Imputation

This Lecture:

Missing data patterns
Imputation methods
- simputation package
- mice package

I use the following packages in this lecture

library(mice) # for visualisation & pmm
library(VIM) # visualisation & several hotdeck imputation methods 
#(fast implementation)
library(simputation) # common interface for several imputation methods
library(magrittr) # for pipe operator
library(naniar) # additional package for practical
library(visdat) # visualisation of datasets
library(UpSetR) # Upset plots
library(ggplot2) # plots

Missing data patterns

`nhanes` data

age: Age group (1=20-39, 2=40-59, 3=60+)

bmi: Body mass index (kg/m**2)

hyp: High blood pressure, hypertension (1=no,2=yes)

chl: Total serum cholesterol (mg/dL)

head(nhanes, n = 10)

##    age  bmi hyp chl
## 1    1   NA  NA  NA
## 2    2 22.7   1 187
## 3    1   NA   1 187
## 4    3   NA  NA  NA
## 5    1 20.4   1 113
## 6    3   NA  NA 184
## 7    1 22.5   1 118
## 8    1 30.1   1 187
## 9    2 22.0   1 238
## 10   2   NA  NA  NA

Visualise missing data pattern

VIM::aggr(nhanes, col=c('blue','red'), numbers = TRUE, sortVars = TRUE,
                  labels = names(nhanes), cex.axis = .8, gap = 3, 
                  ylab = c("Histogram of missing data", "Red is Missing Data"))

## 
##  Variables sorted by number of missings: 
##  Variable Count
##       chl  0.40
##       bmi  0.36
##       hyp  0.32
##       age  0.00

pattern <- mice::md.pattern(nhanes)

pattern

##    age hyp bmi chl   
## 13   1   1   1   1  0
## 3    1   1   1   0  1
## 1    1   1   0   1  1
## 1    1   0   0   1  2
## 7    1   0   0   0  3
##      0   8   9  10 27

naniar::gg_miss_upset(nhanes)

Imputation methods

Specifying models in `simputation`

Common structure for specifying an imputation model:

impute_<model>(data, formula, [model-specific options])

Structure of the model in formula:

IMPUTED ~ MODEL_SPECIFICATION [ | GROUPING ]

Regression imputation

imp_1 <- impute_lm(nhanes, bmi ~ age + hyp + chl)
head(imp_1)

##   age      bmi hyp chl
## 1   1       NA  NA  NA
## 2   2 22.70000   1 187
## 3   1 29.63182   1 187
## 4   3       NA  NA  NA
## 5   1 20.40000   1 113
## 6   3       NA  NA 184

head(nhanes)

##   age  bmi hyp chl
## 1   1   NA  NA  NA
## 2   2 22.7   1 187
## 3   1   NA   1 187
## 4   3   NA  NA  NA
## 5   1 20.4   1 113
## 6   3   NA  NA 184

Median imputation

imp_2 <- simputation::impute_median(imp_1, bmi ~ age)
head(imp_2)

##   age      bmi hyp chl
## 1   1 29.61591  NA  NA
## 2   2 22.70000   1 187
## 3   1 29.63182   1 187
## 4   3 25.20000  NA  NA
## 5   1 20.40000   1 113
## 6   3 25.20000  NA 184

imp_2a <- nhanes %>%
          simputation::impute_lm(bmi ~ age + hyp + chl) %>%
          simputation::impute_median(bmi ~ age)
head(imp_2a)

##   age      bmi hyp chl
## 1   1 29.61591  NA  NA
## 2   2 22.70000   1 187
## 3   1 29.63182   1 187
## 4   3 25.20000  NA  NA
## 5   1 20.40000   1 113
## 6   3 25.20000  NA 184

Other methods

impute_cart(): decision tree imputation
impute_hotdeck(): random and sequential hot deck, k-nearest neighbours imputation and predictive mean matching.
impute_multivariate(): imputation based on EM-estimation of multivariate normal parameters, imputation based on iterative Random Forest estimates and stochastic imptuation based on bootstrapped EM-estimatin of multivariate normal parameters.
impute_proxy(): Impute missing values by a constant, by copying another variable, computing transformations from other variables.

