mle {stats4}R Documentation

Maximum Likelihood Estimation

Description

Estimate parameters by the method of maximum likelihood.

Usage

mle(minuslogl, start = formals(minuslogl), method = "BFGS",
    fixed = list(), nobs, ...)

Arguments

minuslogl

Function to calculate negative log-likelihood.

start

Named list. Initial values for optimizer.

method

Optimization method to use. See optim.

fixed

Named list. Parameter values to keep fixed during optimization.

nobs

optional integer: the number of observations, to be used for e.g. computing BIC.

...

Further arguments to pass to optim.

Details

The optim optimizer is used to find the minimum of the negative log-likelihood. An approximate covariance matrix for the parameters is obtained by inverting the Hessian matrix at the optimum.

Value

An object of class mle-class.

Note

Be careful to note that the argument is -log L (not -2 log L). It is for the user to ensure that the likelihood is correct, and that asymptotic likelihood inference is valid.

See Also

mle-class

Examples

## Avoid printing to unwarranted accuracy
od <- options(digits = 5)
x <- 0:10
y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)

## Easy one-dimensional MLE:
nLL <- function(lambda) -sum(stats::dpois(y, lambda, log = TRUE))
fit0 <- mle(nLL, start = list(lambda = 5), nobs = NROW(y))
# For 1D, this is preferable:
fit1 <- mle(nLL, start = list(lambda = 5), nobs = NROW(y),
            method = "Brent", lower = 1, upper = 20)
stopifnot(nobs(fit0) == length(y))

## This needs a constrained parameter space: most methods will accept NA
ll <- function(ymax = 15, xhalf = 6) {
    if(ymax > 0 && xhalf > 0)
      -sum(stats::dpois(y, lambda = ymax/(1+x/xhalf), log = TRUE))
    else NA
}
(fit <- mle(ll, nobs = length(y)))
mle(ll, fixed = list(xhalf = 6))
## alternative using bounds on optimization
ll2 <- function(ymax = 15, xhalf = 6)
    -sum(stats::dpois(y, lambda = ymax/(1+x/xhalf), log = TRUE))
mle(ll2, method = "L-BFGS-B", lower = rep(0, 2))

AIC(fit)
BIC(fit)

summary(fit)
logLik(fit)
vcov(fit)
plot(profile(fit), absVal = FALSE)
confint(fit)

## Use bounded optimization
## The lower bounds are really > 0,
## but we use >=0 to stress-test profiling
(fit2 <- mle(ll, method = "L-BFGS-B", lower = c(0, 0)))
plot(profile(fit2), absVal = FALSE)

## a better parametrization:
ll3 <- function(lymax = log(15), lxhalf = log(6))
    -sum(stats::dpois(y, lambda = exp(lymax)/(1+x/exp(lxhalf)), log = TRUE))
(fit3 <- mle(ll3))
plot(profile(fit3), absVal = FALSE)
exp(confint(fit3))

options(od)

[Package stats4 version 3.2.0 Index]