sarorderedprobit: Bayesian estimation of the SAR ordered probit model

Description

Bayesian estimation of the spatial autoregressive ordered probit model (SAR ordered probit model).

Usage

sarorderedprobit(formula, W, data, subset, ...)
sar_ordered_probit_mcmc(y, X, W, ndraw = 1000, burn.in = 100, thinning = 1, 
  prior=list(a1=1, a2=1, c=rep(0, ncol(X)), T=diag(ncol(X))*1e12, lflag = 0), 
  start = list(rho = 0.75, beta = rep(0, ncol(X)), 
  phi = c(-Inf, 0:(max(y)-1), Inf)),
  m=10, computeMarginalEffects=TRUE, showProgress=FALSE)

Value

Returns a structure of class sarprobit:

beta: posterior mean of bhat based on draws
rho: posterior mean of rho based on draws
phi: posterior mean of phi based on draws
coefficients: posterior mean of coefficients
fitted.values: fitted values
fitted.reponse: fitted reponse
ndraw: \# of draws
bdraw: beta draws (ndraw-nomit x nvar)
pdraw: rho draws (ndraw-nomit x 1)
phidraw: phi draws (ndraw-nomit x 1)
a1: a1 parameter for beta prior on rho from input, or default value
a2: a2 parameter for beta prior on rho from input, or default value
time: total time taken
rmax: 1/max eigenvalue of W (or rmax if input)
rmin: 1/min eigenvalue of W (or rmin if input)
tflag: 'plevel' (default) for printing p-levels; 'tstat' for printing bogus t-statistics
lflag: lflag from input
cflag: 1 for intercept term, 0 for no intercept term
lndet: a matrix containing log-determinant information (for use in later function calls to save time)
W: spatial weights matrix
X: regressor matrix

Arguments

y: dependent variables. vector of discrete choices from 1 to J ({1,2,...,J})
X: design matrix
W: spatial weight matrix
ndraw: number of MCMC iterations
burn.in: number of MCMC burn-in to be discarded
thinning: MCMC thinning factor, defaults to 1.
prior: A list of prior settings for $\rho \sim Beta(a1,a2)$ and $\beta \sim N(c,T)$. Defaults to diffuse prior for beta.
start: list of start values
m: Number of burn-in samples in innermost Gibbs sampler. Defaults to 10.
computeMarginalEffects: Flag if marginal effects are calculated. Defaults to TRUE. Currently without effect.
showProgress: Flag if progress bar should be shown. Defaults to FALSE.
formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data: an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which sarprobit is called.
subset: an optional vector specifying a subset of observations to be used in the fitting process.
...: additional arguments to be passed

Author

Stefan Wilhelm <wilhelm@financial.com>

Details

Bayesian estimates of the spatial autoregressive ordered probit model (SAR ordered probit model) $$ z = \rho W z + X \beta + \epsilon, \epsilon \sim N(0, I_n) $$ $$ z = (I_n - \rho W)^{-1} X \beta + (I_n - \rho W)^{-1} \epsilon $$ where y is a $(n \times 1)$ vector of discrete choices from 1 to J, $y \in \{1,2,...,J\}$, where

$y = 1$ for $-\infty \le z \le \phi_1 = 0$
$y = 2$ for $\phi_1 \le z \le \phi_2$
...
$y = j$ for $\phi_{j-1} \le z \le \phi_j$
...
$y = J$ for $\phi_{J-1} \le z \le \infty$

The vector $\phi=(\phi_1,...,\phi_{J-1})'$ $(J-1 \times 1)$ represents the cut points (threshold values) that need to be estimated. $\phi_1 = 0$ is set to zero by default.

$\beta$ is a $(k \times 1)$ vector of parameters associated with the $(n \times k)$ data matrix X.

$\rho$ is the spatial dependence parameter.

The error variance $\sigma_e$ is set to 1 for identification.

Computation of marginal effects is currently not implemented.

References

LeSage, J. and Pace, R. K. (2009), Introduction to Spatial Econometrics, CRC Press, chapter 10, section 10.2