hyptenyes
## 8 2 2 HyperMed polr hyptenyes
## 9 2 3 HyperMed polr hyptenyes
## 10 2 4 HyperMed polr hyptenyes
## 11 2 5 HyperMed polr hyptenyes
## 12 3 1 HyperMed polr hyptenyes
## 13 3 2 HyperMed polr hyptenyes
## 14 3 3 HyperMed polr hyptenyes
## 15 3 4 HyperMed polr hyptenyes
## 16 3 5 HyperMed polr hyptenyes
## 17 4 1 HyperMed polr hyptenyes
## 18 4 2 HyperMed polr hyptenyes
## 19 4 3 HyperMed polr hyptenyes
## 20 4 4 HyperMed polr hyptenyes
## 21 4 5 HyperMed polr hyptenyes
## 22 5 1 HyperMed polr hyptenyes
## 23 5 2 HyperMed polr hyptenyes
## 24 5 3 HyperMed polr hyptenyes
## 25 5 4 HyperMed polr hyptenyes
## 26 5 5 HyperMed polr hyptenyes
## 27 6 1 HyperMed polr hyptenyes
## 28 6 2 HyperMed polr hyptenyes
## 29 6 3 HyperMed polr hyptenyes
## 30 6 4 HyperMed polr hyptenyes
## 31 6 5 HyperMed polr hyptenyes
## 32 7 1 HyperMed polr hyptenyes
## 33 7 2 HyperMed polr hyptenyes
## 34 7 3 HyperMed polr hyptenyes
## 35 7 4 HyperMed polr hyptenyes
## 36 7 5 HyperMed polr hyptenyes
## 37 8 1 HyperMed polr hyptenyes
## 38 8 2 HyperMed polr hyptenyes
## 39 8 3 HyperMed polr hyptenyes
## 40 8 4 HyperMed polr hyptenyes
## 41 8 5 HyperMed polr hyptenyes
## 42 9 1 HyperMed polr hyptenyes
## 43 9 2 HyperMed polr hyptenyes
## 44 9 3 HyperMed polr hyptenyes
## 45 9 4 HyperMed polr hyptenyes
## 46 9 5 HyperMed polr hyptenyes
## 47 10 1 HyperMed polr hyptenyes
## 48 10 2 HyperMed polr hyptenyes
## 49 10 3 HyperMed polr hyptenyes
## 50 10 4 HyperMed polr hyptenyes
## 51 10 5 HyperMed polr hyptenyes
## 52 11 1 HyperMed polr hyptenyes
## 53 11 2 HyperMed polr hyptenyes
## 54 11 3 HyperMed polr hyptenyes
## 55 11 4 HyperMed polr hyptenyes
## 56 11 5 HyperMed polr hyptenyes
## 57 12 1 HyperMed polr hyptenyes
## 58 12 2 HyperMed polr hyptenyes
## 59 12 3 HyperMed polr hyptenyes
## 60 12 4 HyperMed polr hyptenyes
## 61 12 5 HyperMed polr hyptenyes
## 62 13 1 HyperMed polr hyptenyes
## 63 13 2 HyperMed polr hyptenyes
## 64 13 3 HyperMed polr hyptenyes
## 65 13 4 HyperMed polr hyptenyes
## 66 13 5 HyperMed polr hyptenyes
## 67 14 1 HyperMed polr hyptenyes
## 68 14 2 HyperMed polr hyptenyes
## 69 14 3 HyperMed polr hyptenyes
## 70 14 4 HyperMed polr hyptenyes
## 71 14 5 HyperMed polr hyptenyes
## 72 15 1 HyperMed polr hyptenyes
## 73 15 2 HyperMed polr hyptenyes
## 74 15 3 HyperMed polr hyptenyes
## 75 15 4 HyperMed polr hyptenyes
## 76 15 5 HyperMed polr hyptenyes
## 77 16 1 HyperMed polr hyptenyes
## 78 16 2 HyperMed polr hyptenyes
## 79 16 3 HyperMed polr hyptenyes
## 80 16 4 HyperMed polr hyptenyes
## 81 16 5 HyperMed polr hyptenyes
## 82 17 1 HyperMed polr hyptenyes
## 83 17 2 HyperMed polr hyptenyes
## 84 17 3 HyperMed polr hyptenyes
## 85 