MLE function with array of parameters

Question

I would like to know how to do the maximum likelihood estimation in R when fitting parameters are given in an array. This is needed when the number of parameters is large. So basically, to fit a normal distribution to the data x, I would like to do something like the following

LL <- function(param_array) {
   R = dnorm(x, param_array[1], param_array[2])
  -sum(log(R))
}

mle(LL, start = list(param_array = c(1,1)))

(Instead of this original code in the first section of http://www.r-bloggers.com/fitting-a-model-by-maximum-likelihood/) If I ran the code above I will get an error

Error in dnorm(x, param_array[1], param_array[2]) : argument "param_array" is missing, with no default

Could anyone let me know how to achieve what I want in the correct way?

So what do people do if they have like 50 parameters? Do they type them in by hand? — user113988

Zheyuan Li Zheyuan Li · Accepted Answer · 2016-07-20T08:36:15

stats4::mle is not a long function, you can inspect it in your R console:

> stats4::mle

Note how start is handled:

start <- sapply(start, eval.parent)
nm <- names(start)

case 1

If you do:

LL <- function(mu, sigma) {
   R = dnorm(x, mu, sigma)
  -sum(log(R))
}

mle(LL, start = list(mu = 1, sigma = 1))

you get:

nm
#[1] "mu"  "sigma"

Also,

formalArgs(LL)
#[1] "mu"  "sigma"

case 2

If you do:

LL <- function(param_array) {
   R = dnorm(x, param_array[1], param_array[2])
  -sum(log(R))
}

mle(LL, start = list(param_array = c(1,1)))

you get

nm
#[1] NULL

but

formalArgs(LL)
#[1] param_array

The problem

The evaluation of function LL inside stats::mle is by matching nm to the formal arguments of LL. In case 1, there is no difficulty in matching, but in case 2 you get no match, thus you will fail to evaluate LL.

So what do people do if they have like 50 parameters? Do they type them in by hand?

Isn't this a bogus argument, after a careful reflection? If you really have 50 parameters, does using an array really save your effort?

First, inside your function LL, you have to specify param_array[1], param_array[2], ..., param_array[50], i.e., you still need to manually input 50 parameters into the right positions. While when specifying start, you still need to type in a length-50 vector element by element, right? Isn't this the same amount of work, compared with not using an array but a list?

MLE function with array of parameters

1 Answers