Error during evaluation of expression in optim() - r

Question

I'm implementing a function in R for finding the parameters that minimize the quadratic error for an arbitrary pdf function (e.g., pnorm, punif, pbinom, etc.). The design is such that the user provides probabilities, empirical quantiles, a function name (densit), and a list of parameter names (params) from the densit function (e.g., mean and sd in pnorm). For instances, being for q1, q2, and q3 equal to -1.644854, 0, and 1.644854, and p1, p2, and p3 equal to 0.05, 0.5, 0.95, the function should recover mean and sd as approximately 0 and 1 respectively.
The goal is to feed such expression to optim, so that the latter takes a function (called internally quadraticFun) that should evaluate an expression during optimization; however, I can't make optim work on such expression for estimation. The function is this:
fun <- function(p1 = 0.05, p2 = 0.50, p3 = 0.95, q1, q2, q3, output = "complete", densit, params) {
densit <- substitute(densit)
params <- sapply(params, as.name)
densiCall1 <- as.call(c(as.list(densit), as.list(q1), params))
densiCall2 <- as.call(c(as.list(densit), as.list(q2), params))
densiCall3 <- as.call(c(as.list(densit), as.list(q3), params))
quadratEq <- substitute((densiCall1 - p1)^2 +
(densiCall2 - p2)^2 +
(densiCall3 - p3)^2)
quadraticFun <- function(params) {
eval(quadratEq)
}
initVals <- rep(1, times = length(params))
res <- optim(initVals, quadraticFun) # ERROR SOMEWHERE AROUND HERE...
# if output is set to "complete", return the whole res object, otherwise, return just the parameters
if (output == "parameters") {
return(res$par)
}
return(res)
}
Debugging with the next example indicates that the error shows up during the call optim(initVals, quadraticFun), specifically during evaluation of quadraticFun with the following message:
> findParams(q1 = -1.644854, q2 = 0, q3 = 1.644854, densit = pnorm, params = list("mean", "sd"))
Error in pnorm(-1.644854, mean, sd) :
Non-numeric argument to mathematical function
It seems that the expression resulting is taken literally by the interpreter, i.e., mean and as as symbols to evaluate instead of arguments in the function to optimize.
Thanks in advance for any hint that helps to solve this problem.

Answer 1

Your function quadraticFun was not working, because is did not properly hand over the params parameter to densiCall1 function.
I changed the code a bit so that there is only one call which needs to be evaluated, which is easier to handle. Now densit is a character string, I am sure this you could be changed.
Here is a function I came up with:
findParams <- function(q = c( -1.644854, 0, 1.644854),
p = c(0.05, 0.50, 0.95), output = "complete", densit="pnorm",
params = c("mean", "sd")) {
l <- length(params)
cl <- vector("list", 2 + length(params))
cl[[1]] <- as.name(densit)
cl[[2]] <- q
names(cl) <- c(NA, "q", params)
mode(cl) <- "call"
quadraticFun <- function(x) {
cl[3:(l+2)] <- x
res <- eval(cl)
sum((res - p)^2)
}
initVals <- rep(1, times = l)
res <- optim(initVals, quadraticFun)
if (output == "parameters") {
return(res$par)
}
return(res)
}
And it seems to work:
findParams()
$par
[1] 0.0001065349 1.0001052494
$value
[1] 2.682477e-09
$counts
function gradient
67 NA
$convergence
[1] 0
$message
NULL