GroupFusedMulti: Group Fused Multinomial Logistic Regression

In gfmR: Implements Group Fused Multinomial Regression

Description

This routine fits the group fused multinomial logistic regression model, which uses fusion shrinkage to automatically combine response categories.

Usage

GroupFusedMulti(Y,X,lambda,H,tol1=10^-7,tol2=10^-7,TD=2,rho=10^-8,tau1=10^-9,iter=1e3)

Arguments

Y	A matrix of response category counts where the columns represent the categories and rows represent the observations. Currently supported for n=1.
X	A matrix of predictor variables. The columns represent predictors and rows represent observations.
lambda	tuning parameter for fusion penalty
H	An indicator matrix representing the edge set of the penalty set. The matrix is square and symmetric with dimension number of response categories, and if two categories are in the penalty set a 1 should be in the row column combination.
tol1	Convergence tolerance for ADMM
tol2	Convergence tolerance of ADMM
TD	Step size Adjustment for iterative step size
rho	ADMM step-size parameter, iterative implementation
tau1	The threshold parameter to 0 for final estimates
iter	Maximum number of iterations of the algorithm

Details

Implements the ADMM algorithm for the group fused multinomial regression estimates proposed by Price et. al.

Value

The function returns a list:

Coeff	Final coefficient estimates for the gfmr model
Approx	Final iterates of beta before threshold
Z	Final iterate of Z in the ADMM algorithm
lambda	Tuning Parameter
Converge	Indicator of algorithm convergence
NGroups	Number of groups in final estimates
Groups	The response category groups in the final estimates

Author(s)

Brad Price, [e-mail].

References

Price, B.S, Geyer, C.J. and Rothman, A.J. "Automatic Response Category Combination in Multinomial Logistic Regression." https://arxiv.org/abs/1705.03594.

Examples

## Not run: data(nes96)
attach(nes96)
Response=matrix(0,944,7)
for(i in 1:944){
  if(PID[i]=="strRep"){Response[i,1]=1}
  if(PID[i]=="weakRep"){Response[i,2]=1}
  if(PID[i]=="indRep"){Response[i,3]=1}
  if(PID[i]=="indind"){Response[i,4]=1}
  if(PID[i]=="indDem"){Response[i,5]=1}
  if(PID[i]=="weakDem"){Response[i,6]=1}
  if(PID[i]=="strDem"){Response[i,7]=1}
}

Hmat=matrix(1,dim(Response)[2],dim(Response)[2])
diag(Hmat)=0
ModMat<-lm(popul~age,x=TRUE)$x

X=cbind(ModMat[,1],apply(ModMat[,-1],2,scale))
mod<-GroupFusedMulti(Response,X,lambda=2^4.3,H=Hmat2,rho=10^2,iter=50,tol1=10^-4,tol2=10^-4)
predict(mod,X[1,])

## End(Not run)

gfmR documentation built on May 1, 2019, 8:41 p.m.