| sarorderedprobit {spatialprobit} | R Documentation |
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
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
|
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 " |
data |
an optional data frame, list or environment (or object coercible by |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
... |
additional arguments to be passed |
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.
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 |
Author(s)
Stefan Wilhelm <wilhelm@financial.com>
References
LeSage, J. and Pace, R. K. (2009), Introduction to Spatial Econometrics, CRC Press, chapter 10, section 10.2
See Also
sarprobit for the SAR binary probit model
Examples
library(spatialprobit)
set.seed(1)
################################################################################
#
# Example with J = 4 alternatives
#
################################################################################
# set up a model like in SAR probit
J <- 4
# ordered alternatives j=1, 2, 3, 4
# --> (J-2)=2 cutoff-points to be estimated phi_2, phi_3
phi <- c(-Inf, 0, +1, +2, Inf) # phi_0,...,phi_j, vector of length (J+1)
# phi_1 = 0 is a identification restriction
# generate random samples from true model
n <- 400 # number of items
k <- 3 # 3 beta parameters
beta <- c(0, -1, 1) # true model parameters k=3 beta=(beta1,beta2,beta3)
rho <- 0.75
# design matrix with two standard normal variates as "coordinates"
X <- cbind(intercept=1, x=rnorm(n), y=rnorm(n))
# identity matrix I_n
I_n <- sparseMatrix(i=1:n, j=1:n, x=1)
# build spatial weight matrix W from coordinates in X
W <- kNearestNeighbors(x=rnorm(n), y=rnorm(n), k=6)
# create samples from epsilon using independence of distributions (rnorm())
# to avoid dense matrix I_n
eps <- rnorm(n=n, mean=0, sd=1)
z <- solve(qr(I_n - rho * W), X %*% beta + eps)
# ordered variable y:
# y_i = 1 for phi_0 < z <= phi_1; -Inf < z <= 0
# y_i = 2 for phi_1 < z <= phi_2
# y_i = 3 for phi_2 < z <= phi_3
# y_i = 4 for phi_3 < z <= phi_4
# y in {1, 2, 3}
y <- cut(as.double(z), breaks=phi, labels=FALSE, ordered_result = TRUE)
table(y)
#y
# 1 2 3 4
#246 55 44 55
# estimate SAR Ordered Probit
res <- sar_ordered_probit_mcmc(y=y, X=X, W=W, showProgress=TRUE)
summary(res)
#----MCMC spatial autoregressive ordered probit----
#Execution time = 12.152 secs
#
#N draws = 1000, N omit (burn-in)= 100
#N observations = 400, K covariates = 3
#Min rho = -1.000, Max rho = 1.000
#--------------------------------------------------
#
#y
# 1 2 3 4
#246 55 44 55
# Estimate Std. Dev p-level t-value Pr(>|z|)
#intercept -0.10459 0.05813 0.03300 -1.799 0.0727 .
#x -0.78238 0.07609 0.00000 -10.283 <2e-16 ***
#y 0.83102 0.07256 0.00000 11.452 <2e-16 ***
#rho 0.72289 0.04045 0.00000 17.872 <2e-16 ***
#y>=2 0.00000 0.00000 1.00000 NA NA
#y>=3 0.74415 0.07927 0.00000 9.387 <2e-16 ***
#y>=4 1.53705 0.10104 0.00000 15.212 <2e-16 ***
#---
addmargins(table(y=res$y, fitted=res$fitted.response))
# fitted
#y 1 2 3 4 Sum
# 1 218 26 2 0 246
# 2 31 19 5 0 55
# 3 11 19 12 2 44
# 4 3 14 15 23 55
# Sum 263 78 34 25 400