Abstract

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

Highlights

  • Spatial econometrics models are frequently proposed to analyze spatial data that arise in many disciplines such as urban, real estate, public, agricultural, environmental economics and industrial organizations

  • We specify the prior of all unknown parameters, which led to a proper posterior distribution

  • Spatial data are frequently encountered in practical applications and can be analyzed through the spatial autoregressive (SAR) model

Read more

Summary

Introduction

Spatial econometrics models are frequently proposed to analyze spatial data that arise in many disciplines such as urban, real estate, public, agricultural, environmental economics and industrial organizations. Combining PLA models with SAR models, we consider a class of PLASAR models for spatial data to capture the linear and nonlinear effects between the related variables in addition to spatial dependence between the neighbors in this article. We develop an improved Bayesian method with free-knot splines [43,44,45,46,47,48,49,50,51], along with MCMC techniques to estimate unknown parameters, use a spline approach to approximate the nonparametric functions, and design a Gibbs sampler to explore the joint posterior distributions.

Likelihood
Bayesian Estimation
Priors
The Full Conditional Posterior Distributions of Unknown Quantities
Empirical Illustrations
Simulation
Application
Findings
Summary
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call