International Science Index


Spatial Time Series Models for Rice and Cassava Yields Based On Bayesian Linear Mixed Models


This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

[1] Office of Agricultural Economics, (2012, December 5). Agricultural Production.
[2] P. M. Yelland, "Bayesian forecasting of part demand,” International Journal of Forecasting, vol. 26, pp. 374–396, 2010.
[3] N. M. F. Rahman, "Forecasting of boro rice production in Bangladesh: An ARIMA approach,” Journal of the Bangladesh Agricultural University, vol. 8, no. 1, pp. 103–112, 2010.
[4] P. Tongkhow and N. Kantanantha, "Bayesian models for time series with covariates, trend, seasonality, autoregression and outliers,” Journal of Computer Science, vol. 9, no. 3, pp. 291–298, 2013.
[5] J. C. Wakefield, "Disease mapping and spatial regression with count data,” Biostatistics, vol. 8, pp. 158–183, 2007.
[6] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journal of the Royal Statistical Society Series B, vol. 36, no. 2, pp. 192–236, 1974.
[7] D. G. Clayton and J. Keldor. "Empirical Bayes estimates of age-standardized relative risks for use in disease mapping,” Biometrics, vol. 43, pp. 671–691, 1987.
[8] J. Besag, J. York, and A. Molli, "Bayesian image restoration, with two applications in spatial statistics,” Annals of the Institute of Statistical Mathematics, vol. 43, pp. 1–21, 1991.
[9] M. Diaconoa, A. Castrignanob, A. Troccolic, D. De Benedettob, B. Bassod, and P. Rubino, "Spatial and temporal variability of wheat grain yield and quality in a Mediterranean environment: A multivariate geostatistical approach,” Field Crops Research, vol. 131, pp. 49–62, 2012.
[10] P. Saengseedam, and N. Kantanantha, "Spatial time series forecasts based on Bayesian linear mixed models for rice yields in Thailand,” in Proceedings of the International MultiConference of Engineers and Computer Scientists 2014, Hong Kong, 2014, pp. 1007–1012.
[11] B. T. West, K. B. Welch, and A. T. Galecki, Linear mixed models: A practical guide to using statistical software. New York: Chapman and Hall/CRC, 2007.
[12] B. P. Carlin and S. Banerjee, "Hierarchical multivariate CAR models for spatially correlated survival data,” Bayesian Statistics 7. Oxford: Oxford University Press, pp. 45–64, 2003.
[13] H. Ma and B. P. Carlin, "Bayesian multivariate areal wombling for multiple disease boundary analysis,” Bayesian Analysis, vol. 2, no. 2, pp. 281–302, 2007.
[14] ADB, (2012, June 22). The Rice Situation in Thailand.
[15] I. Nation, (2008, April 16). Rice strain is cause of comparatively low productivity.
[16] T. Srinorakut, (2002, August 7). Research on High Grade Ethanol from Cassava for Decreasing of Chemical Importing. Research Project of Ethanol from Cassava. National Science and Technology Development Agency: NSTDA.
[17] K. Srirot, (2009, May 18). Situation of Raw Material for Ethanol Production of Thailand.
[18] P. Congdon, Bayesian Statistical Modelling. 2nd ed. New York: John Wiley and Sons, 2006.
[19] S. P. Brooks and G. O. Roberts, "Assessing convergence of Markov Chain Monte Carlo algorithms,” Statistics and Computing, vol. 8, pp. 319–335, 1998.
[20] W. Tobler, "A computer movie simulating urban growth in the Detroit region,” Economic Geography, vol. 46, no. 2, pp. 234–240, 1970.