Spatial dependence model with feature difference

• Date: 01 July 2020
• Published date: 01 July 2020
• Author: Tommy K. Y. Cheung,Simon K. C. Cheung
• DOI: http://doi.org/10.1002/for.2633

Received: 25 April 2018 Revised: 3 August 2019 Accepted: 28 October 2019

DOI: 10.1002/for.2633

RESEARCH ARTICLE

Spatial dependence model with feature difference

Tommy K. Y. Cheung1Simon K. C. Cheung 2

1Faculty of Science, Engineering and

Technology, Swinburne University of

Technology,Melbourne, Australia

2Department of Statistics, The University

of Hong Kong, Hong Kong

Correspondence

TommyK. Y. Cheung, Faculty of Science,

Engineering and Technology,Swinburne

University of Technology,Melbourne,

Victoria 3122, Australia.

Email: tommycheung@swin.edu.au

Abstract

This paper presents a new spatial dependence model with an adjustment of fea-

ture difference. The model accounts for the spatial autocorrelation in both the

outcome variables and residuals. The feature difference adjustment in the model

helps to emphasize feature changes across neighboring units, while suppressing

unobserved covariates that are present in the same neighborhood. The predic-

tion at a given unit incorporates components that depend on the differences

between the values of its main features and those of its neighboring units. In

contrast to conventional spatial regression models, our model does not requirea

comprehensive list of global covariates necessary to estimate the outcome vari-

able at the unit, as common macro-level covariates are differenced away in the

regression analysis. Using the real estate market data in Hong Kong, we applied

Gibbs sampling to determine the posterior distribution of each model parame-

ter. The result of our empirical analysis confirms that the adjustment of feature

difference with an inclusion of the spatial error autocorrelation produces better

out-of-sample prediction performance than other conventional spatial depen-

dence models. In addition, our empirical analysis can identify components with

more significant contributions.

KEYWORDS

autoregressive model, Bayesian, spatial models, spatial regression

1INTRODUCTION

In recent years, there have been considerable interest in

the application of spatial models for the analysis of spa-

tially correlated data. Spatial data often have geographic

reference and is highly multivariate. The core of any spa-

tial analysis approach is the concept of spatial interactions.

When locations have been characterized, the relationships

between various features of the spatial units and their

mutual influences can be analyzed. Applying regression

analysis to spatial data often yields a form of spatial depen-

dence structure that captures both the interaction and het-

erogeneity effects among the spatial units. These effects are

usually not apparent empirically. Heterogeneity in a spa-

tial context means that those features describing the data

vary from location to location, while interaction describes

the presence of spatial autocorrelation among the values

of features observed at the spatial units. In our model, fea-

tures are covariates, and when included they yield a better

estimate of the dependent variable. Spatial autocorrelation

is typically multivariate in nature. That is, an observation

of a covariate at one location can be correlated with the

value of the same covariate at another location, and vice

versa.

There are generally three types of interaction effects

that are often captured by a spatial model. They include

the interactions among dependent variables, independent

covariates, and the error terms. Various spatial regression

models can be constructed by considering different com-

binations of these interaction effects. A few notable but

important models in econometric work include the spa-

tial lag model (also known as the spatial autoregressive

Journal of Forecasting. 2020;39:615–627. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 615