R FAQ How does R handle missing values?

Version info: Code for this page was tested in R Under development (unstable) (2012-02-22 r58461) On: 2012-03-28 With: knitr 0.4 

Like other statistical software packages, R is capable of handling missing values. However, to those accustomed to working with missing values in other packages, the way in which R handles missing values may require a shift in thinking. On this page, we will present first the basics of how missing values are represented in R. Next, for those coming from SAS, SPSS, and/or Stata, we will outline some of the differences between missing values in R and missing values elsewhere. Finally, we will introduce some of the tools for working with missing values in R, both in data management and analysis.

Very basics

Missing data in R appears as NA. NA is not a string or a numeric value, but an indicator of missingness. We can create vectors with missing values.

x1 <- c(1, 4, 3, NA, 7)
x2 <- c("a", "B", NA, "NA")

NA is the one of the few non-numbers that we could include in x1 without generating an error (and the other exceptions are letters representing numbers or numeric ideas like infinity). In x2, the third value is missing while the fourth value is the character string "NA". To see which values in each of these vectors R recognizes as missing, we can use the is.na function. It will return a TRUE/FALSE vector with as any elements as the vector we provide.
is.na(x1)
## [1] FALSE FALSE FALSE  TRUE FALSE
is.na(x2)
## [1] FALSE FALSE  TRUE FALSE


We can see that R distinguishes between the NA and "NA" in x2--NA is seen as a missing value, "NA" is not.

Differences from other packages

• NA cannot be used in comparisons: In other packages, a "missing" value is assigned an extreme numeric value--either very high or very low. As a result, values coded as missing can 1) be compared to other values and 2) other values can be compared to missing. In the example SAS code below, we compare the values in y to 0 and to the missing symbol and see that both comparisons are valid (and that the missing symbol is valued at less than zero).
• data test;
input x y;
datalines;
2 .
3 4
5 1
6 0
;

data test; set test;
lowy = (y < 0);
missy = (y = .);
run;

proc print data = test; run;

Obs    x    y    lowy    missy

1     2    .      1       1
2     3    4      0       0
3     5    1      0       0
4     6    0      0       0

We can try the equivalent in R.
x1 < 0
## [1] FALSE FALSE FALSE    NA FALSE
x1 == NA
## [1] NA NA NA NA NA

Our missing value cannot be compared to 0 and none of our values can be compared to NA because NA is not assigned a value--it simply is or it isn't.
• NA is used for all kinds of missing data: In other packages, missing strings and missing numbers might be represented differently--empty quotations for strings, periods for numbers. In R, NA represents all types of missing data. We saw a small example of this in x1 and x2. x1 is a "numeric" object and x2 is a "character" object.
• Non-NA values cannot be interpreted as missing: Other packages allow you to designate values as "system missing" so that these values will be interpreted in the analysis as missing. In R, you would need to explicitly change these values to NA. The is.na function can also be used to make such a change:
• is.na(x1) <- which(x1 == 7)
x1
## [1]  1  4  3 NA NA


NA options in R

We have introduced is.na as a tool for both finding and creating missing values. It is one of several functions built around NA. Most of the other functions for NA are options for na.action.

Just as there are default settings for functions, there are similar underlying defaults for R as a software. You can view these current settings with options(). One of these is the "na.action" that describes how missing values should be treated. The possible na.action settings within R include:

• na.omit and na.exclude: returns the object with observations removed if they contain any missing values; differences between omitting and excluding NAs can be seen in some prediction and residual functions
• na.pass: returns the object unchanged
• na.fail: returns the object only if it contains no missing values

To see the na.action currently in in options, use getOption("na.action"). We can create a data frame with missing values and see how it is treated with each of the above.

(g <- as.data.frame(matrix(c(1:5, NA), ncol = 2)))
##   V1 V2
## 1  1  4
## 2  2  5
## 3  3 NA
na.omit(g)
##   V1 V2
## 1  1  4
## 2  2  5
na.exclude(g)
##   V1 V2
## 1  1  4
## 2  2  5
na.fail(g)
## Error: missing values in object
na.pass(g)
##   V1 V2
## 1  1  4
## 2  2  5
## 3  3 NA


Missing values in analysis

In some R functions, one of the arguments the user can provide is the na.action. For example, if you look at the help for the lm command, you can see that na.action is one of the listed arguments. By default, it will use the na.action specified in the R options. If you wish to use a different na.action for the regression, you can indicate the action in the lm command.