17 4 HyperMed polr hyptenyes
## 86 17 5 HyperMed polr hyptenyes
## 87 18 1 HyperMed polr hyptenyes
## 88 18 2 HyperMed polr hyptenyes
## 89 18 3 HyperMed polr hyptenyes
## 90 18 4 HyperMed polr hyptenyes
## 91 18 5 HyperMed polr hyptenyes
## 92 19 1 HyperMed polr hyptenyes
## 93 19 2 HyperMed polr hyptenyes
## 94 19 3 HyperMed polr hyptenyes
## 95 19 4 HyperMed polr hyptenyes
## 96 19 5 HyperMed polr hyptenyes
## 97 20 1 HyperMed polr hyptenyes
## 98 20 2 HyperMed polr hyptenyes
## 99 20 3 HyperMed polr hyptenyes
## 100 20 4 HyperMed polr hyptenyes
## 101 20 5 HyperMed polr hyptenyes
## 102 21 1 HyperMed polr hyptenyes
## 103 21 2 HyperMed polr hyptenyes
## 104 21 3 HyperMed polr hyptenyes
## 105 21 4 HyperMed polr hyptenyes
## 106 21 5 HyperMed polr hyptenyes
## 107 22 1 HyperMed polr hyptenyes
## 108 22 2 HyperMed polr hyptenyes
## 109 22 3 HyperMed polr hyptenyes
## 110 22 4 HyperMed polr hyptenyes
## 111 22 5 HyperMed polr hyptenyes
## 112 23 1 HyperMed polr hyptenyes
## 113 23 2 HyperMed polr hyptenyes
## 114 23 3 HyperMed polr hyptenyes
## 115 23 4 HyperMed polr hyptenyes
## 116 23 5 HyperMed polr hyptenyes
## 117 24 1 HyperMed polr hyptenyes
## 118 24 2 HyperMed polr hyptenyes
## 119 24 3 HyperMed polr hyptenyes
## 120 24 4 HyperMed polr hyptenyes
## 121 24 5 HyperMed polr hyptenyes
## 122 25 1 HyperMed polr hyptenyes
## 123 25 2 HyperMed polr hyptenyes
## 124 25 3 HyperMed polr hyptenyes
## 125 25 4 HyperMed polr hyptenyes
## 126 25 5 HyperMed polr hyptenyes
## 127 26 1 HyperMed polr hyptenyes
## 128 26 2 HyperMed polr hyptenyes
## 129 26 3 HyperMed polr hyptenyes
## 130 26 4 HyperMed polr hyptenyes
## 131 26 5 HyperMed polr hyptenyes
## 132 27 1 HyperMed polr hyptenyes
## 133 27 2 HyperMed polr hyptenyes
## 134 27 3 HyperMed polr hyptenyes
## 135 27 4 HyperMed polr hyptenyes
## 136 27 5 HyperMed polr hyptenyes
## 137 28 1 HyperMed polr hyptenyes
## 138 28 2 HyperMed polr hyptenyes
## 139 28 3 HyperMed polr hyptenyes
## 140 28 4 HyperMed polr hyptenyes
## 141 28 5 HyperMed polr hyptenyes
## 142 29 1 HyperMed polr hyptenyes
## 143 29 2 HyperMed polr hyptenyes
## 144 29 3 HyperMed polr hyptenyes
## 145 29 4 HyperMed polr hyptenyes
## 146 29 5 HyperMed polr hyptenyes
## 147 30 1 HyperMed polr hyptenyes
## 148 30 2 HyperMed polr hyptenyes
## 149 30 3 HyperMed polr hyptenyes
## 150 30 4 HyperMed polr hyptenyes
## 151 30 5 HyperMed polr hyptenyesThe loggedEvents of the “naive” imputation show that the
constant variable cohort was excluded before the imputation
(as it should be). Furthermore, in the imputation model for
HyperMed, the variable hyptenyes was excluded
(hyptenyes is the dummy variable belonging to
hypten).
