Introduction

Missing values are ubiquitous in data and need to be carefully explored and handled in the initial stages of analysis. In this vignette we describe the tools in the package naniar for exploring missing data structures with minimal deviation from the common workflows of ggplot and tidy data [@Wickham2014; @Wickham2009].

Sometimes researchers or analysts will introduce or describe a mechanism for missingness. For example, they might explain that data from a weather station might has a malfunction when there are extreme weather events, and does not record temperature data when gusts speeds are high. This seems like a nice simple, logical explanation. However, like all good explanations, this one is simple, but the process to get there, probably was not, and likely involved more time than you would have liked developing exploratory data analyses and models.

So when someone presents a really obvious plot like this, with a nice sensible explanation, the initial thought might be:

They worked it out themselves so quickly, so easy!

As if they somehow accidentally solved the problem, it was so easy. They couldn’t not solve it. However, I think that if you manage to get that on the first go, that is more like turning around and throwing a rock into a lake and it landing in a cup in a boat. It is unlikely.

With that thought in mind, this vignette aims to work with the following three questions, using the tools developed in naniar and another package, visdat. Namely, how do we:

1. Start looking at missing data?
2. Explore missingness mechanisms?
3. Model missingness?

How do we start looking at missing data?

When you start with a dataset, you might do something where you look at the general summary, using functions such as:

• summary()
• str()
• skimr::skim, or
• dplyr::glimpse()

These works really well when you’ve got a small amount of data, but when you have more data, you are generally limited by how much you can read.

So before you start looking at missing data, you’ll need to look at the data, but what does that even mean?

The package visdat helps you get a handle on this. visdat provides a visualisation of an entire data frame at once, and was heavily inspired by csv-fingerprint, and the missingness map functions from packages like Amelia::missmap.

There are two main functions in the visdat package:

• vis_dat, and
• vis_miss

library(visdat)
vis_dat(airquality)

vis_miss(airquality)

Exploring missingness relationships

We can identify key variables that are missing using vis_miss, but for further exploration, we need to explore the relationship amongst the variables in this data:

• Ozone,
• Solar.R
• Wind
• Temp
• Month
• Day

Typically, when exploring this data, you might want to explore the variables Solar.R and Ozone, and so plot a scatterplot of solar radiation and ozone, doing something like this:

library(ggplot2)
ggplot(airquality, 
       aes(x = Solar.R, 
           y = Ozone)) + 
  geom_point()

## Warning: Removed 42 rows containing missing values (geom_point).

The problem with this is that ggplot does not handle missings be default, and removes the missing values. This makes them hard to explore, it is a little strange - how do you visualise something that is not there? One approach to visualising missing data comes from ggobi and manet, where we replace “NA” values with values 10% lower than the minimum value in that variable. This is provided with the geom_miss_point() ggplot2 geom, which we can illustrate by exploring the relationship between Ozone and Solar radiation from the airquality dataset.

ggplot(airquality, 
       aes(x = Solar.R, 
           y = Ozone)) + 
  geom_point()

## Warning: Removed 42 rows containing missing values (geom_point).

library(naniar)

ggplot(airquality, 
       aes(x = Solar.R, 
           y = Ozone)) + 
  geom_miss_point()

Being a proper ggplot geom, it supports all of the standard features of ggplot2, such as facets,

ggplot(airquality, 
       aes(x = Solar.R, 
           y = Ozone)) + 
  geom_miss_point() + 
  facet_wrap(~Month)

And different themes

ggplot(airquality, 
       aes(x = Solar.R, 
           y = Ozone)) + 
  geom_miss_point() + 
  facet_wrap(~Month) + 
  theme_dark()

gg_miss_var(airquality)

gg_miss_var(airquality) + theme_bw() 

gg_miss_var(airquality) + labs(y = "Look at all the missing ones")

shadow matrix: A tidy way of representing missing values

Representing missing data structure is achieved using the shadow matrix, introduced in Swayne and Buja. The shadow matrix is the same dimension as the data, and consists of binary indicators of missingness of data values, where missing is represented as “NA”, and not missing is represented as “!NA”. Although these may be represented as 1 and 0, respectively. This representation can be seen in the figure below, adding the suffix “_NA" to the variables. This structure can also be extended to allow for additional factor levels to be created. For example 0 indicates data presence, 1 indicates missing values, 2 indicates imputed value, and 3 might indicate a particular type or class of missingness, where reasons for missingness might be known or inferred. The data matrix can also be augmented to include the shadow matrix, which facilitates visualisation of univariate and bivariate missing data visualisations. Another format is to display it in long form, which facilitates heatmap style visualisations. This approach can be very helpful for giving an overview of which variables contain the most missingness. Methods can also be applied to rearrange rows and columns to find clusters, and identify other interesting features of the data that may have previously been hidden or unclear.

