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)

Arguments

dependent variables. vector of zeros and ones

design matrix

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

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 e

subset

an optional vector specifying a subset of observations to be used in the fitting process.

...

additional arguments to be passed

Value

Returns a structure of class sarprobit:
betaposterior mean of bhat based on draws
rhoposterior mean of rho based on draws
phiposterior mean of phi based on draws
coefficientsposterior mean of coefficients
fitted.valuesfitted values
fitted.reponsefitted reponse
ndraw# of draws
bdrawbeta draws (ndraw-nomit x nvar)
pdrawrho draws (ndraw-nomit x 1)
phidrawphi draws (ndraw-nomit x 1)
a1a1 parameter for beta prior on rho from input, or default value
a2a2 parameter for beta prior on rho from input, or default value
timetotal time taken
rmax1/max eigenvalue of W (or rmax if input)
rmin1/min eigenvalue of W (or rmin if input)
tflag'plevel' (default) for printing p-levels; 'tstat' for printing bogus t-statistics
lflaglflag from input
cflag1 for intercept term, 0 for no intercept term
lndeta matrix containing log-determinant information (for use in later function calls to save time)
Wspatial weights matrix
Xregressor matrix

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