Missing data


exploration, imputation,
and evaluation

Hanne Oberman

Utrecht University

Missing data

NAs


range(your_dataset$Y)
[1] NA NA

Complete-case analysis (CCA)


mean(your_dataset$Y)
[1] NA


mean(your_dataset$Y, na.rm = TRUE)
[1] 0

CCA decreases sample size

CCA biases estimates

CCA yields invalid inferences

Alternative solution

install.packages("mice")
install.packages("ggmice")
install.packages("ggplot2")
install.packages("palmerpenguins")

Notation

  • \(Y\) random variable with missing data

    • \(Y^\mathrm{obs}\) true and observed values of \(Y\)
    • \(Y^\mathrm{mis}\) true but unobserved values of \(Y\)

  • \(X\) complete covariate

  • \(R\) response indicator

    • \(R = 1\) if \(Y\) is observed
    • \(R = 0\) if \(Y\) is missing

Missing data model

\[ P(R|Y^\mathrm{obs}, Y^\mathrm{mis}, X, \psi) \]

%%{
init: {
  "flowchart": {"useMaxWidth": "true", "htmlLabels": "true", "theme": "neutral"},
  "securityLevel": "loose"
}}%%
flowchart TD
    subgraph incomplete variable
          A[Y<sup>obs</sup>]
          B[Y<sup>mis</sup>]
    end
    subgraph covariate
          C[X]
    end
    D(ψ)
    E(R)
    A -.-> E
    B -.-> E    
    C -.-> E 
    D --> E

MCAR: Missing Completely at Random

\[ P(R|Y^\mathrm{obs}, Y^\mathrm{mis}, X, \psi) = P(R|\psi) \]

Examples:

  • data transmission error
  • random sample

MAR: Missing at Random

\[ P(R|Y^\mathrm{obs}, Y^\mathrm{mis}, X, \psi) = P(R|Y^\mathrm{obs}, X, \psi) \]

Examples:

  • income, where we have \(X\) related to wealth
  • branch patterns (e.g. how old are your children?)

MNAR: Missing Not at Random

\[ P(R|Y^\mathrm{obs}, Y^\mathrm{mis}, X, \psi) \text{ does not simplify } \]

Examples:

  • income, without covariates related to income
  • self-reported body weight

Implications

  • Missing Completely At Random (MCAR) \(\approx\) not data dependent
  • Missing At Random (MAR) \(\approx\) seen data dependent
  • Missing Not At Random (MNAR) \(\approx\) unseen data dependent

Imputation

MICE

mice

Case study

set.seed(123)
library(palmerpenguins)
library(mice)
library(ggmice)
library(ggplot2)

Research question

Code 
ggplot(penguins, aes(body_mass_g, flipper_length_mm, color = species)) + 
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) + 
  scale_color_manual(values = c("Adelie" = "darkorange", "Chinstrap" = "darkorchid", "Gentoo" = "cyan4")) +
  theme_classic()

Research question

Code 
ggmice(penguins, aes(body_mass_g, flipper_length_mm, group = species)) + 
  geom_point() +
  geom_smooth(method = "lm", se = FALSE)

Incomplete data

str(penguins)
tibble [344 × 8] (S3: tbl_df/tbl/data.frame)
 $ species          : Factor w/ 3 levels "Adelie","Chinstrap",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ island           : Factor w/ 3 levels "Biscoe","Dream",..: 3 3 3 3 3 3 3 3 3 3 ...
 $ bill_length_mm   : num [1:344] 39.1 39.5 40.3 NA 36.7 39.3 38.9 39.2 34.1 42 ...
 $ bill_depth_mm    : num [1:344] 18.7 17.4 18 NA 19.3 20.6 17.8 19.6 18.1 20.2 ...
 $ flipper_length_mm: int [1:344] 181 186 195 NA 193 190 181 195 193 190 ...
 $ body_mass_g      : int [1:344] 3750 3800 3250 NA 3450 3650 3625 4675 3475 4250 ...
 $ sex              : Factor w/ 2 levels "female","male": 2 1 1 NA 1 2 1 2 NA NA ...
 $ year             : int [1:344] 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 ...

Incomplete data

visdat::vis_dat(penguins)

Response indicator

is.na(penguins)
       species island bill_length_mm bill_depth_mm flipper_length_mm
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       body_mass_g   sex  year
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Response indicator

naniar::vis_miss(penguins)

Missingness rate

colSums(is.na(penguins))
          species            island    bill_length_mm     bill_depth_mm 
                0                 0                 2                 2 
flipper_length_mm       body_mass_g               sex              year 
                2                 2                11                 0

Missingness rate

VIM::aggr(penguins, numbers = TRUE, prop = FALSE)

Missing data pattern

md.pattern(penguins)
    species island year bill_length_mm bill_depth_mm flipper_length_mm
333       1      1    1              1             1                 1
9         1      1    1              1             1                 1
2         1      1    1              0             0                 0
          0      0    0              2             2                 2
    body_mass_g sex   
333           1   1  0
9             1   0  1
2             0   0  5
              2  11 19

