[R] How to filter data using sets generated by flattening with dcast, when I can't store those sets in a data frame

[Jocelyn Ireson-Paine]

This is a fairly long question. It's about a problem that's easy to 
specify in terms of sets, but that I found hard to solve in R by using 
them, because of the strange design of R data structures. In explaining 
it, I'm going to touch on the reshape2 library, dcast, sets, and the 
non-orthogonality of R.

My problem stems from some drug-trial data that I've been analysing for 
the Oxford Pain Research Unit. Here's an example. Imagine a data frame 
representing patients in a trial of pain-relief drugs. The trial lasts for 
ten days. Each patient's pain is measured once a day, and the values are 
recorded in a data frame, one row per patient per day. Like this:

   ID  Day  Pain
    1    1  10
    1    2   9
    1    4   7
    1    7   2
    2    2   8
    2    3   7
    3    1  10
    3    3   6
    3    4   6
    3    8   2

Unfortunately, many patients have measurements missing. Thus, in the 
example above, patient 1 was only observed on days 1, 2, 4, and 7, rather 
than on the full ten days. But a patient's measurements are only useful to 
us if that patient has a certain minimum set of days, so I need to check 
for patients who lack those days. Let's assume that these days are numbers 
1, 4, and 9.

Such a question is trivial to state in terms of sets. Let D(i) denote the 
set of days on which patient i was measured: then I want to find out which 
patients p, or how many patients p, have a D(p) that contains the set 
{1,4,9}.

The obvious way to solve this is to write a function that tells me whether 
one set is a superset of another. Then flatten my data frame so that it 
looks like this:

   ID  Days
    1  {1,2,4,7}
    2  {2,3}
    3  {1,3,4,8}

And finally, filter it by some R translation of

   flattened[ includes( flattened$Days, {1,4,9} ), ]

I started with the built-in functions that operate on sets represented as 
vectors. These are described in
  https://stat.ethz.ch/R-manual/R-devel/library/base/html/sets.html ,
"Set Operations". For example:

   > union( c(1,2,3), c(2,4,6) )
   [1] 1 2 3 4 6
   > intersect( c(1,2,3), c(2,4,6) )
   [1] 2

So I first wrote a set-inclusion function:

   # True if vector a is a superset of vector b.
   #
   includes <- function( a, b )
   {
     return( setequal( union( a, b ), a ) )
   }

Here are some sample calls:

   > includes( c(1), c() )
   [1] TRUE
   > includes( c(1), c(1) )
   [1] TRUE
   > includes( c(1), c(1,2) )
   [1] FALSE
   > includes( c(2,1), c(1,2) )
   [1] TRUE
   > includes( c(2,1,3), c(1,2) )
   [1] TRUE
   > includes( c(2,1,3), c(4,1,2) )
   [1] FALSE

I then made myself a variable holding my sample data frame:

   df <- data.frame( ID = c( 1, 1, 1, 1, 2, 2, 3, 3, 3, 3 )
                   , Day = c( 1, 2, 4, 7, 2, 3, 1, 3, 4, 8 )
                   )

And I tried flattening it, using dcast and an aggregator function as 
described in (amongst many other places) 
http://seananderson.ca/2013/10/19/reshape.html , "An Introduction to 
reshape2" by Sean C. Anderson.

The idea behind this is that (for my data) dcast will call the aggregator 
function once per patient ID, passing it all the Day values for the 
patient. The aggregator must combine them in some way, and dcast puts its 
results into a new column. For example, here's an aggregator that merely 
sums its arguments:

   aggregator_making_sum <- function( ... )
   {
     return( sum( ... ) )
   }

If I call it, I get this:

   >  dcast( df, ID~. , fun.aggregate=aggregator_making_sum )
   Using Day as value column: use value.var to override.
     ID  .
   1  1 14
   2  2  5
   3  3 16

And here's an aggregator that converts the argument list to a string:

   aggregator_making_string <- function( ... )
   {
     return( toString( ... ) )
   }

Calling it gives this:

   >  dcast( df, ID~. , fun.aggregate=aggregator_making_string )
   Using Day as value column: use value.var to override.
     ID          .
   1  1 1, 2, 4, 7
   2  2       2, 3
   3  3 1, 3, 4, 8

In both of these, the three dots denote all arguments to the aggregator, 
as explained in Burns Statistics's 
http://www.burns-stat.com/the-three-dots-construct-in-r/ . My first 
aggregator sums them; my second converts them to a string. Both uses of 
dcast generate a data frame with a column named "." , which contains the 
aggregates. In the second data frame, that may not be so clear: the first 
column of numbers is row numbers; the second column of numbers are the 
IDs; and the remaining columns form the strings, belonging to "." .

