EMalgorithm {EMSNM}

Parameter Estimation

Description

Estimate paramters value by EM algorithm under the assumption of Sigmoid-Normal Model.

Usage

EMalgorithm(X, Y, Z, etat, alphat, sigmat, classsize = 2, learning_rate = 0.1, 
            regular_parameter_eta = 0.001, max_iteration = 10000,
            max_iteration_eta = 10000, compact_flag = FALSE, C0 = 5, C1 = 2, C2 = 9)

Arguments

X

the covariables of the mean of each subgroup

Y

the respond variable

Z

the covaraibles determining subgroup

etat

the coeffients determining subgroup

alphat

the coeffients of the mean of each subgroup

sigmat

the variance of Y

classsize

the number of subgroup types in your model assumption

learning_rate

learning rate of updating eta

regular_parameter_eta

regular value of updating eta by gradiant descending methond.

max_iteration

maximum steps of interation to avoid unlimited looping.

max_iteration_eta

maximal steps of eta interation to avoid unlimited looping.

compact_flag

if the value of eta is limited in a compact set, set it TRUE

C0

the maximum of intercept of eta.

C1

the minimum of the norm of slope of eta

C2

the maximum of the norm of slope of eta

Value

alpha

alpha estimation

eta

eta estimation

sigma

sigma estimation

Author(s)

Linsui Deng

Examples

#data generation
samplesize <- 1000
classsize <- 2
etasize <- 3
alphasize <- 3

set.seed(1)
Xtest <- data.frame(matrix(rnorm(samplesize*etasize),samplesize,etasize))
etatest <- matrix(c(1,2,-1,
                    0,0,0),etasize,classsize)

Ztest <- matrix(rnorm(samplesize*alphasize),samplesize,alphasize)
alphatest <- matrix(c(1,0,2,
                      5,0,7),alphasize,classsize)
sigmatest <- 5

Wtest <- Wgenerate(alpha=alphatest,eta=etatest,X=Xtest,Z=Ztest,sigma=sigmatest)

eta_initial <- matrix(c(rnorm(3),0,0,0),etasize,classsize)
alpha_initial<- matrix(rnorm(alphasize*classsize)*3,alphasize,classsize)
sigma_initial <- 1

EMtheta <- EMalgorithm(X=Wtest$X,Z=Wtest$Z,Y=Wtest$Y,classsize=2,
                       etat=eta_initial,alphat=alpha_initial,sigmat=sigma_initial,
                       learning_rate=0.01,regular_parameter_eta=0.001,
                       max_iteration=1000,max_iteration_eta=10000, 
                       compact_flag = TRUE, C0 = 5, C1 = 2, C2 = 9)