mvlinks: Multivariate link functions in mvord
In mvord: Multivariate Ordinal Regression Models

Description Usage Arguments Details Value

Different link functions are available in mvord:

1
2
3

mvprobit()

mvlogit(df = 8L)

`df`	integer specifying the degrees of freedom of the t copula

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.

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 ≤q x) = F_1(x)
F_biv

a function corresponding to the bivariate distribution of the multivariate distribution F of the subject errors Pr(X ≤q x, Y≤q 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]≤q X≤q U[,1], L[,2]≤q Y ≤q 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 dF_1(x)/dx function,
- dF2dx derivative dF_2(x,y,r)/dx function,
- dF2dr derivative dF_2(x,y,r)/dr function.
If deriv.fun = NULL numeric standard errors will be computed.