Illustration of data structures for facilitating visualisation of missings and not missings

The shadow functions provide a way to keep track of missing values. The as_shadow function creates a dataframe with the same set of columns, but with the column names added a suffix _NA

as_shadow(airquality)

## # A tibble: 153 x 6
##    Ozone_NA Solar.R_NA Wind_NA Temp_NA Month_NA Day_NA
##      <fctr>     <fctr>  <fctr>  <fctr>   <fctr> <fctr>
##  1      !NA        !NA     !NA     !NA      !NA    !NA
##  2      !NA        !NA     !NA     !NA      !NA    !NA
##  3      !NA        !NA     !NA     !NA      !NA    !NA
##  4      !NA        !NA     !NA     !NA      !NA    !NA
##  5       NA         NA     !NA     !NA      !NA    !NA
##  6      !NA         NA     !NA     !NA      !NA    !NA
##  7      !NA        !NA     !NA     !NA      !NA    !NA
##  8      !NA        !NA     !NA     !NA      !NA    !NA
##  9      !NA        !NA     !NA     !NA      !NA    !NA
## 10       NA        !NA     !NA     !NA      !NA    !NA
## # ... with 143 more rows

The bind_shadow argument attaches a shadow to the current dataframe

aq_shadow <- bind_shadow(airquality)

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, union

glimpse(aq_shadow)

## Observations: 153
## Variables: 12
## $ Ozone      <int> 41, 36, 12, 18, NA, 28, 23, 19, 8, NA, 7, 16, 11, 1...
## $ Solar.R    <int> 190, 118, 149, 313, NA, NA, 299, 99, 19, 194, NA, 2...
## $ Wind       <dbl> 7.4, 8.0, 12.6, 11.5, 14.3, 14.9, 8.6, 13.8, 20.1, ...
## $ Temp       <int> 67, 72, 74, 62, 56, 66, 65, 59, 61, 69, 74, 69, 66,...
## $ Month      <int> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, ...
## $ Day        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ Ozone_NA   <fctr> !NA, !NA, !NA, !NA, NA, !NA, !NA, !NA, !NA, NA, !N...
## $ Solar.R_NA <fctr> !NA, !NA, !NA, !NA, NA, NA, !NA, !NA, !NA, !NA, NA...
## $ Wind_NA    <fctr> !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, ...
## $ Temp_NA    <fctr> !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, ...
## $ Month_NA   <fctr> !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, ...
## $ Day_NA     <fctr> !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, !NA, ...

Doing this provides a consistent syntax for referring to variables with missing values.

bind_shadow() also provides a useful pattern to explore missing values, grouping by the missing/complete of one variable and looking at the mean and other summary values. Below we show the mean, sd, variance, and min and max values of Solar.R for when Ozone is present, and when it is missing.

airquality %>%
  bind_shadow() %>%
  group_by(Ozone_NA) %>%
  summarise_at(.vars = "Solar.R",
               .funs = c("mean", "sd", "var", "min", "max"),
               na.rm = TRUE)

## # A tibble: 2 x 6
##   Ozone_NA     mean       sd      var   min   max
##     <fctr>    <dbl>    <dbl>    <dbl> <dbl> <dbl>
## 1      !NA 184.8018 91.15230 8308.742     7   334
## 2       NA 189.5143 87.69478 7690.375    31   332

Below, we can plot the distribution of Temperature, plotting for values of temperature when Ozone is missing, and when it is not missing.

ggplot(aq_shadow,
       aes(x = Temp,
           colour = Ozone_NA)) + 
  geom_density()

Binding the shadow here also has great benefits when combined with imputation.

