R: Maximum likelihood estimation

maxp {hyper2}

R Documentation

Maximum likelihood estimation

Description

Find the maximum likelihood estimate for p, also equal probabilities

Usage

maxp(H, startp=NULL, give=FALSE, fcm=NULL, fcv=NULL, SMALL=1e-6, n=10,
   show=FALSE, justlikes=FALSE, ...)
maxplist(Hlist, startp=NULL, give=FALSE, fcm=NULL, fcv=NULL, SMALL=1e-6, ...)
maxp_single(H, startp=NULL, give=FALSE, fcm=NULL, fcv=NULL, SMALL=1e-6,
   maxtry=100, ...)
maxp_simplex(H, n=100, show=FALSE, give=FALSE, ...)
equalp(H)

Arguments

`H`	A `hyper2` object
`Hlist`	A list with elements all `hyper2` objects
`startp`	A vector of probabilities
`give`	Boolean, with default `FALSE` meaning to return just the evaluate (including fillup), and `TRUE` meaning to return the entire formal output of the optimization routine
`fcm,fcv`	Further problem-specific constraints
`n`	Number of start points to use
`show`	Boolean, with `TRUE` meaning to show successive estimates
`justlikes`	Boolean, with `TRUE` meaning to return just a vector of estimated likelihoods
`SMALL`	Numerical minimum for probabilities
`maxtry`	Integer specifying maximum number of times to try `constrOptim()` with slightly differing start points, to avoid a known R bug which reports `wmmin is not finite`, bugzilla id 17703
`...`	Further arguments which `maxp()` passes to `constrOptim()`

Details

Function maxp() returns the maximum likelihood estimate for p, which has the unit sum constraint implemented.

Function maxplist() does the same but takes a list of hyper2 objects (for example, the output of ggrl()). Note that maxplist() does not have access to the gradient of the objective function, which makes it slow.

If function maxp() is given a suplist object it dispatches to maxplist().

Function maxp_simplex() is intended for complicated or flat likelihood functions where finding local maxima might be a problem. It repeatedly calls maxp_single(), starting from a different randomly chosen point in the simplex each time. This function does not take fcm or fcv arguments, it operates over the whole simplex (hence the name). Further arguments, ..., are passed to maxp_single().

The functions do not work for the masterchef_series6 likelihood function. These require a bespoke optimization as shown in the vignette.

Function equalp() returns the value of p for which all elements are the same.

In functions maxp() etc, arguments fcm and fcv implement linear constraints to be passed to constrOptim(). These constraints are in addition to the usual nonnegativity constraints and unit-sum constraint, and are added to the ui and ci arguments of constrOptim() with rbind() and c() respectively. The operative lines are in maxp_single():

    UI <- rbind(diag(nrow = n - 1), -1, fcm)
    CI <- c(rep(SMALL, n - 1), -1 + SMALL, fcv)

where in UI, the first n-1 rows enforce nonnegativity of p_i, 1<=i<n; row n enforces nonnegativity of the fillup value p_n; and the remaining (optional) rows enforce additional linear constraints. Argument CI is a vector with corresponding elements.

Examples of their use are given in the “icons” vignette.

Note

In manpages elsewhere, n=2 is used for speed reasons. Use the default n=10 or greater in production work.

This functionality is peculiarly susceptible to off-by-one errors.

The built-in datasets generally include a pre-calculated result of running maxp(); thus hyper2 object icons and icons_maxp are included in the same .rda file.

Function maxp() can trigger a known R bug (bugzilla id 17703) which reports “wmmin is not finite”.

Author(s)

Robin K. S. Hankin

Examples


maxp(icons)

W <- hyper2(pnames=letters[1:5])
W1 <- ggrl(W, 'a', letters[2:3],'d')  # W1 is a suplist object
## Not run: maxp(W1)  # takes a long time to maximize a suplist

[Package hyper2 version 2.0-1 Index]