mle2

Maximum Likelihood Estimation

Estimate parameters by the method of maximum likelihood.

Usage

mle2(minuslogl, start, method, optimizer,
    fixed = NULL, data=NULL,
    subset=NULL,
default.start=TRUE, eval.only = FALSE, vecpar=FALSE,
parameters=NULL,
parnames=NULL,
skip.hessian=FALSE,
hessian.opts=NULL,
use.ginv=TRUE,
trace=FALSE,
browse_obj=FALSE,
gr=NULL,
optimfun,…)
calc_mle2_function(formula,parameters, links, start,
   parnames, use.deriv=FALSE, data=NULL,trace=FALSE)

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 be given:

• as a list containing lists, with each list corresponding to the starting values for a particular parameter;

• just for the higher-level parameters, in which case all of the additional parameters generated by model.matrix will be given starting values of zero (unless a no-intercept formula with -1 is specified, in which case all the starting values for that parameter will be set equal)

• (to be implemented!) as an exhaustive (flat) list of starting values (in the order given by model.matrix)

The trace argument applies only when a formula is specified. If you specify a function, you can build in your own print() or cat() statement to trace its progress. (You can also specify a value for trace as part of a control list for optim(): see optim.)

The skip.hessian argument is useful if the function is crashing with a "non-finite finite difference value" error when trying to evaluate the Hessian, but will preclude many subsequent confidence interval calculations. (You will know the Hessian is failing if you use method="Nelder-Mead" and still get a finite-difference error.)

If convergence fails, see the manual page of the relevant optimizer (optim by default, but possibly nlm, nlminb, optimx, or constrOptim if you have set the value of optimizer) for the meanings of the error codes/messages.

Note

Note that the minuslogl function should return the negative log-likelihood, -log L (not the log-likelihood, log L, nor the deviance, -2 log L). It is the user's responsibility to ensure that the likelihood is correct, and that asymptotic likelihood inference is valid (e.g. that there are "enough" data and that the estimated parameter values do not lie on the boundary of the feasible parameter space).

If lower, upper, control$parscale, or control$ndeps are specified for optim fits, they must be named vectors.

The requirement that data be specified when using the formula interface is relatively new: it saves many headaches on the programming side when evaluating the likelihood function later on (e.g. for profiling or constructing predictions). Since data.frame uses the names of its arguments as column names by default, it is probably the easiest way to package objects that are lying around in the global workspace for use in mle2 (provided they are all of the same length).

When optimizer is set to "optimx" and multiple optimization methods are used (i.e. the methods argument has more than one element, or all.methods=TRUE is set in the control options), the best (minimum negative log-likelihood) solution will be saved, regardless of reported convergence status (and future operations such as profiling on the fit will only use the method that found the best result).

Warning

Do not use a higher-level variable named .i in parameters -- this is reserved for internal use.

See Also

mle2-class

Aliases

• mle2
• mle
• calc_mle2_function

Examples

# NOT RUN {
x <- 0:10
y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
d <- data.frame(x,y)

## in general it is best practice to use the `data' argument,
##  but variables can also be drawn from the global environment
LL <- function(ymax=15, xhalf=6)
    -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE))
## uses default parameters of LL
(fit <- mle2(LL))
fit1F <- mle2(LL, fixed=list(xhalf=6))
coef(fit1F)
coef(fit1F,exclude.fixed=TRUE)

(fit0 <- mle2(y~dpois(lambda=ymean),start=list(ymean=mean(y)),data=d))
anova(fit0,fit)
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; note lower must be named
(fit1 <- mle2(LL, method="L-BFGS-B", lower=c(ymax=0, xhalf=0)))
p1 <- profile(fit1)

plot(p1, absVal=FALSE)
## a better parameterization:
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),
   data=d,
   parameters=list(lymax~1,lhalf~1))

# }
# NOT RUN {
## try bounded optimization with nlminb and constrOptim
(fit1B <- mle2(LL, optimizer="nlminb", lower=c(lymax=1e-7, lhalf=1e-7)))
p1B <- profile(fit1B)
confint(p1B)
(fit1C <- mle2(LL, optimizer="constrOptim", ui = c(lymax=1,lhalf=1), ci=2,
   method="Nelder-Mead"))

set.seed(1001)
lymax <- c(0,2)
lhalf <- 0
x <- sort(runif(200))
g <- factor(sample(c("a","b"),200,replace=TRUE))
y <- rnbinom(200,mu=exp(lymax[g])/(1+x/exp(lhalf)),size=2)
d2 <- data.frame(x,g,y)

fit3 <- mle2(y~dnbinom(mu=exp(lymax)/(1+x/exp(lhalf)),size=exp(logk)),
    parameters=list(lymax~g),data=d2,
    start=list(lymax=0,lhalf=0,logk=0))
# }