Visualising imputed values

Using the easy-to-use simputation package, we impute values for Ozone, then visualise the data:

library(simputation)
library(dplyr)

airquality %>%
  impute_lm(Ozone ~ Temp + Wind) %>%
  ggplot(aes(x = Temp,
             y = Ozone)) + 
  geom_point()

Note that we no longer get any errors regarding missing observations - because they are all imputed! But this comes at a cost: we also no longer have information about where the imputations are - they are now sort of invisible.

Using the shadow matrix to keep track of where the missings are, you can actually keep track of the imputations, by colouring by what was previously missing in Ozone.

aq_shadow %>%
  impute_lm(Ozone ~ Temp + Wind) %>%
  ggplot(aes(x = Temp,
             y = Ozone,
             colour = Ozone_NA)) + 
  geom_point()

dplyr::n_distinct(airquality)

## [1] 153

dplyr::n_distinct(airquality$Ozone)

## [1] 68

n_miss(airquality)

## [1] 44

n_miss(airquality$Ozone)

## [1] 37

n_complete(airquality)

## [1] 874

n_complete(airquality$Ozone)

## [1] 116

miss_case_prop(airquality)

## [1] 0.2745098

miss_case_pct(airquality)

## [1] 27.45098

miss_case_summary(airquality)

## # A tibble: 153 x 3
##     case n_missing  percent
##    <int>     <int>    <dbl>
##  1     5         2 33.33333
##  2    27         2 33.33333
##  3     6         1 16.66667
##  4    10         1 16.66667
##  5    11         1 16.66667
##  6    25         1 16.66667
##  7    26         1 16.66667
##  8    32         1 16.66667
##  9    33         1 16.66667
## 10    34         1 16.66667
## # ... with 143 more rows

miss_case_table(airquality)

## # A tibble: 3 x 3
##   n_missing_in_case n_cases  percent
##               <int>   <int>    <dbl>
## 1                 0     111 72.54902
## 2                 1      40 26.14379
## 3                 2       2  1.30719

miss_var_prop(airquality)

## [1] 0.3333333

miss_var_pct(airquality)

## [1] 33.33333

miss_var_summary(airquality)

## # A tibble: 6 x 3
##   variable n_missing   percent
##      <chr>     <int>     <dbl>
## 1    Ozone        37 24.183007
## 2  Solar.R         7  4.575163
## 3     Wind         0  0.000000
## 4     Temp         0  0.000000
## 5    Month         0  0.000000
## 6      Day         0  0.000000

miss_var_table(airquality)

## # A tibble: 3 x 3
##   n_missing_in_var n_vars  percent
##              <int>  <int>    <dbl>
## 1                0      4 66.66667
## 2                7      1 16.66667
## 3               37      1 16.66667

miss_var_run(pedestrian,
             hourly_counts)

## # A tibble: 35 x 2
##    run_length    is_na
##         <int>    <chr>
##  1       6628 complete
##  2          1  missing
##  3       5250 complete
##  4        624  missing
##  5       3652 complete
##  6          1  missing
##  7       1290 complete
##  8        744  missing
##  9       7420 complete
## 10          1  missing
## # ... with 25 more rows

miss_var_span(pedestrian,
              hourly_counts,
              span_every = 100)

## # A tibble: 377 x 5
##    span_counter n_miss n_complete prop_miss prop_complete
##           <int>  <int>      <dbl>     <dbl>         <dbl>
##  1            1      0        100         0             1
##  2            2      0        100         0             1
##  3            3      0        100         0             1
##  4            4      0        100         0             1
##  5            5      0        100         0             1
##  6            6      0        100         0             1
##  7            7      0        100         0             1
##  8            8      0        100         0             1
##  9            9      0        100         0             1
## 10           10      0        100         0             1
## # ... with 367 more rows

Using group_by with naniar

Every miss_* summary function that returns a dataframe can be used with dplyr group_by. For example, if you would like to look at the number of missing values for all variables of pedestrian data.

pedestrian %>% miss_var_summary()

## # A tibble: 9 x 3
##        variable n_missing  percent
##           <chr>     <int>    <dbl>
## 1 hourly_counts      2548 6.758621
## 2     date_time         0 0.000000
## 3          year         0 0.000000
## 4         month         0 0.000000
## 5     month_day         0 0.000000
## 6      week_day         0 0.000000
## 7          hour         0 0.000000
## 8     sensor_id         0 0.000000
## 9   sensor_name         0 0.000000

