[Rd] plogis (and other p* functions), vectorized lower.tail

Ben Bolker bbo|ker @end|ng |rom gm@||@com
Thu Dec 9 16:55:17 CET 2021

On 12/9/21 10:03 AM, Martin Maechler wrote:
>>>>>> Matthias Gondan
>>>>>>      on Wed, 8 Dec 2021 19:37:09 +0100 writes:
>      > Dear R developers,
>      > I have seen that plogis silently ignores vector elements of lower.tail,
> and also of 'log'.
> This is indeed the case for all d*, p*, q* functions.
> Yes, this has been on purpose and therefore documented, in the
> case of plogis, e.g. in the 'Value' section of ?plogis :
>       The length of the result is determined by ‘n’ for ‘rlogis’, and is
>       the maximum of the lengths of the numerical arguments for the
>       other functions.
>   (note: *numerical* arguments: the logical ones are not recycled)
>       The numerical arguments other than ‘n’ are recycled to the length
>       of the result.  Only the first elements of the logical arguments
>       are used.
>   (above, we even explicitly mention the logical arguments ..)
> Recycling happens for the first argument (x,p,q) of these
> functions and for "parameters" of the distribution, but not for
> lower.tail, log.p (or 'log').
>      >> plogis(q=0.5, location=1, lower.tail=TRUE)
>      > [1] 0.3775407
>      >> plogis(q=0.5, location=1, lower.tail=FALSE)
>      > [1] 0.6224593
>      >> plogis(q=c(0.5, 0.5), location=1, lower.tail=c(TRUE, FALSE))
>      > [1] 0.3775407 0.3775407
>      > For those familiar with psychological measurement: A use case of the above function is the so-called Rasch model, where the probability that a person with some specific ability (q) makes a correct (lower.tail=TRUE) or wrong response (lower.tail=FALSE) to an item with a specific difficulty (location). A vectorized version of plogis would enable to determine the likelihood of an entire response vector in a single call. My current workaround is an intermediate call to „Vectorize“.
>      > I am wondering if the logical argument of lower.tail can be vectorized (?). I see that this may be a substantial change in many places (basically, all p and q functions of probability distributions), but in my understanding, it would not break existing code which assumes lower.tail to be a single element. If that’s not
>      > possible/feasible, I suggest to issue a warning if a vector of length > 1 is given in lower.tail. I am aware that the documentation clearly states that lower.tail is a single boolean.
> aah ok, here you say you know that the current behavior is documented.
>      > Thank you for your consideration.
> As you mention, changing this would be quite a large endeavor.
> I had thought about doing that many years ago, not remembering
> details, but seeing that in almost all situations you really
> only need one of the two tails  (for Gaussian- or t- based confidence
> intervals you also only need one, for symmetry reason).
> Allowing the recycling there would make the intermediate C code
> (which does the recycling) larger and probably slightly
> slower because of conceptually two more for loops which would in
> 99.9% only have one case ..
> I'd have found that ugly to add. ... ...
> ... but of course, if you can prove that the code bloat would not be large
> and not deteriorate speed in a measurable way and if you'd find
> someone to produce a comprehensive and tested patch ...
> Martin
>      > With best wishes,
>      > Matthias
>      > [[alternative HTML version deleted]]
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   I agree with everything said above, but think that adding a warning 
when length(lower.tail) > 1 (rather than silently ignoring) might be 
helpful ...  ??

   As for the vectorization, it seems almost trivial to do at the user 
level when needed (albeit it's probably a little bit inefficient):

pv <- Vectorize(plogis, c("q", "location", "scale", "lower.tail"))
pv(q=c(0.5, 0.5), location=1, lower.tail=c(TRUE, FALSE))
[1] 0.3775407 0.6224593

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