R: Log-likelihood profiles at original scale

plotprofmle-methods {sads} | R Documentation

## 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

codesignature(object="profile.mle2")

  The preferred invocation for these methods.

codesignature(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 prado@ib.usp.br

### 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)

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