Two common options with lm are the default, na.omit and na.exclude which does not use the missing values, but maintains their position for the residuals and fitted values.

## use the famous anscombe data and set a few to NA
anscombe <- within(anscombe, {
y1[1:3] <- NA
})
anscombe  # view
##    x1 x2 x3 x4    y1   y2    y3    y4
## 1  10 10 10  8    NA 9.14  7.46  6.58
## 2   8  8  8  8    NA 8.14  6.77  5.76
## 3  13 13 13  8    NA 8.74 12.74  7.71
## 4   9  9  9  8  8.81 8.77  7.11  8.84
## 5  11 11 11  8  8.33 9.26  7.81  8.47
## 6  14 14 14  8  9.96 8.10  8.84  7.04
## 7   6  6  6  8  7.24 6.13  6.08  5.25
## 8   4  4  4 19  4.26 3.10  5.39 12.50
## 9  12 12 12  8 10.84 9.13  8.15  5.56
## 10  7  7  7  8  4.82 7.26  6.42  7.91
## 11  5  5  5  8  5.68 4.74  5.73  6.89

model.omit <- lm(y2 ~ y1, data = anscombe, na.action = na.omit)
model.exclude <- lm(y2 ~ y1, data = anscombe,
na.action = na.exclude)

## compare effects on residuals
resid(model.omit)
##      4      5      6      7      8      9     10     11
##  0.727  1.575 -0.799 -0.743 -1.553 -0.425  2.190 -0.971
resid(model.exclude)
##      1      2      3      4      5      6      7      8      9     10
##     NA     NA     NA  0.727  1.575 -0.799 -0.743 -1.553 -0.425  2.190
##     11
## -0.971

## compare effects on fitted (predicted) values
fitted(model.omit)
##    4    5    6    7    8    9   10   11
## 8.04 7.69 8.90 6.87 4.65 9.55 5.07 5.71
fitted(model.exclude)
##    1    2    3    4    5    6    7    8    9   10   11
##   NA   NA   NA 8.04 7.69 8.90 6.87 4.65 9.55 5.07 5.71


Using na.exclude pads the residuals and fitted values with NAs where there were missing values. Other functions do not use the na.action, but instead have a different argument (with some default) for how they will handle missing values. For example, the mean command will, by default, return NA if there are any NAs in the passed object.

mean(x1)
## [1] NA


If you wish to calculate the mean of the non-missing values in the passed object, you can indicate this in the na.rm argument (which is, by default, set to FALSE).

mean(x1, na.rm = TRUE)
## [1] 2.67


Two common commands used in data management and exploration are summary and table. The summary command (when used with numeric vectors) returns the number of NAs in a vector, but the table command ignores NAs by default.

summary(x1)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's
##    1.00    2.00    3.00    2.67    3.50    4.00       2
table(x1)
## x1
## 1 3 4
## 1 1 1


To see NA among the table output, you can indicate "ifany" or "always" in the useNA argument. The first will show NA in the output only if there is some missing data in the object. The second will include NA in the output regardless.

table(x1, useNA = "ifany")
## x1
##    1    3    4
##    1    1    1    2
table(1:3, useNA = "always")
##
##    1    2    3
##    1    1    1    0


Sorting data containing missing values in R is again different from other packages because NA cannot be compared to other values. By default, sort removes any NA values and can therefore change the length of a vector.

(x1s <- sort(x1))
## [1] 1 3 4
length(x1s)
## [1] 3


The user can specify if NA should be last or first in a sorted order by indicating TRUE or FALSE for the na.last argument.

sort(x1, na.last = TRUE)
## [1]  1  3  4 NA NA


No matter the goal of your R code, it is wise to both investigate missing values in your data and use the help files for all functions you use. You should be either aware of and comfortable with the default treatments of missing values or specifying the treatment of missing values you want for your analysis.

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