An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
When fitted, the fitted.values slot of the object contains the
four joint probabilities, labelled as
$(Y_1,Y_2)$ = (0,0), (0,1), (1,0), (1,1), respectively.
Details
The bivariate probit model was one of the earliest regression
models to handle two binary responses jointly. It has a probit
link for each of the two marginal probabilities, and models the
association between the responses by the $\rho$ parameter
of a standard bivariate normal distribution (with zero means and
unit variances). One can think of the joint probabilities being
$\Phi(\eta_1,\eta_2;\rho)$ where $\Phi$
is the cumulative distribution function of a standard bivariate normal
distribution (i.e., pnorm)
with correlation parameter $\rho$.
The bivariate probit model should not be confused with a bivariate
logit model with a probit link (see binom2.or).
The latter uses the odds ratio to quantify the association. Actually,
the bivariate logit model is recommended over the bivariate probit
model because the odds ratio is a more natural way of measuring the
association between two binary responses.
References
Ashford, J. R. and Sowden, R. R. (1970)
Multi-variate probit analysis.
Biometrics, 26, 535--546.
Documentation accompanying the VGAM package at
http://www.stat.auckland.ac.nz/~yee
contains further information and examples.