But what I want is neither a sum nor a string but a set. Specifically, a 
set that's compatible with the R set operations I called in my 'includes' 
function. Since these sets are vectors, my aggregator should just pack its 
arguments into a vector:

   aggregator_making_set <- function( ... )
   {
     return( c( ... ) )
   }

But when I tried it, I got an error:

   > dcast( df, ID~. , fun.aggregate=aggregator_making_set )
   Using Day as value column: use value.var to override.
   Error in vapply(indices, fun, .default) : values must be length 0,
    but FUN(X[[1]]) result is length 4

It's not an informative error message, because it expects me to know how 
dcast is coded. And I'm surprised that values need to be length 0: length 
1 would seem more appropriate. But perhaps it's trying to say that 'c' 
doesn't work on three-dots argument lists. Let's test that hypothesis:

   test_c_on_three_dots <- function( ... )
   {
     return( c( ... ) )
   }

   >   test_c_on_three_dots( 1 )
   [1] 1
   >   test_c_on_three_dots( 1, 2 )
   [1] 1 2
   >   test_c_on_three_dots( 1, 2, 3 )
   [1] 1 2 3

So 'c' does indeed work on three-dots argument lists. The error must have 
been caused by something else. Let's try making a set and putting it into 
a data frame directly:

   > df <- data.frame( col1=c(1,2), col2=c(3,4) )
   > df
     col1 col2
   1    1    3
   2    2    4
   > set <- union( c(5,6), c(6,7) )
   > set
   [1] 5 6 7
   > df[ 1, ]$col1 <- set
   Error in `$<-.data.frame`(`*tmp*`, "col1", value = c(5, 6, 7)) :
     replacement has 3 rows, data has 1

So that's the problem. Already in 1968, there was a language named Algol68 
which had arrays and, in order to make things easy for its programmers, 
allowed you to create arrays of every data type the language provided. You 
could have arrays of Booleans, arrays of integers, arrays of records, 
arrays of discriminated unions, arrays of procedures, arrays of I/O 
formats, arrays of pointers, and arrays of arrays. The idea was 
"orthogonality" (see for example 
http://stackoverflow.com/questions/1527393/what-is-orthogonality ): that 
the programmer does not have to think about unexpected interactions 
between the concept of array and the concept of the element type, because 
there are none. If you have a data type, you can make arrays of that type. 
Pop-2 (1970), Snobol4 (1966), and Lisp (1958) were similarly generous. But 
R (1993) isn't. It wants to make life hard by forcing me to use different 
kinds of container for different kinds of element. And by providing a nice 
implementation of sets and then not letting me store them.

So I thought about the kinds of data that I _can_ store in a data frame 
and generate by flattening. Strings! So I decided to use my 
aggregator_making_string function to make a string representation of the 
set of days, and to write a set-inclusion function that compared these 
sets against sets represented as vectors:

   includes2 <- function( a_as_string, b )
   {
     a <- as.numeric( unlist( strsplit( a_as_string, split="," ) ) )
     return( setequal( union( a, b ), a ) )
   }

Here are some example calls:

   > includes2( '1,2,3', c(1) )
   [1] TRUE
   > includes2( '1,2,3', c(1,2) )
   [1] TRUE
   > includes2( '1,2,3', c(1,2,4) )
   [1] FALSE
   > includes2( '1,2,3', c(3) )
   [1] TRUE
   > includes2( '1,2,3', c(0,3) )
   [1] FALSE
   >

I then tried using it:

   df <- data.frame( ID = c( 1, 1, 1, 1, 2, 2, 3, 3, 3, 3 )
                   , Day = c( 1, 2, 4, 7, 2, 3, 1, 3, 4, 8 )
                   )

   aggregator_making_string <- function( ... )
   {
     return( toString( ... ) )
   }

   flattened <- dcast( df, ID~. , fun.aggregate=aggregator_making_string )

   # Which patients have a day 1?
   flattened[ includes2( flattened$. , c(1) ), ]

Unfortunately, that didn't work. The final statement selected every row of 
'flattened'. I eventually realised that I had to vectorise 'includes2':

   includes3 <- Vectorize( includes2, "a_as_string" )

And that did work:

   >   flattened[ includes3( flattened$. , c(1) ), ]
     ID          .
   1  1 1, 2, 4, 7
   3  3 1, 3, 4, 8
   >   flattened[ includes3( flattened$. , c(1,2) ), ]
     ID          .
   1  1 1, 2, 4, 7
   >   flattened[ includes3( flattened$. , c(1,3) ), ]
     ID          .
   3  3 1, 3, 4, 8
   >   flattened[ includes3( flattened$. , c(2) ), ]
     ID          .
   1  1 1, 2, 4, 7
   2  2       2, 3

The moral of this email tale is that sets are really useful for filtering 
data, and dcast ought to be really useful for generating sets, but R 
refuses to let me store them in the data frame that dcast generates. I can 
fudge it by representing the sets as strings, but is there a cleaner way 
to solve the problem?

Cheers,

Jocelyn Ireson-Paine
07768 534 091
http://www.jocelyns-cartoons.uk
http://www.j-paine.org