John et al
Thank you for your advice below. It was sloppy of me not to verify my
reproducible code below. I have tried a few of your suggestions and wrapped
the working code into the function below called pl2. The function properly
lands on the right model parameters when I use the optim or nlminb (for nlminb
I had to increase max iterations).
The function is enormously slow. At first, I created the object rr1 with two
calls to sapply(). This works, but creates an extremely large matrix at each
iteration.
library(statmod)
dat <- replicate(20, sample(c(0,1), 2000, replace = T))
a <- b <- rep(1, 20)
Q <- 10
qq <- gauss.quad.prob(Q, dist = 'normal', mu = 0, sigma=1)
nds <- qq$nodes
wts <- qq$weights
rr1 <- sapply(1:nrow(dat), function(j)
sapply(1:Q, function(i)
exp(sum(dbinom(dat[j,], 1, 1/ (1 + exp(- 1.7 * a * (qq$nodes[i] - b))), log =
TRUE))) * qq$weights[i]))
So, I thought to reduce some memory, I would do it this way which is
equivalent, doesn't create such a large matrix, but instead uses an explicit
loop. Both approaches are still equally as slow.
rr1 <- numeric(nrow(dat))
for(j in 1:length(rr1)){
rr1[j] <- sum(sapply(1:Q,
function(i) exp(sum(dbinom(dat[j,], 1, 1/ (1 + exp(- 1.7 * a *
(nds[i] - b))), log = TRUE))) * wts[i]))
}
As you noted, my likelihood is not complex; in fact I have another program that
uses newton-raphson with the analytic first and second derivatives because they
are so easy to find. In that program, the model converges very (very) quickly.
My purpose in using numeric differentiation is experiential in some respects
and hoping to apply this to problems for which the analytic derivatives might
not be so easy to come by.
I think the basic idea here to improve speed is to make a call to the gradient,
which I understand to be the vector of first derivatives of my likelihood
function, is that right? If that is right, in a multi-parameter problem, I'm
not sure how to think about the gradient function. Since I am maximizing w.r.t.
a and b (these are the parameters of the model), I would have a vector of first
partials for a and another for b. So I conceptually do not understand what the
gradient would be in this instance, perhaps some clarification would be helpful.
Below is the working function, which as I noted is enormously slow. Any advice
on speed improvements here would be helpful. Thank you
pl2 <- function(dat, Q, startVal = NULL, ...){
if(!is.null(startVal) && length(startVal) != ncol(dat) ){
stop("Length of argument startVal not equal to
the number of parameters estimated")
}
if(!is.null(startVal)){
startVal <- startVal
} else {
p <- colMeans(dat)
startValA <- rep(1, ncol(dat))
startValB <- as.vector(log((1 - p)/p))
startVal <- c(startValA,startValB)
}
rr1 <- numeric(nrow(dat))
qq <- gauss.quad.prob(Q, dist = 'normal', mu = 0, sigma=1)
nds <- qq$nodes
wts <- qq$weights
dat <- as.matrix(dat)
fn <- function(params){
a <- params[1:20]
b <- params[21:40]
for(j in 1:length(rr1)){
rr1[j] <- sum(sapply(1:Q,
function(i) exp(sum(dbinom(dat[j,], 1, 1/ (1 + exp(- 1.7 * a *
(nds[i] - b))), log = TRUE))) * wts[i]))
}
-sum(log(rr1))
}
#opt <- optim(startVal, fn, method = "BFGS", hessian = TRUE)
opt <- nlminb(startVal, fn)
#opt <- Rcgmin(startVal, fn)
opt
#list("coefficients" = opt$par, "LogLik" = -opt$value,
"Std.Error" = sqrt(diag(solve(opt$hessian))))
}
dat <- replicate(20, sample(c(0,1), 2000, replace = T))
r2 <- pl2(datat, Q =10)
-----Original Message-----
From: Prof J C Nash (U30A) [mailto:nas...@uottawa.ca]
Sent: Wednesday, February 18, 2015 9:07 AM
To: r-help@r-project.org; Doran, Harold
Subject: Re: [R] multiple parameter optimization with optim()
Some observations -- no solution here though:
1) the code is not executable. I tried. Maybe that makes it reproducible!
Typos such as "stat mod", undefined Q etc.
2) My experience is that any setup with a ?apply approach that doesn't then
check to see that the structure of the data is correct has a high probability
of failure due to mismatch with the optimizer requirements.
It's worth being VERY pedestrian in setting up optimization functions and
checking obsessively that you get what you expect and that there are no regions
you are likely to wander into with divide by 0, log(negative), etc.
3) optim() is a BAD choice here. I wrote the source for three of the codes, and
the one most appropriate for many parameters (CG) I have been deprecating for
about 30 years. Use Rcgmin or something else instead.
4) If possible, analytic gradients are needed for CG like codes. You probably
need to dig out some source code for dbinom() to do this, but your function is
not particularly complicated, and doesn't have "if"
statements etc. However, you could test a case using the numDeriv gradient that
is an option for Rcgmin, but it will be painfully slow.
For a one-off computation, that may still be acceptable.
JN
On 15-02-18 06:00 AM, r-help-requ...@r-project.org wrote:
> Message: 37
> Date: Tue, 17 Feb 2015 23:03:24 +0000
> From: "Doran, Harold" <hdo...@air.org>
> To: "r-help@r-project.org" <r-help@r-project.org>
> Subject: [R] multiple parameter optimization with optim()
> Message-ID: <d10931e1.23c0e%hdo...@air.org>
> Content-Type: text/plain; charset="UTF-8"
>
> I am trying to generalize a working piece of code for a single parameter to a
> multiple parameter problem. Reproducible code is below. The parameters to be
> estimated are a, b, and c. The estimation problem is such that there is one
> set of a, b, c parameters for each column of the data. Hence, in this sample
> data with 20 columns, there are 20 a params, 20 b-params, and 20 c-params.
>
> Because I am estimating so many parameters, I am not certain that I have
> indicated to the function properly the right number of params to estimate and
> also if I have generated starting values in a sufficient way.
>
> Thanks for any help.
> Harold
>
> dat <- replicate(20, sample(c(0,1), 2000, replace = T)) library(stat
> mod) qq <- gauss.quad.prob(Q, dist = 'normal', mu = 0, sigma = 1) nds
> <- qq$nodes wts <- qq$weights fn <- function(params){ a <-
> params[1:ncol(dat)] b <- params[1:ncol(dat)] c <- params[1:ncol(dat)]
> L <- sapply(1:ncol(dat), function(i) dbinom(dat[,i], 1, c + ((1 -
> c)/(1 + exp(-1.7 * a * (nds[i] - b)))) * wts[i]))
> r1 <- prod(colSums(L * wts))
> -log(r1)
> }
> startVal <- rep(.5, ncol(dat))
> opt <- optim(startVal, fn)
>
> [[alternative HTML version deleted]]
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