Task 3
We did not change the visitSequence in
impnaive. Find out how that affected the imputed values of
BMI.
complete().
Solution 3
naiveDF1 <- complete(impnaive, 1)
naivecalcBMI <- with(naiveDF1, wgt/hgt^2)
impDF1 <- complete(imp, 1)
impcalcBMI <- with(impDF1, wgt/hgt^2)
cbind(naiveBMI = naiveDF1$BMI, naivecalcBMI,
impBMI = impDF1$BMI, impcalcBMI)[which(is.na(EP16dat1$BMI)), ]## naiveBMI naivecalcBMI impBMI impcalcBMI
## [1,] 29.28804 29.28669 12.29198 12.29198
## [2,] 45.77853 46.16466 26.31271 26.31271
## [3,] 37.58893 39.85655 21.32477 21.32477
## [4,] 28.24545 27.92749 12.11641 12.11641
## [5,] 28.50083 29.28615 26.55661 26.55661
## [6,] 46.22079 54.49122 37.22307 37.22307
## [7,] 29.81680 30.72272 19.89599 19.89599
## [8,] 26.36511 26.52057 28.69099 28.69099
## [9,] 22.31422 22.70998 25.80886 25.80886
## [10,] 41.53878 40.16697 38.69418 38.69418
## [11,] 26.62512 26.52057 29.93671 29.93671
## [12,] 24.03070 23.29698 22.30932 22.30932
## [13,] 24.27618 24.21038 22.70058 22.70058
## [14,] 30.84897 31.17668 26.87031 26.87031
## [15,] 26.25750 25.79309 36.32201 36.32201
## [16,] 34.54235 37.10645 31.52410 31.52410
## [17,] 25.74718 24.18514 22.72177 22.72177
## [18,] 24.53319 24.53319 21.04168 21.04168
## [19,] 20.19399 20.71344 22.31184 22.31184
## [20,] 27.45674 27.01934 26.08453 26.08453
## [21,] 26.38655 20.85066 21.31324 21.31324
## [22,] 24.40756 25.05929 25.05159 25.05159
## [23,] 29.13142 28.21474 25.19507 25.19507
## [24,] 24.69459 22.67395 20.61340 20.61340
## [25,] 29.53453 29.26408 31.60415 31.60415
## [26,] 39.57982 45.89482 44.32482 44.32482
## [27,] 36.31558 36.02272 34.53010 34.53010
## [28,] 25.24027 24.41214 23.56695 23.56695
## [29,] 25.39970 26.25655 26.99558 26.99558
## [30,] 28.27628 26.45250 24.79892 24.79892
## [31,] 26.49935 25.15391 26.77051 26.77051
## [32,] 21.78935 22.95737 33.93099 33.93099
## [33,] 31.93006 33.12522 36.44915 36.44915
## [34,] 27.43844 26.45250 43.50957 43.50957
## [35,] 20.36067 21.41254 21.04539 21.04539
## [36,] 41.14373 44.28506 22.62897 22.62897
## [37,] 29.95326 29.75790 31.75090 31.75090When we compare the imputed and calculated values of BMI
from impnaive we can see that the imputed hgt
and wgt give a different BMI than is imputed.
This is because BMI is imputed before wgt,
which means that the most recent imputed value of wgt is
from the previous iteration.
Changing the visitSequence in imp prevented
this inconsistency.
Convergence
In order to obtain correct results, the MICE algorithm needs to have converged. This can be checked visually by plotting summaries of the imputed values accross the iterations.
The mean and variance of the imputed values per iteration and
variable are stored in the elements chainMean and
chainVar of the mids object.
Task
Plot them to see if our imputation imp has
converged.
Solution
# implemented plotting function (use layout to change the number of rows and columns)
plot(imp, layout = c(6, 6))
The chains in imp seem to have converged, however it is
difficult to judge this based on only 10 iterations. In practice, more
iterations should be done.
