[R] evaluating function over seq of values

[Bert Gunter]

The apply() family of functions **are** loops (at the interpreted
level). They are **not vectorized** (looping at the C level). Their
typical virtue is in code clarity and (sometimes) the utiity of the
return structure, not greater efficiency. Sometimes they are a bit
faster, sometimes a bit slower, than *well-written* explicit loops.

Note that in your likelihood function, N can be a vector of values, so
you can compute the likelihood for all values of N and just access the
value you want via subscripting rather than repeatedly computing it
for different N's.  If all you want to do is maximize over a grid of
values, I don't know why you need optim() at all -- but I probably
just don't get what you're doing.

Cheers,
Bert




Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Mon, Feb 13, 2017 at 8:41 AM, Evan Cooch <evan.cooch at gmail.com> wrote:
> The MWE (below) shows what I'm hoping to get some help with:
>
> step 1\ specify the likelihood expression I want to evaluate using a
> brute-force grid search (not that I would do this in practice, but it is a
> convenient approach to explain the idea in a class...).
>
> step 2\ want to evaluate the likelihood at each of a sequence of values of N
> (for this example, seq(80,200,1)).
>
> step 3\ take all of the values of the likelihood at each value for N, and
> (say) plot them
>
> I'm sure there is a clever way to vectorize all this, but my token attempts
> at wrestling sapply into submission have failed me here. In my MWE, I use a
> simple loop, which has the advantages of working, and being completely
> transparent as to what it is doing. For teaching purposes, this is perhaps
> fine, but I'm curious as to how I could accomplish the same thing avoiding
> the loop.
>
> Thanks in advance...
>
> -----<MWE code below>-----
>
>
> # ML estimation by simple grid search
>
> rm(list=ls())
> library("optimx")
>
> # set up likelihood function
>
> f_like <- function(par) {
>                             p1 <- par[1];
>                             p2 <- par[2];
>                             p3 <- par[3];
>                             p4 <- par[4];
>                                    lfactorial(N)-lfactorial(N-79) +
>                                     (30*log(p1)+(N-30)*log(1-p1)) +
>                                     (15*log(p2)+(N-15)*log(1-p2)) +
>                                     (22*log(p3)+(N-22)*log(1-p3)) +
>                                     (45*log(p4)+(N-45)*log(1-p4)) }
>
>
> # do the otimization using optimx nested in a loop (works, but guessing
> there is an
> # easier way using lapply or some such...)
>
> count <- 1;
>
> dat <- matrix(c(0,0,0),length(seq(80,200,1)),3)
>
> for (N in seq(80,200,1)) {
>
> results_optx <- optim(c(0.2,0.2,0.2,0.2), f_like,
>      method = "L-BFGS-B", lower=c(0.005,0.005,0.005,0.005),
> upper=c(0.990,0.995,0.995,0.995),
>       hessian = TRUE,control=list(fnscale=-1))
>
> like_mod <- results_optx$value;
>  dat[count,1] <- count;
>  dat[count,2] <- N;
>  dat[count,3] <- like_mod;
> count=count+1;
> }
>
> plot(dat[,2],dat[,3],type="l",bty="n",  xlim=c(79,205), yaxs =
> "i",main="likelihood profile",xlab="N", ylab="Likelihood")
>
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