hyper2 (version 2.0-1)

maxp: 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 \(p_i\), \(1\leq p < n\); 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.

See Also

gradient,fillup

Examples

# NOT RUN {
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)
# }
# NOT RUN {
  # takes a long time to maximize a suplist

# }