rrmultinom {RRMLRfMC}

rrmultinom

Description

This function is used to fit the reduced rank multinomial logistic regression for markov chain

Usage

rrmultinom(I, z1 = NULL, z2 = NULL, T, R, eps = 1e-05, ref = NULL)

Arguments

I

a U by U incidence matrix with elements; U is number of states; I(i,j)=1 if state j can be accessed from state i in one step and 0 otherwise

z1

a n by p matrix with covariates involved in the dimension reduction(DR), n is the number of subjects, p is the number of covariates involved in DR

z2

a n by q matrix with study covariates (not in dimension reduction), q is the number of study covariates

T

a M by 3 state matrix,

• the first column is a subject number between 1,..,n;

• the second column is time;

• the third column is the state occupied by subject in column 1 at time indicated in column 2

R

the rank

eps

the tolerance for convergence; the default is 10^-5

ref

a vector of reference categories; the default is NULL and if NULL is used, the function will use the first category as the reference category for each row

Value

a list of outputs:

• Alpha: the final A matrix

• Gamma: the final G matrix

• Beta: the coefficient matrix for variables involved in reduced rank

• Dcoe: the coefficient matrix for the fixed variables

• Dsderr: the standard error matrix for the fixed variables

• Dpval: the p-value matrix for the fixed variables

• coemat: the overall coefficient matrix

• niter: the iteration number to get converged

• df: the degrees of freedom

• loglik: the final loglikelihood

• converge: three possible values with 0 means fail to converge, 1 means converges, and 2 means the maximum iteration is achieved

Examples

# generate the Markov chain
U=7
I1=I2=I3=rep(1,7)
I4=c(0,0,0,1,1,1,1)
I5=I6=I7=rep(0,7)
I=rbind(I1,I2,I3,I4,I5,I6,I7)
# prepare the data
data=cogdat
n=length(unique(data[,1]))
M=nrow(data)+n
Mc=0
z=matrix(0,n,9)
colnames(z)=colnames(data)[5:13]
T=matrix(0,M,3)
for(i in 1:n){
 subdat=data[which(data[,1]==i),,drop=FALSE]
 z[i,]=subdat[1,5:13]
 mc=nrow(subdat)
 T[(Mc+1):(Mc+mc+1),1]=i
 T[(Mc+1):(Mc+mc+1),2]=0:mc
 T[(Mc+1):(Mc+mc+1),3]=c(subdat[1,3],subdat[,4])
 Mc=Mc+mc+1
}
#z1=z[,c(1:3),drop=FALSE]
z2=z[,4,drop=FALSE]
# fit the model with rank 1
rrmultinom(I,z1=NULL,z2,T,1,eps=9,ref=c(1,1,1,4))