stats4 (version 3.6.2)

# mle: 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`.

## Value

An object of class `mle-class`.

## 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.

`mle-class`

## Examples

Run this code
``````# NOT RUN {
## 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)
# }
``````

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