ordprobit.univar: Maximum likelihood for ordinal probit model
In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description Usage Arguments Details Value References See Also Examples

Maximum likelihood for ordinal probit: Newton-Raphson minimization of negative log-likelihood, and conversion to uniform/normal scales for fitting copula model in case of repeated measures with fixed cluster size

1 2	ordprobit.univar(x,y,iprint=F,mxiter=20,toler=1.e-6) mord2uu(xmat,yvec,nrep,b0cut,bvec) # multivariate ordinal to (0,1) vector

`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,...,ncateg or 0,1,...(ncateg-1), where ncateg is the number of categories. Missing values are not allowed.
`iprint`	print flag for the iterations for numerical maximum likelihood, default is FALSE
`mxiter`	maximum number of Newton-Raphson iterations
`toler`	tolerance for convergence in Newton-Raphson iterations
`xmat`	vector or matrix of explanatory variables; like above x
`yvec`	similar to above y
`nrep`	number of repeated measures or cluster size for each subject/unit
`b0cut`	vector of cutpoints
`bvec`	vector of regression coefficients

If ordprobit for repeated measures ordinal probit fails to converge from the simple starting point in that function, this function ordprobit.univar should provide a better starting point. It is also equivalent to ordprobit with an identity latent correlation matrix.

The ordinal probit model is similar to the ordinal logit model (proportion odds logistic regression : polr in library MASS), The parameter estimate of ordinal logit are roughly 1.8 to 2 times those of ordinal probit (the signs of the parameters in polr may be different, as this function may be using a different orientation for the latent variable).

For ordprobit.univar(), 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 for value of negative log-likelihood, evaluated at MLE; $cutpts for MLE of ordered cutpoint parameters; $beta for MLE of regression parameters; $cov for estimated covariance matrix of the parameters.

For mord2uu, a list with components $uudat for transform of cdf to U(0,1), $zzdat for transform of cdf to N(0,1).

Anderson JA and Pemberton JD (1985). The grouped continuous model for multivariate ordered categorical variables and covariate adjustment. Biometrics, 41, 875-885.

ordinal

data(ordinalex)
xvec=c(t(ordinalex$xx))
yvec=c(t(ordinalex$yy))
ord.univar=ordprobit.univar(xvec,yvec,iprint=TRUE)
print(ord.univar)
ord.univar2=ordprobit.univar(xvec,yvec-1,iprint=TRUE)
print(ord.univar2) # same as ord.univar
ordtr=mord2uu(xvec,yvec,4,ord.univar$cutpts,ord.univar$beta)
ordtr2=mord2uu(xvec,yvec-1,4,ord.univar$cutpts,ord.univar$beta) #same
max(abs(ordtr$uudat-ordtr2$uudat))