gmmsslm (version 1.1.5)

erate: Error rate of the Bayes rule for a g-class Gaussian mixture model

Description

Error rate of the Bayes rule for a g-class Gaussian mixture model

Usage

erate(dat, p, g, pi = NULL, mu = NULL, sigma = NULL, paralist = NULL, clust)

Value

errval

a value of error rate

Arguments

dat

An \(n\times p\) matrix where each row represents an individual observation

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A \(p \times g\) matrix for the initial values of the location parameters.

sigma

A \(p\times p\) covariance matrix,or a list of g covariance matrices with dimension \(p\times p \times g\). It is assumed to fit the model with a common covariance matrix if sigma is a \(p\times p\) covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

paralist

A list containing the required parameters \((\pi, \mu, \Sigma)\).

clust

An n-dimensional vector of class partition.

Details

The error rate of the Bayes rule for a g-class Gaussian mixture model is given by $$ err(y;\theta)=1-\sum_{i=1}^g\pi_i Pr\{R(y;\theta)=i\mid Z \in C_i\}. $$ Here, we write $$ Pr\{R(y;\theta) \in C_i\mid Z\in C_i\}=\frac{\sum_{j=1}^nI_{C_i}(z_j)Q[z_j,R(y;\theta) ]}{\sum_{j=1}^nI_{C_i}(z_j)}, $$ where \(Q[u,v]=1\) if \(u=v\) and \(Q[u,v]=0\) otherwise, and \(I_{C_i}(z_j)\) is an indicator function for the \(i\)th class.

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
xi<-c(-0.5,1)
m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi)
zm<-dat$clust
zm[m==1]<-NA
inits<-initialvalue(g=4,zm=zm,dat=dat$Y)
# \donttest{
fit_pc<-gmmsslm(dat=dat$Y,zm=zm,pi=inits$pi,mu=inits$mu,sigma=inits$sigma,xi=xi,type='full')
parlist<-paraextract(fit_pc)
erate(dat=dat$Y,p=3,g=4,paralist=parlist,clust=dat$clust)
# }