On the specification of regression models with spatial dependence : an application of the accessibility concept (original) (raw)
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Regional Science and Urban Economics, 1992
Spatially correlated residuals lead to various serious problems in applied spatial research. In this paper several conventional specification and estimation procedures for models with spatially dependent residuals are compared with alternative procedures. The essence of the latter is a search procedure for spatially lagged variables. By incorporating the omitted spatially lagged variables into the model spatially dependent residuals may be remedied, in particular if the spatial dependence is substantive. The efficacy of the conventional and alternative procedures in small samples will be investigated by means of Monte Carlo techniques for an irregular lattice structure.
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.
2002 Annual Meeting July 28 31 Long Beach Ca, 2002
A common test for spatial dependence in regression analysis with continuous dependent variables is the Moran's I. For limited dependent variable models, the standard definition of a residual breaks down because y i is qualitative. Efforts to correct for potential spatial effects in limited dependent variable models have relied on ad-hoc methods such as including a spatial lag variable or using a regular sample that omits neighboring observations. Kelejian and Prucha have recently developed a version of Moran's I for limited dependent variable models. We present the statistic in a more accessible way and use it to test the value of previously-used ad-hoc techniq ues with a specific data set.
A Structural Equation Approach to Models with Spatial Dependence
Geographical Analysis, 2008
In this paper we propose a Structural Equations Model (SEM) approach to spatial dependence models. Latent variables are used to represent spatial spill-over effects in the structural model of which the observed spatially lagged variables are indicators. This approach allows for more information and modeling flexibility than the representation of spatial spill-over effects in terms of Wy or Wx. Furthermore, we propose a Full Information Maximum Likelihood (FIML) estimator as an alternative to the estimators commonly used, notably the iterative and two-stage estimators for the error and lag model, respectively. We also show that the estimation procedures included in the software packages Mx and LISREL 8 to estimate SEMs can be applied in a straightforward way to estimate spatial dependence models in a standard fashion.
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.
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.
Sociological Methodology, 1992
Course Description. Spatial interdependence is ubiquitous throughout the social sciences. The likelihood and outcomes of demonstrations, riots, coups, and revolutions in one country almost certainly depend in substantively crucial ways on such occurrences in other countries (e.g., through demonstration effects or snowballing). Election outcomes and candidate qualities or strategies in some contests surely depend on those in others, and representatives' votes in legislatures certainly depend on others' votes or expected votes. In micro-behavioral research, long-standing and recently surging interest in contextual or network effects often refers to the effects on each individual's behavior or opinion from sets of other individuals' opinions or behaviors; e.g., a respondent's opinion on some policy likely depends on the opinions of her state, district, community, or social group. In international relations, states' entry decisions in wars, alliances, and organizations, e.g., heavily depend on how many and who else enters and how. In comparative and international political economy, globalization, i.e., international economic integration, implies strategic (and nonstrategic) interdependence in national-level macroeconomic policymaking. This course provides an introduction to spatial and spatiotemporal econometric models for continuous and limited dependent variables that can address such interedependence, with an emphasis on social science applications. Course Objectives. The main objective of this course is to teach students how to incorporate the interdependence implied by most social scientific theories into their empirical analysis. Participants will learn inter alia how to 1) diagnose spatial patterns in their data, 2) estimate the structural parameters of spatial and spatiotemporal regression models, 3) calculate and present spatial and spatiotemporal effects, and 4) use spatial modeling to discriminate between the multiple sources of spatial correlation-common exposure, interdependence, and selection-and, when it exists, evaluate the nature of the interdependence (e.g., strategic free-riding behavior, learning, coercion) among units of observation. Course Prerequisites. Students should have a basic understanding of matrix algebra, probability theory, first-year calculus, and regression as well as some familiarity with a software package that can be used for spatial analysis (e.g., MATLAB, STATA, or R). We do not use a textbook, but Anselin (2006) and Franzese and Hays (2008) provide overviews of all but a few of the topics we will cover. Ward and Gleditsch (2008) is an excellent introductory textbook for spatial regression models.