Description Usage Arguments Details Value Author(s) References
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).
1 2 3 4 5 6 |
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 |
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 |
n.draws |
A positive integer. The number of MCMC draws. The
default is |
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 |
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 |
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 |
cov.start |
A positive definite matrix. The first elements in the
blocks determined by the selection and outcome sizes should be set
to |
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 |
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 |
verbose |
Logical. If |
minConst |
Logical. If |
trace |
Logical. If |
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.)
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. |
Lane F. Burgette, Department Statistical Science, Duke University, lb131@stat.duke.edu.
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.
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