mylogLikePoisMix: Function to compute the loglikelihood of the mixture.

In poisson.glm.mix: Fit High Dimensional Mixtures of Poisson GLMs

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)

poisson.glm.mix documentation built on Aug. 19, 2023, 9:06 a.m.