endogMNP: Fitting the Multinomial Probit Model with Endogenous...

In endogMNP: R Package for Fitting Multinomial Probit Models with Endogenous Selection

Description

endogMNP is used to fit a Bayesian multinomial probit model with endogenous selection or switching via Markov chain Monte Carlo. The computation uses the efficient partial marginal data augmentation algorithm that is developed by Burgette and Nordheim (2009), which is an extension of the sampler of Imai and van Dyk (2005).

Usage

endogMNP(selForm, outForm, dataSet = parent.frame(),
                selBase = NULL, outBase = NULL, latent=FALSE, 
                invcdf = FALSE, n.draws = 5000, p.var = "Inf",
                p.df = n.dim+1, p.scale = 1, coef.start = 0,
                cov.start = 1, burnin = 0, thin = 0, verbose = FALSE,
		minConst=TRUE, trace=TRUE)

Arguments

selForm	A symbolic description of the selection model portion of the model where the left-hand side indicates the category into which each observation has been selected.
outForm	A symbolic description of the outcome equation. The left-hand side is the response of interest.
dataSet	An optional data frame in which to interpret the variables in selForm and outForm. The default is the environment in which endogMNP is called.
selBase	The name of the base category for the selection equation. The default is the lowest level of the selection variable.
outBase	The name of the base category for the outcome equation. The default is the lowest level of the response variable.
latent	Logical. Store latent vectors?
invcdf	Logical. If TRUE, then the inverse cdf method is used for truncated normal sampling. If FALSE, then the rejection sampling method is used. The default is FALSE.
n.draws	A positive integer. The number of MCMC draws. The default is 5000.
p.var	A positive definite matrix. The prior variance of the coefficients. A scalar input can set the prior variance to the diagonal matrix whose diagonal element is equal to that value. The default is "Inf", which represents an improper noninformative prior distribution on the coefficients.
p.df	A positive integer greater than the dimension of the implied covariance matrix. The prior degrees of freedom parameter for the covariance matrix. The default is the dimension of the covariance matrix plus one.
p.scale	A block-diagonal, positive definite matrix whose leading diagonal elements are set to 1. The first block has the size of the selection covariance matrix, and the other blocks are of the size of the outcome covariance matrices. This is the prior scale matrix for the covariance matrix. A scalar input can be used to set the scale matrix to a diagonal matrix with diagonal elements equal to the scalar input value, except that the first element in each block is set to one. The default is 1.
coef.start	A vector. The starting values for the coefficients. A scalar input sets the starting values for all the coefficients equal to that value. The default is 0.
cov.start	A positive definite matrix. The first elements in the blocks determined by the selection and outcome sizes should be set to 1. This is the starting value for the covariance matrix. The leading diagonal elements are set to 1 if they are not already. A scalar input can be used to set the starting value to a diagonal matrix with diagonal elements equal to the scalar input value, except those of the leading diagonal elements are set to one. The default is 1.
burnin	A positive integer. The burn-in interval for the Markov chain. It is the number of initial Gibbs draws that should not be stored. The default is 0.
thin	A positive integer. The thinning interval for the Markov chain. This is the number of Gibbs draws between the recorded values that are skipped. The default is 0.
verbose	Logical. If TRUE, messages along with a progress report of the Gibbs sampling are printed. The default is FALSE.
minConst	Logical. If TRUE, the covariance matrix is minimally constrained, which is to say only enough of the elements of the covariance matrix are constrained to be 1 in order to make the model identifiable. If FALSE, all of the diagonal elements of the covariance matrix are constrained to be 1. This can improve convergence in some cases.
trace	Logical. If TRUE, the trace restriction will be used to identify the model. This argument is ignored if minConst=FALSE.

Details

To fit the multinomial probit model when only the most preferred choice is observed, use the syntax for the formula, outForm = y1 ~ x1 + x2, where y is a factor variable indicating the most preferred choice and x1 and x2 are individual-specific covariates. The selection process is modeled by selForm = y2 ~ x2 + x3 where y2 contains the selection category. The y1 and y2 variables may contain missing values (coded as NA), however the x variables must be fully observed. Further, all but one of the selection categories must have at least some observed outcomes. (I.e., for a selection model we should observe the outcome for all selection groups except one.)

Value

An object of class endogMNP containing the following elements:

call	The matched call.
param	A matrix of the Gibbs draws for each parameter; i.e., the coefficients and covariance matrix. For the covariance matrix, the elements on or above the diagonal are returned.
x	The matrix of covariates.
y	The vector matrix of the selection and response variables.
n.dim	The number of columns in the covariance matrix.
n.obs	The number of observations.
coefnames	The names of the coefficients.
W	The three dimensional array of the latent variable, W. The first dimension represents the alternatives, and the second dimension indexes the observations. The third dimension represents the Gibbs draws. Note that the latent variables for the base categories are set to 0, and therefore omitted from the output.
p.scale	The prior scale of the covariance.
n.cov	The number of covariates.
nu0	The prior degrees of freedom.
p.var	The prior variance.
n.param	The number of parameters in the fit model.
minConst	Indicator of whether the covariance matrix was minimally constrained.
n.dim1	The number of dimensions for the selection equation.
n.dim2	The number of dimensions of each outcome equation.
n.rep	The number of stored Gibbs iterations.
selForm	The symbolic selection equation formula.
outForm	The symbolic outcome equation formula.
dataSet	The data-set.
selBase	The base category for the selection model.
outBase	The base category for the outcome.

Author(s)

Lane F. Burgette, Department Statistical Science, Duke University, [e-mail].

References

Burgette, Lane F. and Erik V. Nordheim (2009). “A Full Gibbs Sampler for a Multinomial Probit Model with Endogeneity.” Available on request from the first author.

Imai, Kosuke and David A. van Dyk (2005). “A Bayesian Analysis of the Multinomial Probit Model Using Data Augmentation.” Journal of Econometrics. 124(2): 311-34.

endogMNP documentation built on May 1, 2019, 10:56 p.m.