sads (version 0.2.2)

plotprofmle-methods: Plot of log-likelihood profiles at original scale

Description

Given a likelihood profile of a model (object of the class profile.mle or profile.mle2), plots the relative log-likelihood profiles and the plausibility intervals for each one of the (or selected ones) parameters of a model.

Usage

plotprofmle(object, nseg=20, ratio=log(8), which=NULL, ask=NULL, 
    col.line="blue", varname=NULL, ...)

Arguments

object

list of profile data; object of class mle2 or profile.mle2.

nseg

positive integer; number of segments used by spline to interpolate the line of log-likelihood profile

ratio

real positive or NULL; log-likelihood ratio that defines the likelihood interval to be shown in the plot.

which

vector of positive integers; if a subset of profiles is required, the indexes of the mle's in profobj to be plotted.

ask

logical; if TRUE, the user is _ask_ed before each plot, see par(ask=.)

col.line

name; line color for the plausibility interval.

varname

vector of names; labels for the x-axis. If NULL defaults the names of mle's in profobj.

...

further arguments to be passed to plot.

encoding

UTF-8

Details

Log-likelihood profile plots are the basic diagnostic for model fitting by maximum likelihood methods. The profiles show the minimum of the log-likelihood function for a given value of a focal parameter, near the maximum likelihood estimate (mle) of this parameter. Profile objects in R (classes profile.mle and profile.mle2) return transformed values of the likelihood function, which are based on the deviance (=minus twice log-likelihood). These values are called 'z' and are the signed square-root of the deviance difference from the minimum deviance. As samples get larger, z-profiles tends to be symmetrical V-shaped, and are used to calculate confidence intervals using an approximation to the Chi-square distribution (see details in Bolker (2008) and in the bbmle vignette (vignette('mle2',package='bbmle')).

In its original form (e.g. Edwards 1972), likelihood profiles do not use z-transformed values, and can be interpreted directly, even if they are asymmetric. At the scale of the log-likelihood function, all values of the parameters resulting in a negative log-likelihood less or equal to a given value k are exp(k) times as plausible as the mle. Hence, exp(k) is a likelihood ratio, and delimits a plausibility interval (or likelihood interval) for the mle's. Function plotprofmle plots profiles of the negative log-likelihood functions, along with the limits of likelihood interval for a given log-likelihood ratio.

References

Bolker, B. 2008. Ecological Models and Data in R. Princeton: Princeton University Press. Edwards, A.W.F. 1972. Likelihood -- An Account of the Statistical Concept of Likelihood and its Application to Scientific Inference. New York: Cambridge University Press. Royall, R.M. 2000. Statistical Evidence: A Likelihood Paradigm. London: Chapman and Hall.

See Also

profile.mle.class, mle, mle-class from stats; profile.mle2.class, mle2, mle2-class from bbmle package.

Examples

birds.pln <- fitsad(birds, "lnorm")
birds.pln.p <- profile(birds.pln)
par(mfrow=c(1,2))
plotprofmle(birds.pln.p)
par(mfrow=c(1,1))