Abstract
Maximum likelihood estimation has been the standard method employed for estimating spatial econometric models. This chapter introduces these methods, examines the specific case of a spatial error model, and provides an example based on a large data set. In addition, the chapter sets forth various solutions to the computational difficulties that arise for large data sets.
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References
Anselin L (1988) Spatial econometrics: methods and models. Kluwer, Dordrecht
Barry R, Pace RK (1999) LA Monte Carlo estimator of the log determinant of large sparse matrices. Linear Algebra Appl 289(1–3):41–54
Beron KJ, Vijverberg WPM (2004) Probit in a spatial context: a Monte Carlo analysis. In: Anselin L, Florax RJGM, Rey SJ (eds) Advances in spatial econometrics: methodology, tools and applications. Springer, Berlin/Heidelberg/New York, pp 169–195
Bivand R (2010) Computing the Jacobian in spatial models: an applied survey (17 Aug 2010). NHH Department of Economics discussion paper No. 20/2010. Available at SSRN: https://doi.org/10.2139/ssrn.1966039
Burridge P (2012) A research agenda on general-to-specific spatial model search. Invest Reg 21:71–90
Chen J, Jennrich R (1996) The signed root deviance profile and confidence intervals in maximum likelihood analysis. J Am Stat Assoc 91(435):993–998
Cramer JS (1986) Econometric applications of maximum likelihood methods. Cambridge University Press, Cambridge
Davidson R, MacKinnon J (2004) Econometric theory and methods. Oxford University Press, New York
George A, Liu J (1981) Computer solution of large sparse positive definite systems. Prentice-Hall, Englewood Cliffs
Geweke J (1991) Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints. In: Computer science and statistics: proceedings of the twenty-third symposium on the interface. American Statistical Association, Alexandria, pp 571–578
Griffith D (1989) Advanced spatial statistics. Kluwer, Dordrecht
Griffith D (2004) Faster maximum likelihood estimation of very large spatial autoregressive models: an extension of the Smirnov-Anselin result. J Stat Comput Simul 74(12):855–866
Haining R (1990) Spatial data analysis in the social and environmental sciences. Cambridge University Press, Cambridge
Hajivassiliou V, McFadden D (1990) The method of simulated scores for the estimation of LDV models with an application to external debt crises. Cowles Foundation discussion paper 967, Yale University
Keane M (1994) A computationally practical simulation estimator for panel data. Econometrica 62(1):95–116
LeSage JP, Pace RK (2007) A matrix exponential spatial specification. J Econ 140(1):190–214
LeSage J, Pace RK (2009) Introduction to spatial econometrics. Taylor and Francis/CRC, Boca Raton
Mardia KV, Marshall RJ (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71(1):135–146
Martin RJ (1993) Approximations to the determinant term in Gaussian maximum likelihood estimation of some spatial models. Commun Stat Theory Methods 22(1):189–205
Ord JK (1975) Estimation methods for models of spatial interaction. J Am Stat Assoc 70(1):120–126
Pace RK, Barry RP (1997) Quick computation of spatial autoregressive estimators. Geogr Anal 29(3):232–246
Pace RK, LeSage JP (2002) Semiparametric maximum likelihood estimates of spatial dependence. Geogr Anal 34(1):76–90
Pace RK, LeSage JP (2004) Chebyshev approximation of log-determinants of spatial weight matrices. Comput Stat Data Anal 45(1):179–196
Pace RK, LeSage J (2009) A sampling approach to estimating the log determinant used in spatial likelihood problems. J Geogr Syst 11(3):209–225
Pace RK, LeSage J (2011) Fast simulated maximum likelihood estimation of the spatial probit model capable of handling large samples. Available at SSRN: https://doi.org/10.2139/ssrn.1966039
Pace RK, Zhu S (2012) Separable spatial modelling of spillovers and dependence. J Geogr Syst 14(1):75–90
Pace RK, Zou D (2000) Closed-form maximum likelihood estimates of nearest neighbor spatial dependence. Geogr Anal 32(2):154–172
Phinikettos I, Gandy A (2011) Fast computation of high-dimensional multivariate normal probabilities. Comput Stat Data Anal 55(4):1521–1529
Smirnov O, Anselin L (2001) Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach. Comput Stat Data Anal 35(8):301–319
Walde J, Larch M, Tappeiner G (2008) Performance contest between MLE and GMM for huge spatial autoregressive models. J Stat Comput Simul 78(2):151–166
Zhang Y, Leithead WE, Leithead DJ (2007) Approximate implementation of logarithm of matrix determinant in Gaussian processes. J Stat Comput Simul 77(4):329–348
Zhu S, Pace RK. (2011) Spatially interdependent mortgage decisions. J Real Estate Financ Econ 49(4):598–620
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I would like to thank Mark Mclean, James LeSage, and Shuang Zhu for their very helpful comments.
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Kelley Pace, R. (2019). Maximum Likelihood Estimation. In: Fischer, M., Nijkamp, P. (eds) Handbook of Regional Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36203-3_88-1
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DOI: https://doi.org/10.1007/978-3-642-36203-3_88-1
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