plotprofmle-methods {sads}

Log-likelihood profiles at original scale

Description

Given a likelihood profile of a model (object of the class profile.mle or profile.mle2), the function plotprofmle plots the relative log-likelihood profiles and the plausibility intervals for each one of the (or selected ones) parameters of a model. These same plausibility regions might be returned by likelregions.

Usage

plotprofmle(object, nseg=20, ratio=log(8), which=NULL, ask=NULL, 
    col.line="blue", varname=NULL, ...)
likelregions(object, nseg=100, ratio=log(8), ...)

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; log-likelihood ratio that defines the likelihood interval to be shown in the plot by plotprofmle or returned by likelregions. Set to NULL to suppress intervals from being displayed.

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.

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.

Function likelregions returns the limits of the likelihood intervals for each parameter. This might be seen as an analog function for confint, and will return very similar values for corresponding ratios if the profile is symmetric and monotonic. However, if the profile is ill-behaved, likelregions might return more than one interval for each parameter, whereas confint will return NA with a warning.

Methods

plotprofmle

signature(object="profile.mle2"):The preferred invocation for these methods.

plotprofmle

signature(object="mle2"):A convenience wrapper that calls profile on the mle2 object and runs the former method.

likelregions

signature(object="profile.mle2"):The preferred invocation for these methods.

likelregions

signature(object="mle2"):A convenience wrapper that calls profile on the mle2 object and runs the former method.

Author(s)

João L.F. Batista, Andre Chalom, Paulo I. Prado [e-mail]

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))
likelregions(birds.pln.p)
# Compare with the confidence intervals
confint(birds.pln.p)