# Maximum Likelihood for Ordinal Model Maximum Likelihood for Ordinal Probit and Logit: Newton-Raphson minimization of negative log-likelihood. ```r 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. ## Returns 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 ## 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. ## 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 ```r ################################################################################ # 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) ``` ## Author(s) Aristidis K. Nikoloulopoulos A.Nikoloulopoulos@uea.ac.uk Harry Joe harry.joe@ubc.ca

iee.ord function