mle2: Maximum Likelihood Estimation

In bbolker/bbmle: Tools for General Maximum Likelihood Estimation

Maximum Likelihood Estimation

Description

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,
namedrop_args=TRUE,
...)
calc_mle2_function(formula,parameters, links, start,
   parnames, use.deriv=FALSE, data=NULL,trace=FALSE)

Arguments

minuslogl	Function to calculate negative log-likelihood, or a formula
start	Named list. Initial values for optimizer
method	Optimization method to use. See optim.
optimizer	Optimization function to use. Currently available choices are "optim" (the default), "nlm", "nlminb", "constrOptim", "optimx", and "optimize". If "optimx" is used, (1) the optimx package must be explicitly loaded with load or require(Warning: Options other than the default may be poorly tested, use with caution.)
fixed	Named list. Parameter values to keep fixed during optimization.
data	list of data to pass to negative log-likelihood function: must be specified if minuslogl is specified as a formula
subset	logical vector for subsetting data (STUB)
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.) If vecpar is TRUE, then you should use parnames to define the parameter names for the negative log-likelihood function.
parameters	List of linear models for parameters. MUST BE SPECIFIED IN THE SAME ORDER as the start vector (this is a bug/restriction that I hope to fix soon, but in the meantime beware)
links	(unimplemented) specify transformations of parameters
parnames	List (or vector?) of parameter names
gr	gradient function
...	Further arguments to pass to optimizer
formula	a formula for the likelihood (see Details)
trace	Logical: print parameter values tested?
browse_obj	Logical: drop into browser() within the objective function?
skip.hessian	Bypass Hessian calculation?
hessian.opts	Options for Hessian calculation, passed through to the hessian function
use.ginv	Use generalized inverse (ginv) to compute approximate variance-covariance
optimfun	user-supplied optimization function. Must take exactly the same arguments and return exactly the same structure as optim.
use.deriv	(experimental, not yet implemented): construct symbolic derivatives based on formula?
namedrop_args	hack: drop names in sub-lists occurring in data?

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.

Value

An object of class "mle2".

Warning

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

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).

See Also

mle2-class

Examples

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))

## End(Not run)

bbolker/bbmle documentation built on Dec. 12, 2023, 9:07 a.m.