SMCEM_onestep {CondMVT}

Data Imputation Using SEM and MCEM (Single Iteration, Degrees of Freedom Known)

Description

This sub-package contains the subroutines for iterative imputation of missing values as well as parameter estimation (for the location vector and the scatter matrix) in multivariate t distribution using Stochastic EM (SEM) and Monte Carlo EM (MCEM). In this case, the degrees of freedom for the distribution are known or fixed a priori. SEM is implemented when the analyst specifies a single draw in the E-step. In case we have multiple draws in the E-step, the algorithm changes to MCEM. In both algorithms, the function SMCEM_onestep is run when we are only interested in the imputed values and the parameter updates in a single iteration.

Usage

SMCEM_onestep(Y,mu,Sigma,df,nob)

Arguments

Y

the multivariate t dataset

mu

the location vector, which must be specified. In cases where it is unknown, starting values are provided.

Sigma

scatter matrix, which must be specified. In cases where it is unknown, starting values are provided.

df

degrees of freedom, which must be specified.

nob

number of draws in the E-step

Value

Completed dataset, updated location vector, and scatter matrix when employing the SEM and MCEM algorithms. All outputs are numeric.

Examples

# 3-dimensional multivariate t distribution
n <- 10
p=3
df=3
mu=c(1:3)
A <- matrix(rt(p^2,df), p, p)
A <- tcrossprod(A,A) #A %*% t(A)

Y7 <-mvtnorm::rmvt(n, delta=mu, sigma=A, df=df)
Y7
TT=Y7 #Complete Dataset

#Introduce MAR Data
Y8= MISS(TT,20) #The newly created incomplete dataset.

#Initializing Values
mu_stat=c(0.5,1,2)
Sigma_stat=matrix(c(0.33,0.31,0.3,0.31,0.335,0.295,0.3,0.295,0.32),3,3)

#Imputing Missing Values and Updating Parameter Estimates
#Single Iteration (SEM)
SEM1=SMCEM_onestep(Y=Y8,mu= mu_stat,Sigma=A,df=df,nob=1)

#Single Iteration (MCEM)
MCEM1=SMCEM_onestep(Y=Y8,mu= mu_stat,Sigma=A,df=df,nob=100)

#Results for Newly Completed Dataset (SEM)
SEM1$Y2    #Newly completed Dataset (with imputed values)
SEM1$mu	   #updated location vector
SEM1$Sigma #updated scatter matrix

#Results for Newly Completed Dataset (MCEM)
MCEM1$Y2    #Newly completed Dataset (with imputed values)
MCEM1$mu	   #updated location vector
MCEM1$Sigma #updated scatter matrix