mylogLikePoisMix {poisson.glm.mix}

Function to compute the loglikelihood of the mixture.

Description

This function computes the observed loglikelihood given the means and the mixing proportions of each component. Instead of computing L_{i}=\log\sum_{k=1}^{K}g_{ik}, i=1,\ldots,n, where g_{ik}:=\pi_{k}\prod_{j=1}^{J}\prod_{\ell=1}^{L_j}f(y_{ij\ell}|\mu_{ijlk;m}), h_{ik}:=\log g_{ik} are computed for all i . Let h_{i}^{*}=\max\{h_{ik},k=1,\ldots,K\}, then L_{i}=h_{i}^{*}+\log\sum_{k=1}^{K}\exp(h_{ik}-h^{*}_{i}).

Usage

mylogLikePoisMix(y, mean, pi)

Arguments

y

a numeric array of count data with dimension n\times d.

mean

a list of length K (the number of mixture components) of positive data. Each list element is a matrix with dimension n\times d containing d Poisson means for each of the n observations.

pi

a numeric vector of length K (the number of mixture components) containing the mixture weights.

Value

ll

the value of the loglikelihood.

Author(s)

Panagiotis Papastamoulis

Examples

## This example computes the loglikelihood of a K = 10 component 
##      Poisson GLM mixture. The number of response variables is
##      d = 6, while the sample size equals to n = 5000. They are
##      stored in the array sim.data[,-1]. The number of covariates
##      equals 1 (corresponding to sim.data[,1]). We will use a 
##      random generation of the regression coefficients alpha and 
##      beta, in order to show that the loglikelihood can be computed 
##      without computational errors even in cases where the parameters
##      are quite ''bad'' for the data.   

data("simulated_data_15_components_bjk_full")
K <- 10
d <- 6
n <- dim(sim.data)[1]
condmean=vector("list",length=K)
weights<-rep(1,K)/K
ar<-array(data=NA,dim=c(n,d))
for (k in 1:K){
for (i in 1:d){
ar[,i]<-runif(n)+(1+0.1*(runif(n)-1))*sim.data[,1]}
condmean[[k]]<-ar}
mylogLikePoisMix(sim.data[,-1],condmean,weights)