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Last data update: 2014.03.03

R: Find maximum likelihood estimate (MLE) of 5 parameters given...

mix.mle

R Documentation

Find maximum likelihood estimate (MLE) of 5 parameters given input vector of observations, initial parameter values, and a method specifying distributions.

Description

Algorithm computes maximum likelihood estimates of the parameters of either the normal mixtuture distribution or the facing gamma distribution model for a dimorphic trait.

Usage

mix.mle(input, method = "normal", mix.prob = NULL, 
    dist1.par1 = NULL, dist1.par2 = NULL, 
    dist2.par1 = NULL, dist2.par2 = NULL, 
    lower = NULL, upper = NULL, distlist = NULL,
    optim.lower = rep(0, 5), optim.upper = c(1, rep(NA, 4)), ...)

Arguments

`input`	Vector of (numeric) trait observations. Observations should be strictly positive.
`method`	Either `"normal"` or `"facing.gamma"`. Initial parameter estimation is implemented for `"normal"`, but is only appropriate when `mix.prob` is close to 0.5. User supplies initial parameter estimates for the facing gamma mixture distribution.
`mix.prob`	The initial probability of mixture distributions, specifying the proportion of the upper distribution.
`dist1.par1`	First parameter of the lower distribution. This specifies the mean for `method="normal"`, and the shape for `method="facing.gamma"`.
`dist1.par2`	Second parameter of the lower distribution. This specifies the standard deviation for `method="normal"`, and the scale for `method="facing.gamma"`.
`dist2.par1`	First parameter of the upper distribution, specifying parameters as in `dist1.par1`.
`dist2.par2`	Second parameter of the upper distribution, specifying parameters as in `dist1.par2`.
`distlist`	Optionally, the user can specify their own list containing a lower and upper distribution (PDF) function. Each density function must take observations and 2 positional parameters, as per `dnorm`. Distributions taking >2 parameters may be used, but the remaining parameters must be encapsulated as fixed values within the functions. If distlist is specified, then `method` is set to `"user"`.
`lower`	For `method="facing.gamma"`, the lower bound may be set to minimum trait size minus 0.5%, 1%, or more of the range of trait sizes. Otherwise ignored.
`upper`	For `method="facing.gamma"`; the upper bound may be set to maximum trait size plus 0.5%, 1%, or more of the range of trait sizes. Otherwise ignored.
`optim.lower, optim.upper`	Numeric vector. lower and upper bounds used by `optim`, specifying: `c(mix.prob, dist1.par1, dist1.par2, dist2.par1, dist2.par2)`. By default, `mix.prob` is bounded between 0 and 1, and distribution parameters are bounded from below by 0. `optim` calls these by position; thus order is significant and names are not needed.
`...`	Additional arguments are passed to optim. In particular, `control=list(trace=5, REPORT=1)` displays information about the optimization process.

Details

Computes maximum likelihood estimates of the parameters of either the normal mixture distribution or the facing gamma distribution model for a dimorphic trait.

Value

An object of class discrimARTs, which is a list containing the original input data and parameter values, as well as output from optim.

`neglogLik`	Numeric. Negative 2 x log likelihood of final optimized parameters.
`MLE.est`	Named vector containing the final optimized parameter values.

Note

In general, method="normal" is converges well for a range of initial values. method="facing.gamma" requires more care.

References

Rowland JM, Qualls CR. 2005. Likelihood models for discriminating alternative phenotypes in morphologically dimorphic species.
Evolutionary Ecology Research 7: 421-434.

Examples

data(x_gideon)

## Assuming normal, estimate initial conditions from data
fit.default.gideon <- mix.mle(x_gideon$horn)

## Estimation of mixture of normals, explicitly specifying method and parameters
fit.gideon <- mix.mle(x_gideon$horn, method='normal', 
    mix.prob=0.5, dist1.par1=100, dist1.par2=10, dist2.par1=300, dist2.par2=10)

## Default printing and plotting methods
print(fit.gideon)

## Compare results
layout(1:2)
plot(fit.gideon)
plot(fit.default.gideon)