mvord (version 1.1.1)

mvlinks: Multivariate link functions in mvord

Description

Different link functions are available in mvord:

Usage

mvprobit()
mvlogit(df = 8L)

Arguments

df

integer specifying the degrees of freedom of the t copula

Value

The functions mvlogit() and mvprobit() returns an object of class 'mvlink'. An object of class 'mvlink' is a list containing the following components:

• name

  name of the multivariate link function

• df

  degrees of freedom of the t copula; returned only for mvlogit()

• F_uni

  a function corresponding to the univariate margins of the multivariate distribution $F$ of the subject errors; the function returns $Pr(X\le x)=F_1(x)$

• F_biv

  a function corresponding to the bivariate distribution of the multivariate distribution $F$ of the subject errors $Pr(X\le x,Y\le y|r)=F_2(x,y,r)$;

• F_biv_rect

  the function computes the rectangle probabilities from based on F_biv; the function has the matrices U (upper bounds) and L (lower bounds) as well as vector r containing the correlation coefficients corresponding to the bivariate distribution as arguments; the matrices U and L both have two columns, first corresponding to the bounds of x, second to the bounds of y; the number of rows corresponds to the number of observations; the rectangle probabilities are defined as $Pr(L[,1]\le X\le U[,1],L[,2]\le Y\le U[,2]|r)=F_2(U[,1],U[,2],r)-F_2(U[,1],L[,2],r)-F_2(L[,1],U[,2],r)+F_2(L[,1],L[,2],r)$

• F_multi

  the function computes the multivariate probabilities for distribution function $F$; the function has the matrices U (upper bounds) and L (lower bounds) as well as the list list_R containing for each observation the correlation matrix; F is needed for the computation of the fitted/predicted joint probabilities. If NULL only marginal probabilities can be computed.

• deriv.fun

  (needed for computation of analytic standard errors) a list containing the following gradient functions:

  • dF1dx derivative $d{F}_1(x)/dx$ function,

  • dF2dx derivative $d{F}_2(x,y,r)/dx$ function,

  • dF2dr derivative $d{F}_2(x,y,r)/dr$ function.

  If deriv.fun = NULL numeric standard errors will be computed.

Details

We allow for two different link functions, the multivariate probit link and the multivariate logit link. For the multivariate probit link a multivariate normal distribution for the errors is applied. The normal bivariate probabilities which enter the pairwise log-likelihood are computed with the package pbivnorm.

For the multivariate logit link a $t$ copula based multivariate distribution with logistic margins is used. The mvlogit() function has an optional integer valued argument df which specifies the degrees of freedom to be used for the $t$ copula. The default value of the degrees of freedom parameter is 8. We restrict the degrees of freedom to be integer valued because the most efficient routines for computing bivariate $t$ probabilities do not support non-integer degrees of freedom. For further details see vignette.