Multivariate Imputation by Chained Equations (mice)

Default imputation

imp <- mice(nhanes, print = FALSE)

Defaults:

pmm, predictive mean matching (numeric data)
logreg, logistic regression imputation (binary data, factor with 2 levels)
polyreg, polytomous regression imputation (unordered cateogrical data, factor > 2 levels)
polr, proportional odds model (ordered data, factor > 2 levels)

Check imputations

stripplot(imp, chl, pch = 19, xlab = "Imputation number")

Vary number of imputations

Just 4 imputed datasets instead of the default (5)

imp <- mice(nhanes, m = 4, print = F)

Predictor matrix

imp$pred

##     age bmi hyp chl
## age   0   1   1   1
## bmi   1   0   1   1
## hyp   1   1   0   1
## chl   1   1   1   0

1 = column used to impute row

Initial predictor matrix

ini <- mice(nhanes, maxit = 0, print = F)
pred <- ini$pred
pred

##     age bmi hyp chl
## age   0   1   1   1
## bmi   1   0   1   1
## hyp   1   1   0   1
## chl   1   1   1   0

Change predictor matrix

We do not use hyp to impute any other variables

pred[ ,"hyp"] <- 0
pred

##     age bmi hyp chl
## age   0   1   0   1
## bmi   1   0   0   1
## hyp   1   1   0   1
## chl   1   1   0   0

imp <- mice(nhanes, m = 4, init = pred, print = F)

Changing imputation methods

imp$meth

##   age   bmi   hyp   chl 
##    "" "pmm" "pmm" "pmm"

str(nhanes)

## 'data.frame':    25 obs. of  4 variables:
##  $ age: num  1 2 1 3 1 3 1 1 2 2 ...
##  $ bmi: num  NA 22.7 NA NA 20.4 NA 22.5 30.1 22 NA ...
##  $ hyp: num  NA 1 1 NA 1 NA 1 1 1 NA ...
##  $ chl: num  NA 187 187 NA 113 184 118 187 238 NA ...

str(nhanes2)

## 'data.frame':    25 obs. of  4 variables:
##  $ age: Factor w/ 3 levels "20-39","40-59",..: 1 2 1 3 1 3 1 1 2 2 ...
##  $ bmi: num  NA 22.7 NA NA 20.4 NA 22.5 30.1 22 NA ...
##  $ hyp: Factor w/ 2 levels "no","yes": NA 1 1 NA 1 NA 1 1 1 NA ...
##  $ chl: num  NA 187 187 NA 113 184 118 187 238 NA ...

imp <- mice(nhanes2, m = 4, init = pred, print = F, seed = 101)
imp$meth

##      age      bmi      hyp      chl 
##       ""    "pmm" "logreg"    "pmm"

Available methods

methods(mice)

##  [1] mice.impute.2l.bin       mice.impute.2l.lmer     
##  [3] mice.impute.2l.norm      mice.impute.2l.pan      
##  [5] mice.impute.2lonly.mean  mice.impute.2lonly.norm 
##  [7] mice.impute.2lonly.pmm   mice.impute.cart        
##  [9] mice.impute.jomoImpute   mice.impute.lda         
## [11] mice.impute.logreg       mice.impute.logreg.boot 
## [13] mice.impute.mean         mice.impute.midastouch  
## [15] mice.impute.norm         mice.impute.norm.boot   
## [17] mice.impute.norm.nob     mice.impute.norm.predict
## [19] mice.impute.panImpute    mice.impute.passive     
## [21] mice.impute.pmm          mice.impute.polr        
## [23] mice.impute.polyreg      mice.impute.quadratic   
## [25] mice.impute.rf           mice.impute.ri          
## [27] mice.impute.sample       mice.mids               
## [29] mice.theme              
## see '?methods' for accessing help and source code

Extracting imputed data

The 3rd imputed dataset

c3 <- complete(imp, 3) 
md.pattern(c3, plot = FALSE)

##  /\     /\
## {  `---'  }
## {  O   O  }
## ==>  V <==  No need for mice. This data set is completely observed.
##  \  \|/  /
##   `-----'

##    age bmi hyp chl  
## 25   1   1   1   1 0
##      0   0   0   0 0

All imputed datasets in long format

complete(imp, "long")