We see that this is in hourly_counts. We can then explore this by month, and filder by the variable being hourly_counts, since it is the only one with missing values.

pedestrian %>%
 group_by(month) %>%
 miss_var_summary() %>%
 filter(variable == "hourly_counts")

## # A tibble: 12 x 4
##        month      variable n_missing   percent
##        <ord>         <chr>     <int>     <dbl>
##  1   January hourly_counts         0  0.000000
##  2  February hourly_counts         0  0.000000
##  3     March hourly_counts         0  0.000000
##  4     April hourly_counts       552 19.166667
##  5       May hourly_counts        72  2.419355
##  6      June hourly_counts         0  0.000000
##  7      July hourly_counts         0  0.000000
##  8    August hourly_counts       408 13.709677
##  9 September hourly_counts         0  0.000000
## 10   October hourly_counts       412  7.436823
## 11  November hourly_counts       888 30.833333
## 12  December hourly_counts       216  7.258065

Modelling missingness

The final question we proposed in this vignette was:

3. Can we model missingness?

Sometimes it can be impractical to explore all of the variables that have missing data. One approach, however, is to model missing data using methods from Tierney et el. (2015).

Here, the approach is to predict the proportion of missingness in a given case, using all variables. There is a little helper function to add a column with the proportion of cases or rows missing - add_prop_miss. This created a column named “prop_miss”, which is the proportion of missing values in that row.

airquality %>%
  add_prop_miss() %>%
  head()

## # A tibble: 6 x 7
##   Ozone Solar.R  Wind  Temp Month   Day prop_miss_all
##   <int>   <int> <dbl> <int> <int> <int>         <dbl>
## 1    41     190   7.4    67     5     1     0.0000000
## 2    36     118   8.0    72     5     2     0.0000000
## 3    12     149  12.6    74     5     3     0.0000000
## 4    18     313  11.5    62     5     4     0.0000000
## 5    NA      NA  14.3    56     5     5     0.3333333
## 6    28      NA  14.9    66     5     6     0.1666667

We can then use a model like decision trees to predict which variables and their values are important for predicting the proportion of missingness:

library(rpart)
library(rpart.plot)

airquality %>%
  add_prop_miss() %>%
  rpart(prop_miss_all ~ ., data = .) %>%
  prp(type = 4, extra = 101, prefix = "Prop. Miss = ")

# library(visdat)
# vis_miss(messy_airquality)

Here we can see that this produces quite a complex tree - this can be pruned back and the depth of the decision tree controlled.

Summary

The tools in naniar help us identify where missingness is, while maintaining a tidy workflow. We care about these mechanisms or these patterns because they can help us understand potential mechanisms, such as equipment failures, and then identify possible solutions based upon this evidence.

Future development

• Make naniar work with big data tools like sparklyr, and sparklingwater.
• Further develop methods for handling and visualising imputations, and multiple imputation. Other plans to extend the geom_miss_ family to include:
• Categorical variables
• Bivariate plots: scatterplots, density overlays
• SQL translation for databases
• Big Data tools (sparklyr, sparklingwater)
• Work well with other imputation engines / processes
• Provide tools for assessing goodness of fit for classical approaches of MCAR, MAR, and MNAR (graphical inference from nullabor package)
• Expand ggplot geom_miss_* family

Thank you

Firstly, thanks to Di Cook for giving the initial inspiration for the package and laying down the rich theory and literature that the work in naniar is built upon. Naming credit (once again!) goes to Miles McBain. Among various other things, Miles also worked out how to overload the missing data and make it work as a geom. Thanks also to Colin Fay for helping me understand tidy evaluation and for features such as replace_to_na, miss_*_cumsum, and more.

References

• MANET: http://www.rosuda.org/MANET/
• ggobi: http://www.ggobi.org/
• visdat: https://www.github.com/ropensci/visdat
• Tierney NJ, Harden FA, Harden MJ, Mengersen, KA, Using decision trees to understand structure in missing data BMJ Open 2015;5:e007450. doi: 10.1136/bmjopen-2014-007450