iee.ord {weightedScores}

Maximum Likelihood for Ordinal Model

Description

Maximum Likelihood for Ordinal Probit and Logit: Newton-Raphson minimization of negative log-likelihood.

Usage

iee.ord(x,y,link,iprint=0,maxiter=20,toler=1.e-6)

Arguments

x

vector or matrix of explanatory variables. Each row corresponds to an observation and each column to a variable. The number of rows of x should equal the number of data values in y, and there should be fewer columns than rows. Missing values are not allowed.

y

numeric vector containing the ordinal response. The values must be in the range 1,2,..., number of categories. Missing values are not allowed.

link

The link function.Choices are “logit” for the logit link function, and “probit” for the probit link function.

iprint

logical indicator, default is FALSE, for whether the iterations for numerical maximum likelihood should be printed.

maxiter

maximum number of Newton-Raphson iterations, default = 20.

toler

tolerance for convergence in Newton-Raphson iterations, default = 1.e-6.

Details

The ordinal probit model is similar to the ordinal logit model. The parameter estimate of ordinal logit are roughly 1.8 to 2 times those of ordinal probit.

Value

list of MLE of parameters and their associated standard errors, in the order cutpt1,...,cutpt(number of categ-1),b1,...b(number of covariates).

negloglik

value of negative log-likelihood, evaluated at MLE

gam

MLE of ordered cutpoint parameters

reg

MLE of regression parameters

cov

estimated covariance matrix of the parameters

Author(s)

Aristidis K. Nikoloulopoulos [e-mail]
Harry Joe [e-mail]

References

Anderson, J.A. and Pemberton, J.D. (1985). The grouped continuous model for multivariate ordered categorical variables and covariate adjustment. Biometrics, 41, 875–885.

Examples

  ################################################################################
  #                         Ordinal regression 
  ################################################################################
  ################################################################################
  #                      read and set up data set
  ################################################################################
  data(arthritis)
  nn=nrow(arthritis)
  bas2<-bas3<-bas4<-bas5<-rep(0,nn)
  bas2[arthritis$b==2]<-1
  bas3[arthritis$b==3]<-1
  bas4[arthritis$b==4]<-1
  bas5[arthritis$b==5]<-1
  t2<-t3<-rep(0,nn)
  t2[arthritis$ti==3]<-1
  t3[arthritis$ti==5]<-1
  xdat=cbind(t2,t3,arthritis$trt,bas2,bas3,bas4,bas5,arthritis$age) 
  ydat=arthritis$y
  ################################################################################
  #                      select the link
  ################################################################################
  link="probit"
  ################################################################################
  i.est<- iee.ord(xdat,ydat,link)
  print(i.est)