binom2.rho {VGAM} | R Documentation |
Fits a bivariate probit model to two binary responses.
binom2.rho(lrho = "rhobit", erho=list(), init.rho = 0.4, zero = 3, exchangeable = FALSE)
lrho |
Link function applied to the rho association parameter.
See Links for more choices.
|
erho |
List. Extra argument for the lrho link.
See earg in Links for general information.
|
init.rho |
Initial value for rho.
This should lie between -1 and 1.
|
zero |
Which linear/additive predictor is modelled as an
intercept only? A NULL means none.
|
exchangeable |
Logical.
If TRUE , the two marginal probabilities are constrained to
be equal.
|
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(eta1,eta2;rho) where Phi is the cumulative distribution function of a standard bivariate normal distribution 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.
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
(Y1,Y2) = (0,0), (0,1), (1,0), (1,1), respectively.
The response should be either a 4-column matrix of counts (whose columns correspond to (Y1,Y2) = (0,0), (0,1), (1,0), (1,1) respectively), or a two-column matrix where each column has two distinct values.
By default, a constant rho is fitted because zero=3
.
Set zero=NULL
if you want the rho parameter to
be modelled as a function of the explanatory variables. The value
rho lies in the interval (-1,1), therefore
a rhobit
link is default.
If converge problems occur, try setting init.rho
to some
value, e.g., a negative number such as -0.5.
Thomas W. Yee
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.
binom2.or
,
loglinb2
,
coalminers
,
binomialff
,
rhobit
,
fisherz
.
data(coalminers) coalminers = transform(coalminers, Age = (age - 42) / 5) fit = vglm(cbind(nBnW,nBW,BnW,BW) ~ Age, binom2.rho, coalminers) summary(fit) coef(fit, matrix=TRUE)