
Fits a bivariate probit model to two binary responses. The correlation parameter rho is the measure of dependency.
binom2.rho(lmu = "probit", lrho = "rhobit", imu1 = NULL, imu2 = NULL,
irho = NULL, imethod = 1, zero = "rho",
exchangeable = FALSE, grho = seq(-0.95, 0.95, by = 0.05),
nsimEIM = NULL)
binom2.Rho(rho = 0, imu1 = NULL, imu2 = NULL,
exchangeable = FALSE, nsimEIM = NULL)
Link function applied to the marginal probabilities. Should be left alone.
Link function applied to the Links
for more choices.
Optional initial values for the two marginal probabilities. May be a vector.
Optional initial value for
Specifies which linear/additive predictors are modelled as intercept-only.
A NULL
means none.
Numerically, the CommonVGAMffArguments
for more information.
Logical.
If TRUE
, the two marginal probabilities are constrained to
be equal.
See CommonVGAMffArguments
for more information.
A value of at least 100 for nsimEIM
is recommended;
the larger the value the better.
Numeric vector.
Values are recycled to the needed length,
and ought to be in range, which is
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
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
Explicitly, the default model is
The default models zero = NULL
in order to model
rho as a function of all the explanatory variables.
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.
Ashford, J. R. and Sowden, R. R. (1970) Multi-variate probit analysis. Biometrics, 26, 535--546.
Freedman, D. A. (2010) Statistical Models and Causal Inference: a Dialogue with the Social Sciences, Cambridge: Cambridge University Press.
Freedman, D. A. and Sekhon, J. S. (2010) Endogeneity in probit response models. Political Analysis, 18, 138--150.
rbinom2.rho
,
rhobit
,
pbinorm
,
binom2.or
,
loglinb2
,
coalminers
,
binomialff
,
rhobit
,
fisherz
.
# NOT RUN {
coalminers <- transform(coalminers, Age = (age - 42) / 5)
fit <- vglm(cbind(nBnW, nBW, BnW, BW) ~ Age,
binom2.rho, data = coalminers, trace = TRUE)
summary(fit)
coef(fit, matrix = TRUE)
# }
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