a "formula":
a symbolic description of the model
(currently, all binary outcome variables must have the same regressors).
data
a data.frame containing the data.
start
an optional numeric vector specifying the starting values
for the model coefficients;
if argument startSigma is not specified,
this vector can also include the correlation coefficients;
the order of elements is explained in the section “details”;
if this argument is not specified,
coefficients estimated by univariate probit models
are used as starting values for the model coefficients.
startSigma
optional starting values for the covariance/correlation matrix
of the residuals (must be symmetric and have ones on its diagonal);
if this argument is not specified
and the starting values for the correlation coefficients
are not included in argument start,
the correlation matrix of the ‘response’ residuals,
i.e. y - pnorm( X' beta ),
is used as starting values for sigma.
method
maximisation method / algorithm
(see maxLik).
finalHessian
Calculation of the final Hessian:
either FALSE (no calculation of Hessian),
TRUE (finite-distance calculation of Hessian), or
"BHHH" (calculation based on information equality approach
and finite-distance gradients, the default).
algorithm
algorithm for computing integrals
of the multivariate normal distribution,
either function GenzBretz(), Miwa(), or TVPACK()
(see documentation of pmvnorm)
or character string "GHK"
(see documentation of ghkvec).
nGHK
numeric value specifying the number of simulation draws
of the GHK algorithm for computing integrals
of the multivariate normal distribution.
intGrad
logical. If TRUE,
the computation of the gradients
with respect to the estimated parameters
is done internally in function mvProbitLogLik
when it computes the log-likelihood values.
If the optimization method requires gradients
and this argument is FALSE,
maxLik computes the gradients
by numericGradient,
which is usually slower
than the calculation in function mvProbitLogLik.
This argument should be set to FALSE
if an optimisation algorithm is used that is not based on gradients.
oneSidedGrad
logical. If this argument
and argument intGrad are both TRUE,
the gradients of the log-likelihood function
with respect to the estimated parameters
are obtained by one-sided numeric finit-difference differentiation,
which is faster but less precise
than two-sided numeric finit-difference differentiation.
eps
numeric. The step size for the one-sided numeric
finit-distance differentiation.
Unfortunately, it is currently not possible to set the step size
for the two-sided numeric finit-distance differentiation.
random.seed
an integer used to seed R's random number generator;
this is to ensure replicability
when computing (cumulative) probabilities of the multivariate normal distribution
which is required to calculate the log likelihood values;
set.seed( random.seed ) is called each time before
a (cumulative) probability of the multivariate normal distribution
is computed;
defaults to 123.
x
object of class mvProbit (returned by mvProbit).
digits
positive integer specifiying the minimum number of
significant digits to be printed
(see print.default).
...
additional arguments to mvProbit are passed
to maxLik and pmvnorm;
additional arguments to print.mvProbit are currently ignored.
Details
It is possible to specify starting values
(a) both for the model coefficients and the correlation coefficients
(using argument start alone or arguments start and startSigma
together),
(b) only for the model coefficients (using argument start alone), or
(c) only for the correlation coefficients (using argument startSigma alone).
If the model has n dependent variables (equations)
and k explanatory variables in each equation,
the order of the starting values in argument start must be as follows:
b_{1,1}, ..., b_{1,k},
b_{2,1}, ..., b_{2,k}, ...,
b_{n,1}, ..., b_{n,k},
where b_{i,j} is the coefficient
of the jth explanatory variable in the ith equation.
If argument startSigma is not specified,
argument start can additionally include following elements:
R_{1,2}, R_{1,3}, R_{1,4}, ..., R_{1,n},
R_{2,3}, R_{2,4}, ..., R_{2,n}, ...,
R_{n-1,n},
where R_{i,j} is the correlation coefficient corresponding to
the ith and jth equation.
The ‘state’ (or ‘seed’) of R's random number generator
is saved at the beginning of the mvProbit function
and restored at the end of this function
so that this function does not affect the generation
of random numbers outside this function
although the random seed is set to argument random.seed
and the calculation of the (cumulative) multivariate normal distribution
uses random numbers.
Value
mvProbit returns an object of class "mvProbit"
inheriting from class "maxLik".
The returned object contains the same components as objects
returned by maxLik and additionally
the following components:
call
the matched call.
start
the vector of starting values.
nDep
the number of dependent variables.
nReg
the number of explanatory variables (regressors).
nObs
the number of observations.
dummyVars
vector of character strings
indicating the names of explanatory variables
that contain only zeros and ones or only TRUE and FALSE.
It is NULL, if no explanatory variable is indentified
as a dummy variable.
Author(s)
Arne Henningsen
References
Greene, W.H. (1996):
Marginal Effects in the Bivariate Probit Model,
NYU Working Paper No. EC-96-11.
Available at http://ssrn.com/abstract=1293106.