mlMixModel: Fits a mixture model using the maximum likelihood principle.

Description

This method calculates the maximum likelihood estimations of a mixture model using the expectation-maximization (EM) algorithm. The mixture model may consists of normal components (with a fixed expectation of 0) and exponential components, which may be mirrored in order to model negative values.

Usage

mlMixModel(z, normNull = c(), expNeg = c(), expPos = c(), sdNormNullInit = c(), rateExpNegInit = c(), rateExpPosInit = c(), piInit = c(), maxIter = 500, tol = 0.001)

Arguments

Observed values.

normNull

Indices of the normal components (that have $mu=0$).

expNeg

Indices of the mirrored exponential components.

expPos

Indices of the exponential components.

sdNormNullInit

Initial standard deviations of the normal components.

rateExpNegInit

Initial rates ("lambda") of the exponential components.

rateExpPosInit

Initial rates ("lambda") of the exponential components.

piInit

Initial weights of the components.

maxIter

Maximum number of iterations.

tol

Threshold for convergence. The minimum log likelihood gain between two iterations that must be achieved to continue.

Value

An object of MixModelML-class storing results, data, initial values and information about the convergence.

Details

The EM algorithm is known to converge slowly in some cases and local maxima may avoid finding the optimal solution. Users should try different initial values and different convergence criteria.

The components' indices do not influence the result, but may influence the order in which components are listed or ploted by downstream methods. Indices must be successive integers from 1 to n.

Examples

Run this code

z <- c(rnorm(1000, 0, 0.5), rnorm(1000, 0, 1))
mm <- mlMixModel(z, normNull=1:2, sdNormNullInit=c(0.1, 0.2),
   pi=c(1/2, 1/2), maxIter=500, tol=0.001)
mm

z <- c(rnorm(1000, 0, 3), rnorm(1000, 0, 5), rexp(1000, 5), -rexp(1000, 5))
mm <- mlMixModel(z, normNull=1:2, expNeg=3, expPos=4,
   sdNormNullInit=c(1, 2), rateExpNegInit=8, rateExpPosInit=8,
   pi=c(1/4, 1/4, 1/4, 1/4), maxIter=500, tol=0.001)
mm