Missing data pattern

plot_pattern(penguins)

Imputation workflow

Imputation models

meth <- make.method(penguins)
pred <- make.predictorMatrix(penguins)
plot_pred(pred, method = meth, square = FALSE)

Imputation models

pred <- quickpred(penguins, mincor = 0.4)
plot_pred(pred, method = meth, square = FALSE)

Correlation

plot_corr(penguins, square = FALSE)

Plot \(Y\) by auxiliary variable

ggmice(penguins, aes(sex, flipper_length_mm)) +
  geom_point(size = 2)

Plot \(Y\) by auxiliary variable

ggmice(penguins, aes(x = sex, y = flipper_length_mm)) +
  geom_jitter(height = 0, width = 0.25) +
  geom_boxplot(alpha = 0.1)

Plot \(Y\) by missingness indicator

ggmice(penguins, aes(flipper_length_mm)) +
  geom_histogram(fill = "white") +
  facet_grid(factor(
  is.na(sex), 
  levels = c(TRUE, FALSE), 
  labels = c("missing sex", "observed sex")
  ) ~ ., scales = "free_y")

Plot \(Y\) by auxiliary variables

ggmice(penguins, aes(flipper_length_mm)) +
  geom_histogram(fill = "white") +
  facet_grid(factor(
  is.na(sex), 
  levels = c(TRUE, FALSE), 
  labels = c("missing sex", "observed sex")
  ) ~ species)

Adjust imputation models

meth["flipper_length_mm"] <- "norm"
pred["flipper_length_mm", c("species", "sex")] <- 1
pred["sex", "flipper_length_mm"] <- 1
plot_pred(pred, method = meth, square = FALSE)

Impute

imp <- mice(
  penguins, 
  pred = pred, 
  method = meth, 
  m = 10)

 iter imp variable
  1   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  1   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  2   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  3   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  4   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  5   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex

Trace plot

plot_trace(imp)

Add iterations

imp <- mice.mids(imp, maxit = 25)

 iter imp variable
  6   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  6   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  7   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  8   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  9   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  10   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  11   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  12   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  13   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  14   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   3  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   4  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   5  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   6  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   7  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   8  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   9  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  15   10  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  16   1  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
  16   2  bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g  sex
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Trace plot after iterating

plot_trace(imp)

Stripplot of the outcome

ggmice(imp, aes(x = .imp, y = flipper_length_mm)) +
  geom_point() +
  labs(x = "Imputation number")

Distribution of the outcome

ggmice(imp, aes(x = flipper_length_mm, group = .imp)) +
  geom_density()

Stripplot of predictor variable

ggmice(imp, aes(x = .imp, y = body_mass_g)) +
  geom_point() +
  labs(x = "Imputation number")

Stripplot of auxiliary variable

ggmice(imp, aes(x = .imp, y = sex)) +
  geom_jitter(height = 0.1, width = 0.05) +
  labs(x = "Imputation number")

Analysis results

Research question after imputation

ggmice(imp, aes(x = body_mass_g, y = flipper_length_mm)) +
  geom_point()

Analyze imputated data

fit <- with(imp, lm(flipper_length_mm ~ body_mass_g))
fit$analyses
[[1]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.9891       0.0152  


[[2]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.5145       0.0153  


[[3]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.6768       0.0153  


[[4]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.6814       0.0153  


[[5]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.7793       0.0153  


[[6]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.7109       0.0153  


[[7]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.4643       0.0153  


[[8]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.7935       0.0153  


[[9]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   137.1453       0.0152  


[[10]]

Call:
lm(formula = flipper_length_mm ~ body_mass_g)

Coefficients:
(Intercept)  body_mass_g  
   136.8018       0.0153

Pooled results

Pooling analysis results

est <- pool(fit) 
est$pooled
term m estimate ubar b t dfcom df riv lambda fmi
(Intercept) 10 136.756 3.95 0.041 4 342 335 0.011 0.011 0.017
body_mass_g 10 0.015 0.00 0.000 0 342 334 0.012 0.012 0.018

Flexible approach

fit <- purrr::map(
  complete(imp, "all"), 
  ~lm(flipper_length_mm ~ body_mass_g, data = .x)
  )
est <- pool(fit) 
est$pooled
term m estimate ubar b t dfcom df riv lambda fmi
(Intercept) 10 136.756 3.95 0.041 4 342 335 0.011 0.011 0.017
body_mass_g 10 0.015 0.00 0.000 0 342 334 0.012 0.012 0.018

Take aways

  • Missing data cannot be ignored.
  • To obtain valid inferences, you should investigate the missingness mechanism.
  • Multiple imputation allows you to ‘correct for’ data-dependent missingness.

Take aways

  • The R package mice makes imputation easy…
    • … but specifying imputation models requires careful investigation,
    • … and the imputations cannot be trusted if the algorithm has not converged.
  • After imputation, you can analyze the data as if it were complete, and pool the estimates to obtain valid inferences.

Resources

Thank you!

My personal website (incl. this presentation): hanneoberman.github.io

Hanne Oberman, hanneoberman.github.io/presentations