hetero_sem {BSPADATA}R Documentation

Bayesian fitting of Spatial Error Model (SEM) model with heteroscedastic normal error term.

Description

Performs the Bayesian fitting of Heterocedastic Spatial Error Model (SEM) model with normal error term

Usage

hetero_sem(y, X,Z, W, nsim, burn, step, b_pri, B_pri,g_pri,G_pri, beta_0, gammas_0,
lambda_0, kernel = NULL,
plot = TRUE)

Arguments

y

Object of class matrix, with the dependent variable

X

Object of class matrix, with covariates of mean model

Z

Object of class matrix, with covariates of dispersion model

W

Object of class matrix, nb or listw related to Spatial Contiguity Matrix, Anselin(1988)

nsim

A number that indicates the amount of iterations

burn

A number that indicates the amount of iterations to be burn at the beginning of the chain

step

A number that indicates the length between samples in chain that generate the point estimates for each parameter.

b_pri

A vector with the prior mean of beta

B_pri

A matrix with the prior variance of beta

g_pri

A vector with the prior mean of gamma

G_pri

A vector with the prior variance of gamma

beta_0

A vector with start values for beta chain

gammas_0

A number with start value for gamma chain

lambda_0

A number with start value for lambda chain

kernel

Distribution used in transition kernel to get samples of lambda, it can be "uniform" or "normal"

plot

If it is TRUE present the graph of the chains

Details

hetero_sem is a function made in order to fit Spatial Error Model (SEM) with a normal heteroscedatic disturbance term through MCMC methods as Metropolis-Hastings algorithm, under two proposals for trasition kernel to get samples of spatial lag parameter, lambda, and aided by working variables approach to get samples of conditional posterior distribution of gamma vector.

Value

List with the following:

Bestimado

Estimated coefficients of beta

Gammaest

Estimated coefficient of gamma

Lambdaest

Estimated coefficient of lambda

DesvBeta

Estimated standard deviations of beta

DesvGamma

Estimated standard deviation of gamma

DesvLambda

Estimated standard deviation of lambda

AccRate1

Acceptance Rate for samples of gamma

AccRate2

Acceptance Rate for samples of lambda

BIC

Value of Bayesian Information Criterion

DIC

Value of Deviance Information Criterion

Author(s)

Jorge Sicacha-Parada <jasicachap@unal.edu.co>, Edilberto Cepeda-Cuervo <ecepedac@unal.edu.co>

References

1. Cepeda C. E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio do Janeiro.

2.Cepeda, E. and Gamerman D. (2005). Bayesian Methodology for modeling parameters in the two-parameter exponential family. Estadistica 57, 93 105.

3.Cepeda C., E. and Gamerman D. (2001). Bayesian Modeling of Variance Heterogeneity in Normal Regression Models. Brazilian Journal of Probability and Statistics. 14, 207-221.

4.Luc Anselin, Spatial Econometrics: Methods and Models, Kluwer Academic, Boston, 1988.

5. D. Gamerman, Markov Chains Monte Carlo: Stochastic Simulation for bayesian Inference, Chapman and Hall, 1997.

6. James Le Sage and Kelley Pace, Introduction to Spatial Econometrics, Chapman & Hall/CRC, Boca Raton, 2009.

Examples

library(spdep)
library(mvtnorm)
library(pscl)
n=49
x0=rep(1,n)
x1=runif(n,0,400)
x2=runif(n,10,23)
x3=runif(n,0,10)
X=cbind(x0,x1,x2)
Z=cbind(x0,x1,x3)
gammas=c(-8,0.026,-0.4)
Sigma=diag(c(exp(Z%*%gammas)))
data(oldcol)
W=COL.nb
matstand=nb2mat(W)
A=diag(n)-0.75*matstand
miu=-35+0.35*x1-1.7*x2
Sigma2=t(solve(A))%*%Sigma%*%solve(A)
y=rmvnorm(1,miu,Sigma2)
y_1=t(y)
y=y_1
data(oldcol)
W=COL.nb
hetero_sem(y,X,Z,W,nsim=500,burn=25,step=5,b_pri=rep(0,3),B_pri=diag(rep(1000,3)),g_pri=rep(0,3),
G_pri=diag(rep(1000,3)),
beta_0=rep(0,3),gammas_0=c(10,0,0),lambda_0=0.5,kernel="normal",plot="FALSE")

[Package BSPADATA version 1.0 Index]