To save you some time, I ran the imputation again with 30 iterations and the traceplots confirm convergence:
plot(imp30, layout = c(6, 6))
Continue
In comparison, impnaive had some convergence
problems:
plot(impnaive, layout = c(6, 7))
hgt, and wgt show a clear trend and the
chains do not mix well, i.e., there is more variation between the chains
than within each chain. (the same is the case for BMI).
These are clear signs that there is correlation or identification
problems between these variables and some other variables (which is why
we made adjustments to the predictorMatrix for
imp).
Imputed values
Now that we know that imp has converged, we can compare
the distribution of the imputed values against the distribution of the
observed values. When our imputation models fit the data well, they
should have similar distributions (conditional on the covariates used in
the imputation model).
Task 1
- Plot the distributions of the imputed variables (continuous and categorical).
- Make sure the imputed values are realistic (e.g., height of 2.50m or weight of 10kg for adults).
You can use densityplot() and propplot() to
get plots for all continuous and categorical variables.
propplot() is not part of any package. Copy the
following syntax that defines this function:
imp element of the mids object or create a
complete dataset containing all imputations using the function
complete() and get the summary of that.
Solution 1
# plot densities of continuous variables
densityplot(imp)
# plot for all categorical variables
propplot(imp, legend.position = 'bottom')
# get the summary of the "the" imputed values
sapply(Filter(function(x) nrow(x) > 0, imp$imp),
function(x) summary(unlist(x))
)## $HDL
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2946 1.1362 1.4342 1.4106 1.6614 2.6618
##
## $DBP
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 38.71 63.39 71.77 71.44 78.46 111.44
##
## $bili
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.2331 0.5785 0.7556 0.7684 0.9569 1.7881
##
## $smoke
## never former current
## 4 2 4
##
## $WC
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 57.63 87.10 98.25 99.52 109.17 149.89
##
## $chol
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.964 4.169 5.007 4.946 5.701 7.757
##
## $HyperMed
## Mode NA's
## logical 4065
##
## $alc
## 0 <=1 1-3 3-7 >7
## 243 730 221 161 240
##
## $SBP
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 54.63 111.00 125.98 124.95 138.58 171.71
##
## $wgt
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 28.14 62.81 73.79 76.09 92.02 125.26
##
## $hypten
## no yes
## 167 43
##
## $occup
## working looking for work not working
## 56 4 25
##
## $educ
## Less than 9th grade 9-11th grade High school graduate some college
## 0 0 1 2
## College or above
## 2
##
## $albu
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.293 4.075 4.301 4.290 4.527 5.285
##
## $creat
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4500 0.7150 0.8600 0.8689 0.9800 2.3400
##
## $uricacid
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.090 4.382 5.213 5.295 6.231 10.074
##
## $BMI
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 12.12 24.25 27.47 28.46 31.33 48.05
##
## $hypchol
## no yes
## 363 67
##
## $hgt
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.386 1.532 1.615 1.620 1.680 1.961Unfortunately, we have some negative imputed values for
bili. Often, this would not result in bias in the analysis,
but may be difficult to explain when providing a summary of the imputed
data in a publication. In the present example we can see that the
observed values have a slightly right-skewed distribution compared to
the imputed values. Re-doing the imputation with pmm
instead of norm for bili should fix this.
(However, since the imputations seem fine overall, and there is little
knowledge gain in re-doing the previous steps, we will skip this
repetition in this practical.)
The distributions of the imputed values for hgt and
SBP differ a bit from the distributions of the observed
data.
We also imputed a larger proportion than might have been expected in
the highest category of alc, and the distribution of values
for smoke looks a bit weird (but smoke only
has one missing value, which makes it difficult to judge the
distribution of the imputed values).
Task 2
Investigate if differences in the distributions of observed and imputed values, can be explained by other variables. Check this for
SBPconditional ongenderandhyptenhgtconditional ongenderalcconditional ongenderorsmoke
Solution 2
densityplot(imp, ~SBP|hypten + gender)
densityplot(imp, ~hgt|gender)
propplot(imp, alc ~ gender + smoke, legend.position = 'bottom')
© Nicole Erler