CAMAN (version 0.78)

mixalg.VEM: VEM algorithm

Description

When fitting finite mixture models two cases must be distinguished. The flexible support size case, where no assumption about the number of components k is made in advance and the fixed support size case. For the flexible support size case the VEM-algorithm can be used.

The algorithm proceeds as follows:
Step 1: Define an approximating grid lambda[1], ..., lambda[L]
Step 2: Use the VEM algorithm to maximize L(P) in the simplex \(\Omega\) and identify grid points with positive support.

Usage

mixalg.VEM(mix = NULL, obs=NULL, weights=NULL, data=NULL, pop.at.risk=NULL, 
           var.lnOR=NULL, family="gaussian", limit=0.01, acc=10^(-7), 
           numiter=5000, startk=50)

Value

The function returns a CAMAN.VEM.object object.

Arguments

mix

A CAMAN-object which quantifies a finite mixture model and the input data.

obs

observed / dependent variable. Vector or colname of data. Must be specified!

weights

weights of the data. Vector or colname of data. Default is NULL.

family

the underlying type density function as a character ("gaussian", "poisson" or "binomial")!

data

an optional data frame. obs, weights, pop.at.risk and var.lnOR can be specified as column name of the data frame.

pop.at.risk

population at risk: These data could be used to determine a mixture model for Poisson data. Vector or colname of data. Default isNULL.

var.lnOR

variances of the data: These variances might be given when working with meta analyses! Vector or colname of data. Default is NULL.

limit

parameter to control the limit of union several components. Default is 0.01.

acc

convergence criterion. VEM and EM loops stop when deltaLL<acc. Default is 10^(-7).

numiter

parameter to control the maximal number of iterations in the VEM and EM loops. Default is 5000.

startk

starting/maximal number of components. This number will be used to compute the grid in the VEM. Default is 50.

Author

Peter Schlattmann and Johannes Hoehne

Examples

data(vitA)
m0<-mixalg.VEM(obs="logrr",var.lnOR="var",family="gaussian", data=vitA,startk=20)
plot(m0@totalgrid[,2],m0@totalgrid[,3],type="l",xlab="parameter",ylab="gradient")
m1<-mixalg.EM(obs="logrr",var.lnOR="var" ,family="gaussian",p=c(1),t=c(0),data=vitA)