mle: Maximum Likelihood Estimation

Description

Estimate parameters by the method of maximum likelihood.

Usage

mle2(minuslogl, start, method, optimizer,
    fixed = NULL, data=NULL,
default.start=TRUE, eval.only = FALSE, vecpar=FALSE,
parameters,...)
calc_mle2_function(formula,parameters,start,data=NULL)

Arguments

minuslogl

Function to calculate negative log-likelihood.

start

Named list. Initial values for optimizer.

method

Optimization method to use. See optim.

optimizer

Optimization function to use. (Stub.)

fixed

Named list. Parameter values to keep fixed during optimization.

data

list of data to pass to minuslogl

default.start

Logical: allow default values of minuslogl as starting values?

eval.only

Logical: return value of minuslogl(start) rather than optimizing

vecpar

Logical: is first argument a vector of all parameters? (For compatibility with optim.)

parameters

List of linear models for parameters

...

Further arguments to pass to optimizer

formula

a formula for the likelihood (see Details)

Value

An object of class "mle2".

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.

The minuslogl argument can also specify a formula, rather than an objective function, of the form x~ddistn(param1,...,paramn). In this case ddistn is taken to be a probability or density function, which must have (literally) x as its first argument (although this argument may be interpreted as a matrix of multivariate responses) and which must have a log argument that can be used to specify the log-probability or log-probability-density is required. If a formula is specified, then parameters can contain a list of linear models for the parameters.

If a formula is given and non-trivial linear models are given in parameters for some of the variables, then model matrices will be generated using model.matrix: start can either be an exhaustive list of starting values (in the order given by model.matrix) or values can be given just for the higher-level parameters: in this case, all of the additional parameters generated by model.matrix will be given starting values of zero. In the event of a convergence failure, see optim for the meanings of the error codes.

Examples

Run this code

x <- 0:10
y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
ll <- function(ymax=15, xhalf=6)
    -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE))
(fit <- mle2(ll))
mle2(ll, fixed=list(xhalf=6))

summary(fit)
logLik(fit)
vcov(fit)
p1 <- profile(fit)
plot(p1, absVal=FALSE)
confint(fit)

## use bounded optimization
## the lower bounds are really > 0, but we use >=0 to stress-test profiling
(fit1 <- mle2(ll, method="L-BFGS-B", lower=c(0, 0)))
p1 <- profile(fit1)
plot(p1, absVal=FALSE)

## a better parametrization:
ll2 <- function(lymax=log(15), lxhalf=log(6))
    -sum(stats::dpois(y, lambda=exp(lymax)/(1+x/exp(lxhalf)), log=TRUE))
(fit2 <- mle2(ll2))
plot(profile(fit2), absVal=FALSE)
exp(confint(fit2))
vcov(fit2)
cov2cor(vcov(fit2))

mle2(y~dpois(lambda=exp(lymax)/(1+x/exp(lhalf))),
   start=list(lymax=0,lhalf=0),
   parameters=list(lymax~1,lhalf~1))