# mle

0th

Percentile

##### Maximum Likelihood Estimation

Estimate parameters by the method of maximum likelihood.

Keywords
models
##### 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.

mle-class

• mle
##### Examples
library(stats4) # 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) # } 
Documentation reproduced from package stats4, version 3.6.2, License: Part of R 3.6.2

### Community examples

godcent70@gmail.com at Feb 17, 2019 stats4 v3.5.2

I don't understand why the example that accompanied this function continues to proliferate even though the NLL function gives the impression that it solves the Poisson prolem for the x and y data wheen it does not. 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)) The proper function was given at this link http://r.789695.n4.nabble.com/Maximum-Likelihood-Estimation-Poisson-distribution-mle-stats4-td4635464.html and reproduced below for the convience of the reader. > x <- 0:10 > nLL <- function(lambda) -sum(y*stats::dpois(x, lambda, log=TRUE)) > mle(nLL, start = list(lambda = 5), nobs = NROW(y)) Call: mle(minuslogl = nLL, start = list(lambda = 5), nobs = NROW(y))