R - Impute missing values by group (linear / moving average)

Question

I have a large dataset with a lot of missing values and I want to impute it by group "name" either linearly or with moving average.

d <-  data.frame(
  name = c('a', 'a','a','a','b','b','b','b','c','c','c','c'),
  year = c(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4),
  V = c(NA, 21, 31, 41, 11, NA, NA, 41, NA, NA, NA, 41),
  W = c(11, NA, 31, 41, 11, 21, NA, NA, NA, NA, 31, NA),
  X = c(11, 21, NA, 41, NA, 21, NA, 41, 11, NA, NA, NA),
  Y = c(11, 21, 31, NA, NA, 21, 31, NA, NA, 21, NA, NA),
  Z = c(NA, NA, 31, 41, 11, NA, 31, NA, NA, NA, NA, NA)
)

> d
   name year  V  W  X  Y  Z
1     a    1 NA 11 11 11 NA
2     a    2 21 NA 21 21 NA
3     a    3 31 31 NA 31 31
4     a    4 41 41 41 NA 41
5     b    1 11 11 NA NA 11
6     b    2 NA 21 21 21 NA
7     b    3 NA NA NA 31 31
8     b    4 41 NA 41 NA NA
9     c    1 NA NA 11 NA NA
10    c    2 NA NA NA 21 NA
11    c    3 NA 31 NA NA NA
12    c    4 41 NA NA NA NA

Hopefully the results can be as closed as the following:

   name year  V  W  X  Y  Z
1     a    1 11 11 11 11 11
2     a    2 21 21 21 21 21
3     a    3 31 31 31 31 31
4     a    4 41 41 41 41 41
5     b    1 11 11 11 11 11
6     b    2 21 21 21 21 21
7     b    3 31 31 31 31 31
8     b    4 41 41 41 41 41
9     c    1 11 11 11 11 NA
10    c    2 21 21 21 21 NA
11    c    3 31 31 31 31 NA
12    c    4 41 41 41 41 NA

I found this and this . Tried the following without groupby but it didn't work:

data.frame(lapply(d, function(X) approxfun(seq_along(X), X)(seq_along(X))))

imputeTS::na_ma(d, k = 2, weighting = "simple")

The first one gave an error as below:

Error in approxfun(seq_along(X), X) : 
  need at least two non-NA values to interpolate
In addition: Warning message:
In xy.coords(x, y, setLab = FALSE) :
 Error in approxfun(seq_along(X), X) : 
  need at least two non-NA values to interpolate

So I tried the second one and it keep loading for a long time and nothing happened. According to the reply from the first link,

the package requires time series/vector input (that's why each column has to be called separately).

Any help is greatly appreciated!

Answer 1

You can use zoo::na.spline -

library(dplyr)

d %>%
  group_by(name) %>%
  mutate(across(V:Z, zoo::na.spline, na.rm = FALSE)) %>%
  ungroup

#   name   year     V     W     X     Y     Z
#   <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 a         1    11    11    11    11    11
# 2 a         2    21    21    21    21    21
# 3 a         3    31    31    31    31    31
# 4 a         4    41    41    41    41    41
# 5 b         1    11    11    11    11    11
# 6 b         2    21    21    21    21    21
# 7 b         3    31    31    31    31    31
# 8 b         4    41    41    41    41    41
# 9 c         1    41    31    11    21    NA
#10 c         2    41    31    11    21    NA
#11 c         3    41    31    11    21    NA
#12 c         4    41    31    11    21    NA

For name , "c" I think it would be difficult to impute the missing values only from 1 number.

Answer 2

One issue I see is, that some of the series you want to impute have only 1 non-NA value, thus na_ma or na_interpolation from imputeTS or also other packages can not be applied successfully, since these require at least 2 non-NA values.

That is why in this solution I created a impute_select function for you, that let's you choose, what to to when > 1 values or present, when exactly == 1 values are present or when there are only NAs.

In this case, when > 1 values is present, it uses na_ma , but you could also use na_interpoltion or any other imputation function from imputeTS here. When only 1 value is present, it uses na_locf since this method also works with only 1 value in the series. When no non-NA values are in the series, it uses na_replace, just replacing all the NAs with a default value (I just set it to 11)

By adjusting this function you should be able to individually adjust the imputation for different amounts of NAs in the series.

library("imputeTS")

d <-  data.frame(
  name = c('a', 'a','a','a','b','b','b','b','c','c','c','c'),
  year = c(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4),
  V = c(NA, 21, 31, 41, 11, NA, NA, 41, NA, NA, NA, 41),
  W = c(11, NA, 31, 41, 11, 21, NA, NA, NA, NA, 31, NA),
  X = c(11, 21, NA, 41, NA, 21, NA, 41, 11, NA, NA, NA),
  Y = c(11, 21, 31, NA, NA, 21, 31, NA, NA, 21, NA, NA),
  Z = c(NA, NA, 31, 41, 11, NA, 31, NA, NA, NA, NA, NA)
)

impute_select <- function(x) {
  # select a method to use when more than 1 values are available
  if (sum(!is.na(x)) > 1) {
    result <- na_ma(x)
  }
  # Select value when only 1 value is in series
  if (sum(!is.na(x)) == 1) {
    result <- na_locf(x)
  }
  # Select method, when no non-NA value is present
  else {
    result <- na_replace(x, 11)
  }
}

# This code is to apply the function row-wise to your data frame
# Since usually the imputation would happen column-wise instead
d[,3:7] <- t(apply(d[,3:7], MARGIN =1, FUN = impute_select))

d

This are the results (hopefully exactly what you wanted):

 name year VWXYZ 1 a 1 11 11 11 11 11 2 a 2 21 11 21 21 11 3 a 3 31 31 11 31 31 4 a 4 41 41 41 11 41 5 b 1 11 11 11 11 11 6 b 2 11 21 21 21 11 7 b 3 11 11 11 31 31 8 b 4 41 11 41 11 11 9 c 1 11 11 11 11 11 10 c 2 21 21 21 21 21 11 c 3 31 31 31 31 31 12 c 4 41 41 41 41 41