# mle {stats4}

### 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.

### Values

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)

Documentation reproduced from R 3.0.2. License: GPL-2.