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 0 1 2 0 1 2 3 4 5 6 0 1 2 3 4 0 1 2 3 4 5 6 7 8
```

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 133.429 148.618 255.474605 160.1145 235.8605 57706.598 1000 ab
## seq.int 180.231 203.632 270.517868 223.1330 309.9640 2671.845 1000 ab
## seq 2255.960 2626.685 4207.210575 2933.1590 3466.4605 88721.432 1000 d
## seq.int_mapply 227.854 258.235 499.000451 292.7210 397.4110 105037.011 1000 b
## seq_mapply 953.293 1079.126 1534.250895 1203.9320 1543.2495 57174.117 1000 c
## colon_mapply 167.094 195.832 383.431252 220.4645 299.0845 61779.643 1000 ab
## rep.int 2.053 4.516 5.807329 5.7480 6.9800 30.792 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
```