##     .imp .id   age  bmi hyp chl
## 1      1   1 20-39 30.1  no 238
## 2      1   2 40-59 22.7  no 187
## 3      1   3 20-39 27.2  no 187
## 4      1   4 60-99 22.0  no 184
## 5      1   5 20-39 20.4  no 113
## 6      1   6 60-99 27.5 yes 184
## 7      1   7 20-39 22.5  no 118
## 8      1   8 20-39 30.1  no 187
## 9      1   9 40-59 22.0  no 238
## 10     1  10 40-59 22.5 yes 187
## 11     1  11 20-39 33.2  no 238
## 12     1  12 40-59 20.4  no 229
## 13     1  13 60-99 21.7  no 206
## 14     1  14 40-59 28.7 yes 204
## 15     1  15 20-39 29.6  no 187
## 16     1  16 20-39 27.2  no 118
## 17     1  17 60-99 27.2 yes 284
## 18     1  18 40-59 26.3 yes 199
## 19     1  19 20-39 35.3  no 218
## 20     1  20 60-99 25.5 yes 199
## 21     1  21 20-39 30.1  no 131
## 22     1  22 20-39 33.2  no 229
## 23     1  23 20-39 27.5  no 131
## 24     1  24 60-99 24.9  no 184
## 25     1  25 40-59 27.4  no 186
## 26     2   1 20-39 33.2 yes 229
## 27     2   2 40-59 22.7  no 187
## 28     2   3 20-39 22.0  no 187
## 29     2   4 60-99 30.1  no 199
## 30     2   5 20-39 20.4  no 113
## 31     2   6 60-99 26.3  no 184
## 32     2   7 20-39 22.5  no 118
## 33     2   8 20-39 30.1  no 187
## 34     2   9 40-59 22.0  no 238
## 35     2  10 40-59 35.3 yes 218
## 36     2  11 20-39 33.2 yes 187
## 37     2  12 40-59 20.4 yes 186
## 38     2  13 60-99 21.7  no 206
## 39     2  14 40-59 28.7 yes 204
## 40     2  15 20-39 29.6  no 187
## 41     2  16 20-39 22.5  no 238
## 42     2  17 60-99 27.2 yes 284
## 43     2  18 40-59 26.3 yes 199
## 44     2  19 20-39 35.3  no 218
## 45     2  20 60-99 25.5 yes 186
## 46     2  21 20-39 29.6  no 187
## 47     2  22 20-39 33.2  no 229
## 48     2  23 20-39 27.5  no 131
## 49     2  24 60-99 24.9  no 218
## 50     2  25 40-59 27.4  no 186
## 51     3   1 20-39 35.3 yes 199
## 52     3   2 40-59 22.7  no 187
## 53     3   3 20-39 28.7  no 187
## 54     3   4 60-99 28.7  no 184
## 55     3   5 20-39 20.4  no 113
## 56     3   6 60-99 27.4  no 184
## 57     3   7 20-39 22.5  no 118
## 58     3   8 20-39 30.1  no 187
## 59     3   9 40-59 22.0  no 238
## 60     3  10 40-59 27.4  no 187
## 61     3  11 20-39 30.1  no 131
## 62     3  12 40-59 22.5  no 131
## 63     3  13 60-99 21.7  no 206
## 64     3  14 40-59 28.7 yes 204
## 65     3  15 20-39 29.6  no 187
## 66     3  16 20-39 30.1 yes 199
## 67     3  17 60-99 27.2 yes 284
## 68     3  18 40-59 26.3 yes 199
## 69     3  19 20-39 35.3  no 218
## 70     3  20 60-99 25.5 yes 184
## 71     3  21 20-39 22.0  no 118
## 72     3  22 20-39 33.2  no 229
## 73     3  23 20-39 27.5  no 131
## 74     3  24 60-99 24.9  no 206
## 75     3  25 40-59 27.4  no 186
## 76     4   1 20-39 33.2  no 218
## 77     4   2 40-59 22.7  no 187
## 78     4   3 20-39 29.6  no 187
## 79     4   4 60-99 20.4  no 187
## 80     4   5 20-39 20.4  no 113
## 81     4   6 60-99 22.7  no 184
## 82     4   7 20-39 22.5  no 118
## 83     4   8 20-39 30.1  no 187
## 84     4   9 40-59 22.0  no 238
## 85     4  10 40-59 28.7  no 184
## 86     4  11 20-39 28.7  no 187
## 87     4  12 40-59 26.3  no 184
## 88     4  13 60-99 21.7  no 206
## 89     4  14 40-59 28.7 yes 204
## 90     4  15 20-39 29.6  no 187
## 91     4  16 20-39 30.1  no 199
## 92     4  17 60-99 27.2 yes 284
## 93     4  18 40-59 26.3 yes 199
## 94     4  19 20-39 35.3  no 218
## 95     4  20 60-99 25.5 yes 186
## 96     4  21 20-39 33.2  no 199
## 97     4  22 20-39 33.2  no 229
## 98     4  23 20-39 27.5  no 131
## 99     4  24 60-99 24.9  no 199
## 100    4  25 40-59 27.4  no 186

