## Speed test of sequence generation for unbalanced simulation

I have a simulation package that allows for the simulation of regression models including nested data structures. You can see the package on github here: simReg. Over the weekend I updated the package to allow for the simulation of unbalanced designs. I’m hoping to put together a new vigenette soon highlighting the functionality.

I am working on a simulation that uses the unbalanced functionality and while simulating longitudinal data I’ve found the function is much slower than the cross sectional counterparts (and balanced designs). I’ve ran some additional testing and I believe I have the speed issues narrowed down to the fact that I am generating a time variable. Essentially, I have a vector of number of observations per cluster. The function then turns this vector of lengths into a time variable starting at 0 up to the maximum number of observations minus 1 by 1. As an example:

``````x <- round(runif(5, min = 3, max = 10), 0)
unlist(lapply(1:length(x), function(xx) (1:x[xx]) - 1))``````
``##  [1] 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 6``

From the code above, you can see that there the number of observations is generated using `runif` which is saved to the object `x`. Then I use a combination of lapply, unlist, and the ‘:’ operator to generate the sequence. This is the same code used in my package above to generate the time variable.

As such, I was interested in testing various ways to generate the sequence and do a performance comparison. I compared the following ways, the `':'` operator, `seq.int`, `seq`, `do.call` with `mapply`, and `rep.int` for the balanced case as a comparison to how it was done before. This was all done with the great `microbenchmark` package.

Here are the results from the 7 comparisons:

``````library(microbenchmark)
x <- round(runif(100, min = 3, max = 15), 0)
microbenchmark(
colon = unlist(lapply(1:length(x), function(xx) (1:x[xx]) - 1)),
seq.int = unlist(lapply(1:length(x), function(xx) seq.int(0, x[xx] - 1, 1))),
seq = unlist(lapply(1:length(x), function(xx) seq(0, x[xx] - 1, 1))),
seq.int_mapply = do.call(c, mapply(seq.int, 0, x - 1)),
seq_mapply = do.call(c, mapply(seq, 0, x - 1)),
colon_mapply = do.call(c, mapply(':', 0, x - 1)),
rep.int = rep.int(1:8 - 1, times = 100), # balanced case for reference.
times = 1000L
)``````
``````## Unit: microseconds
##            expr      min        lq        mean   median        uq       max neval  cld
##           colon   96.890  119.8810  175.096814  132.608  209.3800  3007.675  1000  b
##         seq.int  123.986  145.9505  209.669046  161.346  246.5345  2408.685  1000  b
##             seq 1787.116 2045.5555 2914.030581 2357.367 3505.6695 18720.988  1000    d
##  seq.int_mapply  135.482  163.8090  240.447820  180.642  271.9885  4331.693  1000  b
##      seq_mapply  723.386  828.4860 1297.687641  908.338 1515.1280 52677.410  1000   c
##    colon_mapply  119.059  144.5140  207.652022  162.783  244.4820  1878.668  1000  b
##         rep.int    2.053    3.6950    5.845916    4.927    6.9800   210.201  1000 a``````

The results (in microseconds) show that this is where the significant slowdown is coming in my package implementing the unbalanced cases, although it appears that the ‘:’ operator is the second best alternative. For those that have not seen the significant speed bump of the `seq.int` and `rep.int` over the `seq` and `rep` alternatives should also pay close attention (compare lines 2 and 3 above).

I’d be interested in alternative procedures that I am not aware of as well. Although not a big deal when running the package once, doing it 50,000 times does add up.

Lastly, for those that are interested, we can show they are all equivalent methods (except for the `rep.int` case).

``````identical(
unlist(lapply(1:length(x), function(xx) (1:x[xx]) - 1)),
unlist(lapply(1:length(x), function(xx) seq.int(0, x[xx] - 1, 1))),
unlist(lapply(1:length(x), function(xx) seq(0, x[xx] - 1, 1))),
do.call(c, mapply(seq.int, 0, x - 1)),
do.call(c, mapply(seq, 0, x - 1)),
do.call(c, mapply(':', 0, x - 1))
)``````
``## [1] TRUE``