Effective sample size for spatial regression models (original) (raw)

Effective Geographic Sample Size in the Presence of Spatial Autocorrelation

Http Dx Doi Org 10 1111 J 1467 8306 2005 00484 X, 2008

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases. This property suggests the research question asking what the number of independent observations, say n à , is that is equivalent to the sample size, n, of a data set. This is the notion of effective sample size. Intuitively speaking, when zero spatial autocorrelation prevails, n à ¼ n; when perfect positive spatial autocorrelation prevails in a univariate regional mean problem, n à ¼ 1. Equations are presented for estimating n à based on the sampling distribution of a sample mean or sample correlation coefficient with the goal of obtaining some predetermined level of precision, using the following spatial statistical model specifications: (1) simultaneous autoregressive, (2) geostatistical semivariogram, and spatial filter. These equations are evaluated with simulation experiments and are illustrated with selected empirical examples found in the literature.

Improved inferences for spatial regression models

Regional Science and Urban Economics, 2015

The quasi-maximum likelihood (QML) method is popular in the estimation and inference for spatial regression models. However, the QML estimators (QMLEs) of the spatial parameters can be quite biased and hence the standard inferences for the regression coefficients (based on t-ratios) can be seriously affected. This issue, however, has not been addressed. The QMLEs of the spatial parameters can be bias-corrected based on the general method of Yang (2015b, J. of Econometrics 186, 178-200). In this paper, we demonstrate that by simply replacing the QMLEs of the spatial parameters by their bias-corrected versions, the usual t-ratios for the regression coefficients can be greatly improved. We propose further corrections on the standard errors of the QMLEs of the regression coefficients, and the resulted t-ratios perform superbly, leading to much more reliable inferences.

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.

The Biggest Myth in Spatial Econometrics

SSRN Electronic Journal, 2000

There is near universal agreement that estimates and inferences from spatial regression models are sensitive to particular specifications used for the spatial weight structure in these models. We find little theoretical basis for this commonly held belief, if estimates and inferences are based on the true partial derivatives for a well-specified spatial regression model. We conclude that this myth may have arisen from past applied work that incorrectly interpreted the model coefficients as if they were partial derivatives, or from use of misspecified models.

Selected Challenges From Spatial Statistics For Spatial Econometricians

Comparative Economic Research, 2012

Griffith and Paelinck (2011) present selected non-standard spatial statistics and spatial econometrics topics that address issues associated with spatial econometric methodology. This paper addresses the following challenges posed by spatial autocorrelation alluded to and/or derived from the spatial statistics topics of this book: the Gaussian random variable Jacobian term for massive datasets; topological features of georeferenced data; eigenvector spatial filtering-based georeferenced data generating mechanisms; and, interpreting random effects.

Specification and estimation of spatial linear regression models

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.

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.