Pooling analyses

fit <- with(imp, lm(bmi ~ chl))
fit

## call :
## with.mids(data = imp, expr = lm(bmi ~ chl))
## 
## call1 :
## mice(data = nhanes2, m = 4, printFlag = F, seed = 101, init = pred)
## 
## nmis :
## age bmi hyp chl 
##   0   9   8  10 
## 
## analyses :
## [[1]]
## 
## Call:
## lm(formula = bmi ~ chl)
## 
## Coefficients:
## (Intercept)          chl  
##    22.15053      0.02338  
## 
## 
## [[2]]
## 
## Call:
## lm(formula = bmi ~ chl)
## 
## Coefficients:
## (Intercept)          chl  
##     19.9017       0.0367  
## 
## 
## [[3]]
## 
## Call:
## lm(formula = bmi ~ chl)
## 
## Coefficients:
## (Intercept)          chl  
##     20.2657       0.0371  
## 
## 
## [[4]]
## 
## Call:
## lm(formula = bmi ~ chl)
## 
## Coefficients:
## (Intercept)          chl  
##    19.04484      0.04203

summary(fit$analyses[[2]])

## 
## Call:
## lm(formula = bmi ~ chl)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.6367 -3.6490 -0.3548  2.8947  7.3974 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 19.90171    4.98265   3.994 0.000571 ***
## chl          0.03670    0.02496   1.470 0.155057    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.549 on 23 degrees of freedom
## Multiple R-squared:  0.0859, Adjusted R-squared:  0.04616 
## F-statistic: 2.161 on 1 and 23 DF,  p-value: 0.1551

pool.fit <- pool(fit)
summary(pool.fit)

##                estimate  std.error statistic       df      p.value
## (Intercept) 20.34068248 4.54833393  4.472117 17.81040 0.0003016604
## chl          0.03480344 0.02379386  1.462707 16.27191 0.1625944773

Other packages for imputation

mi
Hmisc
Amelia
mix

Practical

Extra slides

Visualization

naniar::gg_miss_fct(x = nhanes, fct = age)

Visualization

visdat::vis_miss(nhanes)

Convergence

plot(imp)

Seed values

imp <- mice(nhanes, m = 4, init = pred, print = F, seed = 101)

Imputation

Jolien Cremers

Statistical Programming with R

Imputation

This Lecture:

I use the following packages in this lecture

Missing data patterns

`nhanes` data

Visualise missing data pattern

Imputation methods

Specifying models in `simputation`

Regression imputation

Median imputation

Other methods

Multivariate Imputation by Chained Equations (mice)

Check imputations

Vary number of imputations

Predictor matrix

Initial predictor matrix

Change predictor matrix

Changing imputation methods

Available methods

Extracting imputed data

Pooling analyses

Other packages for imputation

Practical

Extra slides

Visualization

Visualization

Convergence

Seed values

Imputation

Jolien Cremers

Statistical Programming with R

Imputation

This Lecture:

I use the following packages in this lecture

Missing data patterns

nhanes data

Visualise missing data pattern

Imputation methods

Specifying models in simputation

Regression imputation

Median imputation

Other methods

Multivariate Imputation by Chained Equations (mice)

Check imputations

Vary number of imputations

Predictor matrix

Initial predictor matrix

Change predictor matrix

Changing imputation methods

Available methods

Extracting imputed data

Pooling analyses

Other packages for imputation

Practical

Extra slides

Visualization

Visualization

Convergence

Seed values

`nhanes` data

Specifying models in `simputation`