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

[Martin Maechler]

>>>>> Sokol Serguei on Thu, 9 Dec 2021 17:13:36 +0100 writes:

    > On 09/12/2021 16:55, Ben Bolker wrote:
    >> 
    >> 
    >> 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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    >>>      > https://stat.ethz.ch/mailman/listinfo/r-devel
    >>> 
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    >>> R-devel using r-project.org mailing list
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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

    > .. or directly use mapply()

    > mapply(plogis, q=c(0.5, 0.5), location=1, lower.tail=c(TRUE, FALSE))
    > [1] 0.3775407 0.6224593

Very nice, yes.  Also, there's no need to recycle/vectorize yourself:
 q=0.5  is sufficient:

 > mapply(plogis, q=0.5, location=1, lower.tail=c(TRUE, FALSE))
 [1] 0.3775407 0.6224593


Martin