Assessing inference from imputed data in a modelling context

Dealing With Missing Data in R

Nicholas Tierney

Statistician

Exploring parameters of one model

lm(Temp ~ Ozone + Solar.R + Wind + Month + day, data = airquality)

Complete case analysis
Imputation using the imputed data from the last lesson

Combining the datasets together

#1.  Complete cases
aq_cc <- airquality %>%
  na.omit() %>%
  bind_shadow() %>%
  add_label_shadow()

#2. Imputation using the imputed data from the last lesson
aq_imp_lm <- bind_shadow(airquality) %>%
  add_label_shadow() %>%
  impute_lm(Ozone ~ Temp + Wind + Month + Day) %>%
  impute_lm(Solar.R ~ Temp + Wind + Month + Day)

# 3. Bind the models together
bound_models <- bind_rows(cc = aq_cc,
                          imp_lm = aq_imp_lm,
                          .id = "imp_model")

Combining the datasets together

bound_models

imp_model Ozone Solar.R Wind Temp Month Day Ozone_NA Solar.R_NA any_missing
cc        41     190     7.4   67     5   1   !NA        !NA    Not Missing
cc        36     118     8.0   72     5   2   !NA        !NA    Not Missing
cc        12     149    12.6   74     5   3   !NA        !NA    Not Missing
cc        18     313    11.5   62     5   4   !NA        !NA    Not Missing
cc        23     299     8.6   65     5   7   !NA        !NA    Not Missing
...   
imp_lm    30     193     6.9   70     9  26   !NA        !NA    Not Missing
imp_lm    NA     145    13.2   77     9  27    NA        !NA        Missing
imp_lm    14     191    14.3   75     9  28   !NA        !NA    Not Missing
imp_lm    18     131     8.0   76     9  29   !NA        !NA    Not Missing
imp_lm    20     223    11.5   68     9  30   !NA        !NA    Not Missing

Exploring the models

model_summary <- bound_models %>% 
  group_by(imp_model) %>%
  nest() %>%
  mutate(mod = map(data, 
                   ~lm(Temp ~ Ozone + Solar.R + Wind + Temp + Days + Month 
                       data = .)),
         res = map(mod, residuals),
         pred = map(mod, predict),
         tidy = map(mod, broom::tidy))
model_summary

# A tibble: 2 x 6
  imp_model data                mod      res         pred        tidy            
  <chr>     <list>              <list>   <list>      <list>      <list>          
1 cc        <tibble [111 × 13]> <S3: lm> <dbl [111]> <dbl [111]> <tibble [3 × 5]>
2 imp_lm    <tibble [153 × 13]> <S3: lm> <dbl [153]> <dbl [153]> <tibble [3 × 5]>

Exploring coefficients of multiple models

model_summary %>% 
  select(imp_model,
         tidy) %>%
  unnest()

# A tibble: 6 x 6
  imp_model term        estimate std.error statistic  p.value
  <chr>     <chr>          <dbl>     <dbl>     <dbl>    <dbl>
1 cc        (Intercept) 68.5       1.53       44.8   1.31e-71
2 cc        Ozone        0.194     0.0210      9.26  2.22e-15
3 cc        Solar.R      0.00604   0.00766     0.789 4.32e- 1
4 imp_lm    (Intercept) 67.2       1.30       51.5   2.68e-97
5 imp_lm    Ozone        0.215     0.0180     12.0   1.40e-23
6 imp_lm    Solar.R      0.00787   0.00630     1.25  2.13e- 1

Exploring residuals of multiple models

model_summary %>% 
  select(imp_model,
         res) %>%
  unnest() %>%
  ggplot(aes(x = res,
             fill = imp_model)) +
  geom_histogram(position = "dodge")

Exploring predictions of multiple models

model_summary %>% 
  select(imp_model,
         pred) %>%
  unnest() %>%
  ggplot(aes(x = pred,
             fill = imp_model)) +
  geom_histogram(position = "dodge")

Let's practice!

Dealing With Missing Data in R