Published date:Apr 16 2019

Journal Title: KnE Engineering

Issue title: International Conference on Basic Sciences and Its Applications (ICBSA-2018)

Pages:204–214

DOI: 10.18502/keg.v1i2.4445

Mohammad Masjkur

Henk Folmer

Spatial data are susceptible to covariates measured with errors. However, the errorprone covariates and the random errors are usually assumed to be symmetrically, normally distribution. The purpose of this paper is to analyze Bayesian inference of spatial regression models with a covariate measured with Skew-normal error by way of Monte Carlo simulation. We consider the spatial regression models with different degree of spatial correlation in the covariate of interest and measurement error variance. The simulation examines the performance of Bayesian estimators in the case of (i) Naive models without measurement error correction; (ii) Normal distribution for the error-prone covariate and random errors; (iii) Skew-normal distribution (SN) for the error-prone covariate and normal distribution for random errors. We use the relative bias (RelBias) and Root Mean Squared Error (RMSE) as valuation criteria. The main result is that the Skew-normal prior estimator outperform the normal, symmetrical prior distribution and the Naive models without measurement error correction.

Keywords: Spatial regression, measurement error, Bayesian analysis, Skew-normal distribution

[1] LeSage, J. P. (1999). The Theory and Practice of Spatial Econometrics. Department of Economics. University of Toledo.


[2] Anselin, L. (2007). Spatial Econometrics, in A Companion to Theoretical Econometrics. Badi H. Baltagi, Ed., pp. 310-330, John Wiley & Sons. New York.


[3] Waller, L. A, Gotway C. A. (2004). Applied Spatial Statistics for Public Health Data, Vol. 368. John Wiley & Sons: Hoboken, New Jersey, U.S.A.


[4] Li Y. et al. (2009). Spatial linear mixed models with covariate measurement errors, Stat. Sinica 19(3), 1077-1093.


[5] Huque M. H. et al. (2014). On the impact of covariate measurement error on spatial regression modelling, Environmetrics. 25, 560-570. [doi: 10.1002/env.2305].


[6] Huque M. H. et al. (2016). Spatial regression with covariate measurement error: A semiparametric approach. Biometrics. 72(3), 678-86. [doi: 10.1111/biom.12474].


[7] Arellano-Valle R. B., et al. (2005). Skew-normal measurement error models. J. Multivariate Anal., 96, 265-281. [doi: 10.1016/j.jmva.2004.11.002].


[8] Kheradmandi A. et al. (2015). Estimation in skew-normal linear mixed measurement error models. J. Multivariate Anal. 136, 1-11. [doi: 10.1016/j.jmva.2014.12.007].


[9] Muff S. et al. (2015). Bayesian analysis of measurement error models using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. C. Appl. Stat. 64(2), 231-252.


[10] Hossain S. et al. (2009). Bayesian adjustment for covariate measurement errors: A flexible parametric approach, Statist. Med. 28, 1580–1600. [doi: 10.1002/sim.3552].


[11] Azzalini A. (1985). A class of distributions which includes the normal ones Scand. J. Stat. 12(2), 17-18.


[12] Plant, R.E. (2012). Spatial Data Analysis in Ecology and Agriculture Using R. CRC Press. New York.


[13] LeSage, J. P. (2014). Spatial econometric panel data model specification: A Bayesian approach, Spat. Statist. 9, 122-145. [http://dx.doi.org/10.1016/j.spasta.2014.02.002].


[14] Gelman A., Carlin J. B., Stern H. S., Dunson D. B., Vehtari A., and Rubin, D.B. (2014). Bayesian Data Analysis, Chapman & Hall/CRC, New York, NY.


[15] Su Y S. et al. (2015). R2jags: A package for running jags from R, R package version 0.5-7.


[16] Spiegelhalter D. J. et al. (2014). The deviance information criterion: 12 years on, J. R. Stat. Soc. Ser. B. Stat. Methodol. 76, 485-493.