Example 2014.12: Changing repeated measures data from wide to narrow format

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Data with repeated measures often come to us in the “wide” format, as shown below for the HELP data set we use in our book. Here we show just an ID, the CESD depression measure from four follow-up assessments, plus the baseline CESD.

Obs    ID    CESD1    CESD2    CESD3    CESD4    CESD

  1     1       7        .        8        5      49
  2     2      11        .        .        .      30
  3     3      14        .        .       49      39
  4     4      44        .        .       20      15
  5     5      26       27       15       28      39

Frequently for data analysis we need to convert the data to the “long” format, with a single column for the repeated time-varying CESD measures and column indicating the time of measurement. This is needed, for example, in SAS proc mixed or in the lme4 package in R. The data should look something like this:

 Obs    ID    time    CESD    cesd_tv

   1     1     1       49         7
   2     1     2       49         .
   3     1     3       49         8
   4     1     4       49         5

In section 2.3.7 (2nd Edition) we discuss this problem, and we provide an example in section 7.10.9. Today we’re adding a blog post to demonstrate some handy features in SAS and how the problem can be approached using plain R and, alternatively, using the new-ish R packages dplyr and tidyr, contributed by Hadley Wickham.

We’ll begin by making a narrower data frame with just the columns noted above. We use the select() function from the dplyr package to do this; the syntax is simply to provide the the name of the input data frame as the first argument and then the names of the columns to be included in the output data frame. We use this function instead of the similar base R function subset(..., select=) because of dplyr’s useful starts_with() function. This operates on the column names as character vectors in a hopefully obvious way.

wide = select(ds, id, starts_with("cesd"))

Now we’ll convert to the long format. The standard R approach is to use the reshape() function. The documentation for this is a bit of a slog, and the function can generate error messages that are not so helpful. But for simple problems like this one, it works well.
long = reshape(wide, varying = c("cesd1", "cesd2", "cesd3", "cesd4"),
               v.names = "cesd_tv",
               idvar = c("id", "cesd"), direction="long")
long[long$id == 1,]

       id cesd time cesd_tv
1.49.1  1   49    1       7
1.49.2  1   49    2      NA
1.49.3  1   49    3       8
1.49.4  1   49    4       5

In the preceding, the varying parameter is a list of columns which vary over time, while the id.var columns appear at each time. The v.names parameter is the name of the column which will hold the values of the varying variables.

Another option would be to use base R knowledge to separate, rename, and then recombine the data as follows. The main hassle here is renaming the columns in each separate data frame so that they can be combined later.
c1 = subset(wide, select= c(id, cesd, cesd1))
c1$time = 1
names(c1)[3] = "cesd_tv"

c2 = subset(wide, select= c(id, cesd, cesd2))
c2$time = 2
names(c2)[3] = "cesd_tv"

c3 = subset(wide, select= c(id, cesd, cesd3))
c3$time = 3
names(c3)[3] = "cesd_tv"

c4 = subset(wide, select= c(id, cesd, cesd4))
c4$time = 4
names(c4)[3] = "cesd_tv"

long = rbind(c1,c2,c3,c4)

     id cesd cesd_tv time
1     1   49       7    1
454   1   49      NA    2
907   1   49       8    3
1360  1   49       5    4

This is cumbersome, but effective.

More interesting is to use the tools provided by dplyr and tidyr.
gather(wide, key=names, value=cesd_tv, cesd1,cesd2,cesd3,cesd4) %>%
mutate(time = as.numeric(substr(names,5,5))) %>%
arrange(id,time) -> long


  id cesd names cesd_tv time
1  1   49 cesd1       7    1
2  1   49 cesd2      NA    2
3  1   49 cesd3       8    3
4  1   49 cesd4       5    4
5  2   30 cesd1      11    1
6  2   30 cesd2      NA    2

The gather() function takes a data frame (the first argument) and returns new columns named in the key and value parameter. The contents of the columns are the names (in the key) and the values (in the value) of the former columns listed. The result is a new data frame with a row for every column in the original data frame, for every row in the original data frame. Any columns not named are repeated in the output data frame. The mutate function is like the R base function transform() but has some additional features and may be faster in some settings. Finally, the arrange() function is a much more convenient sorting facility than is available in standard R. The input is a data frame and a list of columns to sort by, and the output is a sorted data frame. This saves us having to select out a subject to display

The %>% operator is a “pipe” or “chain” operator that may be familiar if you’re a *nix user. It feeds the result of the last function into the next function as the first argument. This can cut down on the use of nested parentheses and may make reading R code easier for some folks. The effect of the piping is that the mutate() function should be read as taking the result of the gather() as its input data frame, and sending its output data frame into the arrange() function. For Ken, the right assignment arrow (-> long) makes sense as a way to finish off this set of piping rules, but Nick and many R users would prefer to write this as long = gather... or long <- gather.. , etc.

In SAS, we'll make the narrow data set using the keep statement in the data step, demonstrating meanwhile the convenient colon operator, that performs the same function provided by starts_with() in dplyr.
data all;
set "c:/book/help.sas7bdat";

data wide;
set all;
keep id cesd:;

The simpler way to make the desired data set is with the transpose procedure. Here the by statement forces the variables listed in that statement not to be transposed. The notsorted options save us having to actually sort the variables. Otherwise the procedure works like gather(): each transposed variable becomes a row in the output data set for every observation in the input data set. SAS uses standard variable names for gather()'s key (SAS: _NAME_)and value (SAS: COL1) though these can be changed.
proc transpose data = wide out = long_a;
by notsorted id notsorted cesd;

data long;
set long_a;
time = substr(_name_, 5);
rename col1=cesd_tv;

proc print data = long;
where id eq 1;
var id time cesd cesd_tv; 

 Obs    ID    time    CESD    cesd_tv

   1     1     1       49         7
   2     1     2       49         .
   3     1     3       49         8
   4     1     4       49         5

As with R, it's trivial, though somewhat cumbersome, to generate this effect using basic coding.
data long;
set wide;
time = 1; cesd_tv = cesd1; output;
time = 2; cesd_tv = cesd2; output;
time = 3; cesd_tv = cesd3; output;
time = 4; cesd_tv = cesd4; output;

proc print data = long;
where id eq 1;
var id time cesd cesd_tv; 

 Obs    ID    time    CESD    cesd_tv

   1     1     1       49         7
   2     1     2       49         .
   3     1     3       49         8
   4     1     4       49         5

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