Specification and estimation of spatial linear regression models (original) (raw)
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Empirical Models of Spatial Inter‐Dependence
Oxford Handbooks Online, 2008
This article discusses the role of ‘spatial interdependence’ between units of analysis by using a symmetric weighting matrix for the units of observation whose elements reflect the relative connectivity between unitiand unitj. It starts by addressing spatial interdependence in political science. There are two workhorse regression models in empirical spatial analysis: spatial lag and spatial error models. The article then addresses OLS estimation and specification testing under the null hypothesis of no spatial dependence. It turns to the topic of assessing spatial lag models, and a discussion of spatial error models. Moreover, it reports the calculation of spatial multipliers. Furthermore, it presents several newer applications of spatial techniques in empirical political science research: SAR models with multiple lags, SAR models for binary dependent variables, and spatio-temporal autoregressive (STAR) models for panel data.
An empirical evaluation of spatial regression models
Computers & Geosciences, 2006
Conventional statistical methods are often ineffective to evaluate spatial regression models. One reason is that spatial regression models usually have more parameters or smaller sample sizes than a simple model, so their degree of freedom is reduced. Thus, it is often unlikely to evaluate them based on traditional tests. Another reason, which is theoretically associated with statistical methods, is that statistical criteria are crucially dependent on such assumptions as normality, independence, and homogeneity. This may create problems because the assumptions are open for testing. In view of these problems, this paper proposes an alternative empirical evaluation method. To illustrate the idea, a few hedonic regression models for a house and land price data set are evaluated, including a simple, ordinary linear regression model and three spatial models. Their performance as to how well the price of the house and land can be predicted is examined. With a cross-validation technique, the prices at each sample point are predicted with a model estimated with the samples excluding the one being concerned. Then, empirical criteria are established whereby the predicted prices are compared with the real, observed prices. The proposed method provides an objective guidance for the selection of a suitable model specification for a data set. Moreover, the method is seen as an alternative way to test the significance of the spatial relationships being concerned in spatial regression models.
Specification searches in spatial econometrics: the relevance of Hendry’s methodology
Regional Science and Urban Economics, 2003
This article brings together a number of new specification search strategies in spatial econometric modeling. In the literature, experimental results for several forward stepwise strategies aimed at remedying spatial dependence, have been reported. Essentially, these strategies boil down to the expansion of a spatial linear regression model with spatially lagged variables, conditional upon the results of misspecification tests. We investigate a Hendry-like specification strategy, starting from the spatial common factor model and subsequently reducing the number of spatially lagged variables on the basis of significance tests. The experimental simulations pertain to various small to large sample sizes, with spatial processes modeled on regular lattice surfaces. Our main conclusion is that the classical forward stepwise approach outperforms the Hendry strategy in terms of finding the true data generating process as well as in the observed accuracy of the estimators for spatial and non-spatial parameters. It also dominates concurrent forward stepwise strategies recently suggested in the literature.
Applied Spatial Econometrics: Raising the Bar
Spatial Economic Analysis, 2010
This paper places the key issues and implications of the new 'introductory' book on spatial econometrics by James LeSage & Kelley Pace (2009) in a broader perspective: the argument in favour of the spatial Durbin model, the use of indirect effects as a more valid basis for testing whether spatial spillovers are significant, the use of Bayesian posterior model probabilities to determine which spatial weights matrix best describes the data, and the book's contribution to the literature on spatiotemporal models. The main conclusion is that the state of the art of applied spatial econometrics has taken a step change with the publication of this book.
The theory and practice of spatial econometrics
1999
This text provides an introduction to spatial econometric theory along with numerous applied illustrations of the models and methods described. The applications utilize a set of MATLAB functions that implement a host of spatial econometric estimation methods. The intended audience is faculty, students and practitioners involved in modeling spatial data sets. The MATLAB functions described in this book have been used in my own research as well as teaching both undergraduate and graduate econometrics courses. They are available on the Internet at http://www.econ.utoledo.edu along with the data sets and examples from the text.
Pitfalls in Higher Order Model Extensions of Basic Spatial Regression Methodology
Review of Regional Studies
Spatial regression methodology has been around for most of the 50 years (1961-2011) that the Southern Regional Science Association has been in existence. Cliff and Ord (1969) devised a parsimonious specification for the structure of spatial dependence among observations that could be used to empirically model spatial interdependence. Later work (Cliff and Ord, 1973, 1981; Ord, 1975) further developed these ideas into basic spatial regression models, which were popularized and augmented by Anselin (1988). We discuss several issues that have arisen in recent work that attempts to extend basic models of spatial interdependence to include more types of spatial and non-spatial interdependencies. Understanding these issues should help future work avoid several pitfalls that plague current and past attempts at extensions along these lines.
2018
The applications of standard regression analysis on spatial data are not appropriate because of the characteristics of the spatial data. Spatial data has two characteristics are spatial dependence and spatial heterogeneity. Modeling spatial data using standard linear regression model leads to bias, inconsistency and inefficient results. Several models have been developed to accommodate the characteristics of the spatial data. However, the models generally developed to solve only one problem of the spatial data (e.g., spatial dependence or spatial heterogeneity). Four kinds of spatial econometrics models usually used to accommodate spatial dependence are spatial autoregressive (SAR), spatial lagged exogenous variables (SLX), spatial error model (SEM), and spatial Durbin model (SDM). To accommodate the spatial heterogeneity, geographically weighted regression (GWR) or varying coefficient model (VCM) is usually used. Our research proposed to develop a new model to accommodate two chara...
Spatial Dependence in Regressors and its Effect on Estimator Performance
Social Science Research Network, 2011
In econometrics most work focuses on spatial dependence in the regressand or disturbances. However, LeSage and Pace (2009); Pace and LeSage (2009) showed that the bias in β from applying OLS to a regressand generated from a spatial autoregressive process was exacerbated by spatial dependence in the regressor. Also, the marginal likelihood function or restricted maximum likelihood (REML) function includes a determinant of a function of the spatial parameter and the regressors. Therefore, high dependence in the regressor may affect the likelihood through this term. Finally, the notion of effective sample size for dependent data suggests that the loss of information from dependence may have implications for the information content of various instruments when using instrumental variables. Empirically, many common economic regressors such as income, race, and employment show high levels of spatial autocorrelation. Based on these empirical results, we conduct a Monte Carlo study using maximum likelihood, restricted maximum likelihood, and two instrumental variable specifications for the lag y model (SAR) and spatial Durbin model (SDM) in the presence of correlated regressors while varying signal-to-noise, spatial dependence, and weight matrix specifications. We find that REML outperforms ML in the presence of correlated regressors and that instrumental variable performance is affected by such dependence. The combination of correlated regressors and the SDM provides a challenging environment for instrumental variable techniques. In addition, we examine the estimation of marginal effects and show that this can behave better than estimation of component parameters. We also make suggestions for improving Monte Carlo experiments.