How to fill NA with median?

Question

Example data:

set.seed(1)
df <- data.frame(years=sort(rep(2005:2010, 12)), 
                 months=1:12, 
                 value=c(rnorm(60),NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA))

head(df)
  years months      value
1  2005      1 -0.6264538
2  2005      2  0.1836433
3  2005      3 -0.8356286
4  2005      4  1.5952808
5  2005      5  0.3295078
6  2005      6 -0.8204684

Tell me please, how i can replace NA in df$value to median of others months? "value" must contain the median of value of all previous values for the same month. That is, if current month is May, "value" must contain the median value for all previous values of the month of May.

Answer 1

you want to use the test is.na function:

df$value[is.na(df$value)] <- median(df$value, na.rm=TRUE)

which says for all the values where df$value is NA, replace it with the right hand side. You need the na.rm=TRUE piece or else the median function will return NA

to do this month by month, there are many choices, but i think plyr has the simplest syntax:

library(plyr)
ddply(df, 
      .(months), 
      transform, 
      value=ifelse(is.na(value), median(value, na.rm=TRUE), value))

you can also use data.table. this is an especially good choice if your data is large:

library(data.table)
DT <- data.table(df)
setkey(DT, months)

DT[,value := ifelse(is.na(value), median(value, na.rm=TRUE), value), by=months]

There are many other ways, but there are two!

Answer 2

Here's the most robust solution I can think of. It ensures the years are ordered correctly and will correctly compute the median for all previous months in cases where you have multiple years with missing values.

# first, reshape your data so it is years by months:
library(reshape2)
tmp <- dcast(years ~ months, data=df)  # convert data to years x months
tmp <- tmp[order(tmp$years),]          # order years
# now calculate the running median on each month
library(caTools)
# function to replace NA with rolling median
tmpfun <- function(x) {
  ifelse(is.na(x), runquantile(x, k=length(x), probs=0.5, align="right"), x)
}
# apply tmpfun to each column and convert back to data.frame
tmpmed <- as.data.frame(lapply(tmp, tmpfun))
# reshape back to long and convert 'months' back to integer
res <- melt(tmpmed, "years", variable.name="months")
res$months <- as.integer(gsub("^X","",res$months))

Answer 3

Or with ave

df <- data.frame(years=sort(rep(2005:2010, 12)),
months=1:12,
value=c(rnorm(60),NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA))
df$value[is.na(df$value)] <- with(df, ave(value, months, 
   FUN = function(x) median(x, na.rm = TRUE)))[is.na(df$value)]

---

Since there are so many answers let's see which is fastest.

plyr2 <- function(df){
  medDF <- ddply(df,.(months),summarize,median=median(value,na.rm=TRUE))
df$value[is.na(df$value)] <- medDF$median[match(df$months,medDF$months)][is.na(df$value)]
  df
}
library(plyr)
library(data.table)
DT <- data.table(df)
setkey(DT, months)


benchmark(ave = df$value[is.na(df$value)] <- 
  with(df, ave(value, months, 
               FUN = function(x) median(x, na.rm = TRUE)))[is.na(df$value)],
          tapply = df$value[61:72] <- 
            with(df, tapply(value, months, median, na.rm=TRUE)),
          sapply = df[61:72, 3] <- sapply(split(df[1:60, 3], df[1:60, 2]), median),
          plyr = ddply(df, .(months), transform, 
                       value=ifelse(is.na(value), median(value, na.rm=TRUE), value)),
          plyr2 = plyr2(df),
          data.table = DT[,value := ifelse(is.na(value), median(value, na.rm=TRUE), value), by=months],
          order = "elapsed")
        test replications elapsed relative user.self sys.self user.child sys.child
3     sapply          100   0.209 1.000000     0.196    0.000          0         0
1        ave          100   0.260 1.244019     0.244    0.000          0         0
6 data.table          100   0.271 1.296651     0.264    0.000          0         0
2     tapply          100   0.271 1.296651     0.256    0.000          0         0
5      plyr2          100   1.675 8.014354     1.612    0.004          0         0
4       plyr          100   2.075 9.928230     2.004    0.000          0         0

I would have bet that data.table was the fastest.

[ Matthew Dowle ] The task being timed here takes at most 0.02 seconds (2.075/100). data.table considers that insignificant. Try setting replications to 1 and increasing the data size, instead. Or timing the fastest of 3 runs is also a common rule of thumb. More verbose discussion in these links :

• Evidence that data.table isn't always fastest
• Benchmarks in Averaging column values for specific sections of data corresponding to other column values
• London R presentation, June 2012 (slide 21 headed "Other")
• A transform by group benchmark in an extreme case

Answer 4

This is a way using plyr, it is not very pretty but I think it does what you want:

library("plyr")

# Make a separate dataframe with month as first column and median as second:
medDF <- ddply(df,.(months),summarize,median=median(value,na.rm=TRUE))

# Replace `NA` values in `df$value` with medians from the second data frame
# match() here ensures that the medians are entered in the correct elements.
df$value[is.na(df$value)] <- medDF$median[match(df$months,medDF$months)][is.na(df$value)]

Answer 5

Sticking with base R, you can also try the following:

medians = sapply(split(df[1:60, 3], df[1:60, 2]), median)
df[61:72, 3] = medians

Answer 6

There is another way to do this with dplyr.

If you want to replace all columns with their median, do:

library(dplyr)
df %>% 
   mutate_all(~ifelse(is.na(.), median(., na.rm = TRUE), .))

If you want to replace a subset of columns (such as "value" in OP's example), do:

df %>% 
  mutate_at(vars(value), ~ifelse(is.na(.), median(., na.rm = TRUE), .))