Type: Package
Title: Reduced-Rank Multinomial Logistic Regression for Markov Chains
Version: 0.4.0
Description: Fit the reduced-rank multinomial logistic regression model for Markov chains developed by Wang, Abner, Fardo, Schmitt, Jicha, Eldik and Kryscio (2021)<doi:10.1002/sim.8923> in R. It combines the ideas of multinomial logistic regression in Markov chains and reduced-rank. It is very useful in a study where multi-states model is assumed and each transition among the states is controlled by a series of covariates. The key advantage is to reduce the number of parameters to be estimated. The final coefficients for all the covariates and the p-values for the interested covariates will be reported. The p-values for the whole coefficient matrix can be calculated by two bootstrap methods.
License: GPL-2
Encoding: UTF-8
LazyData: true
Imports: nnet
Depends: R (≥ 3.5.0)
RoxygenNote: 7.1.1
Suggests: rmarkdown, knitr
NeedsCompilation: no
Packaged: 2021-06-04 19:05:32 UTC; pwa24
Author: Pei Wang [aut, cre], Richard Kryscio [aut]
Maintainer: Pei Wang <wangp33@miamioh.edu>
Repository: CRAN
Date/Publication: 2021-06-07 07:20:07 UTC

Aupdate

Description

This function is used to update A matrix

Usage

Aupdate(Dfix, Gamma, Adata, R, p, q, I, iniA, eps, refA)

Arguments

Dfix

the coefficient matrix for study covariates

Gamma

the G matrix value

Adata

the dataset

R

the rank of reduced rank model

p

the number of covariates in the dimension reduction

q

the numbne of study covariates

I

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

iniA

initial value for the iteration

eps

the tolerance for convergence, default is 10^-5

refA

a vector of reference categories

Value

a list of outputs:

Gupdate

Description

This function is used to update G matrix

Usage

Gupdate(A, Gdata, p, q, I, refG)

Arguments

A

numeric matrix

Gdata

the dataset used to update G

p

the number of covariates in the dimension reduction

q

the numbne of study covariates

I

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

refG

a vector of reference categories

Value

a list of outputs:

Cognitive Dataset

Description

A dataset containing the states and covariates of 649 participants enrolled in the BRAiNS cohort at the University of Kentucky's Alzheimer's Disease Research Center.

Usage

cogdat

Format

A data frame with 6240 rows and 14 columns:

ID

used to denote the participants; from 1 to 649

visitno

used to denote the visit number for each participant

prstate

denote the previous state

custate

denote the current state

bagec

baseline age (centered at age 72)

famhx

family history of dementia

HBP

self reported high blood pressure

apoe4

at least one Apolipoprotein-E (APOE) gene \epsilon4 allele

smk1

cigarette smoking level (none versus < 10)

smk2

cigarette smoking level (11-19)

smk2

cigarette smoking level (>= 20 pack years))

lowed

low education

headinj

self reported head injury

derivativeB

Description

This function is used to calculate the loglikelihood with a given matrix B=AG

Usage

derivativeB(B, I, zy, refd)

Arguments

B

a numeric coefficient matrix

I

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

zy

the variable values for a given observation

refd

a vector of reference categories

Value

loglikelihood

derivatives

Description

This function is used calculate the derivative values (first and second derivatives for Newton-Raphson method) and loglikelihood when updating A

Usage

derivatives(A, Gamma, Dmat, I, zy, refA)

Arguments

A

matrix with value from previous iteration

Gamma

G matrix values

Dmat

the coefficient matrix for the fixed variables,

I

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

zy

the variable values for a given observation

refA

a vector of reference categories

Value

a list of outputs:

expand

Description

This function is used to expand the Y(category) to a indicator vector

Usage

expand(pri, curr, I, refE)

Arguments

pri

the prior state

curr

the current state

I

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

refE

a vector with the reference categories

Value

ry: a indicator vector

norm

Description

This function is used to normalize a vector to have unit length

Usage

norm(x)

Arguments

x

a numeric vector

Value

a normalized vector with length 1

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:

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))

sdfun

Description

This function is used get the standard error matrix from bootstrap method It returns the matrices of standard error and p-value for the coefficient matrix

Usage

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

Arguments

I

a U by U incidence matrix with elements; U is the 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

B

the bootstrap number

tpoint

a matrix has two columns with the participants' visit information about timeline

ref

a vector of reference categories

Value

a list of outputs:

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]
# find the standard deviation matrix for the model with rank 1
sdfun(I,z1=NULL,z2,T,1,eps = 9,2,ref=c(1,1,1,4))