Volume 6, Issue 2, April 2018, Page: 49-57
Correlated Spatiotemporal Data Modeling Using Generalized Additive Mixed Model and Bivariate Smoothing Techniques
Sabyasachi Mukherjee, Department of Mathematics, NSHM Knowledge Campus, Durgapur, India
Tapan Kumar Garai, Department of Agriculture, Government of West Bengal, Medinipur, India
Received: Apr. 4, 2018;       Accepted: Apr. 28, 2018;       Published: May 22, 2018
DOI: 10.11648/j.sjams.20180602.11      View  981      Downloads  56
Abstract
Background: The present article tries to analyze a correlated spatiotemporal data using an advance regression modeling techniques. Spatiotemporal data contains the information of both space and time simultaneously. Naturally, it is very much complicated and not easy to model. This article focuses on some modeling techniques to analyze a correlated spatiotemporal agricultural dataset. This dataset contains information of soil parameters for five years across the twenty six different locations with their geographical status in term of longitude and latitude. Soil pH and fertility index are the two major limiting factors in agriculture. These two parameters are governed by many other factors viz. fertilizer use, cropping intensity, soil type, geographical location, soil health management etc. Objective: The present study has been set up to explore whether there is any spatial gradient in the average pH levels across the geographical locations while fertility index and cropping intensity are acting as possible confounder. Methods: Soil pH is the response variable which varies with respect to time and space generally has a correlated structure. Besides this, some random effects component with fixed effects having a nonlinear association with the response is observed here. Generalized additive mixed model (GAMM) regression and Bivariate Smoothing techniques have been exercised to arrive at a meaningful conclusion. Conclusions: It is found that the pH value varies with change in latitude. Besides this, year, fertility index of available potassium and phosphate are also significant cofactors of this study. Final model has been selected through minimum AIC value (204.9) and model checking plots.
Keywords
Spatiotemporal Data, Spatial Gradient, PH, Fertility Index, Cropping Intensity, GAMM, Bivariate Smoothing
To cite this article
Sabyasachi Mukherjee, Tapan Kumar Garai, Correlated Spatiotemporal Data Modeling Using Generalized Additive Mixed Model and Bivariate Smoothing Techniques, Science Journal of Applied Mathematics and Statistics. Vol. 6, No. 2, 2018, pp. 49-57. doi: 10.11648/j.sjams.20180602.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Aerts, M., Claeskens, G., Wand, M. P., 2002. Some theory for penalized spline generalized additive models. Journal of Statistical Planning and Inference. 103, 455–470.
[2]
Ali, S. J, 2005. Fertilizer Recommendation for Principal Crops and Cropping Sequences of West Bengal. Booklet No.1 Department of Agriculture, Covernment of West Bengal, Kolkata – 700001
[3]
Antoaneta, A., 1995. Effects of Fertilizers Application And Soil pH on the Acidic and Sorptio Properties of Maize Trees. Bulg. J. Plant Physiol. 21(1), 52–57.
[4]
Annual Report, 2005. Office of the Deputy Director of Agriculture, Burdwan District, West Bengal, India.
[5]
Biswas, T. D., Mukherjee, S. K., 2006. Text Book of Soil Science. Tata-McGraw Hill Publishing Company Limited, New Delhi.
[6]
Breslow, N. E., Clayton, D. G., 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association. 88, 9–25.
[7]
Brumback, B., Rice, J. A., 1998. Smoothing spline models for the analysis of nested and crossed samples of curves. J. Am. Statist. Ass. 93, 961-1006.
[8]
Chatterjee, S., Hadi, A. S., 2006. Regression Analysis by Example, fifth ed. John Wiley & Sons, New Jersey.
[9]
Das, R. N., Kim, J., Mukherjee, S., 2017. Correlated log-normal composite error models for different scientific domains. Model Assisted Statistics and Applications. 12, 39–53
[10]
Das, R. N., Mukhopadhyay, A. C., 2017. Correlated random effects regression analysis for a log-normally distributed variable, Journal of Applied Statistics. 44:5, 897-915
[11]
Fahrmeir, L., Lang, S., 2001. Bayesian inference for generalized additive mixed models based on Markov random field priors. J. R. Statist. Soc. 50, 201 - 220.
[12]
Green, P. J., Silverman, B. W., 1994. Nonparametric Regression and Generalized Linear Models: A roughness penalty approach, first ed. Chapman and Hall, London.
[13]
HaÈrdle, W., 1990. Applied Non-parametric Regression Analysis, first ed. Cambridge University Press, Cambridge.
[14]
Hastie, T., Tibshirani, R., 1990. Generalized Additive Models, first ed. Chapman and Hall, London.
[15]
Hart, J. D., 1991. Kernel regression estimation with time series errors. J. R. Statist. Soc. B, 53, 173-187.
[16]
Hastie, T., Tibshirani, R., Friedman, J., 2001. The elements of statistical learning, first ed. Springer, USA
[17]
Hastie, T., Tibshirani, R., 1995. Generalized additive models for medical research. Statistical Methods in Medical Research. 4, 187-196
[18]
Kohn, R., Ansley, C. F., Tharm, D., 1991. The performance of cross-validation and maximum likelihood estimators of spline smoothing parameters. J. Am. Statist. Ass. 86, 1042-1050.
[19]
Lin, X., D. Zhang, 1999. Inference in generalized additive mixed models using smoothing splines. Journal of the Royal Statistical Society. Series B, 61, 381–400.
[20]
Mamouridis, V., 2011. Additive Mixed Models applied to the study of red shrimp landings: comparison between frequentist and Bayesian perspectives.
[21]
McCullagh, P., Nelder, J. A., 1989. Generalized Linear Models, 2nd ed., Chapman and Hall, London.
[22]
Mukherjee S., Kapoor S., Banerjee P., 2017. Diagnosis and Identification of Risk Factors for Heart Disease Patients Using Generalized Additive Model and Data Mining Techniques. J Cardiovasc Disease Res.; 8(4):137-44.
[23]
Official website of Burdwan District. West-Bengal, India, bardhaman.nic.in/home.html
[24]
Padoan, S. A., Wand, M. P., 2008. Mixed Model- based Additive Models for Sample Extremes. Statistics & Probability Letters. vol. 78, issue 17, 2850-2858.
[25]
Rice, J. A., Silverman, B. W., 1991. Estimating the mean and covariance structure non-parametrically when the data are curves. J. R. Statist. Soc. B, 53, 233-243.
[26]
Ruppert, D., Wand, M. P., Carroll, R. J., 2003. Semi parametric Regression, first ed. Cambridge University Press, New York.
[27]
Scheipl, F., 2010. amer version 0.6.5.: Using lme4 to fit Generalized Additive Mixed Model. R package. http://cran.r-project.org.
[28]
Scheipl, F., Munchen, L., 2010. amer: Using lme4 to fit Generalized Additive Mixed Models.
[29]
Verbyla, A. P., 1995. A mixed model formulation of smoothing splines and test linearity in generalized linear model. Technical Report 95/5, Department of Statistics, University of Adelaide, Adelaide.
[30]
Wahba, G., 1985. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Ann. Statist. 13, 1378-1402.
[31]
Wang, Y., 1998. Mixed effects smoothing spline analysis of variance. J. R. Statist. Soc. B, 60, 159-174.
[32]
Wand, M. P., 2003. Smoothing and mixed models. Computational Statistics. 18, 223–249.
[33]
Wand, M. P., Coull, B. A., French, J. L., Ganguli, B., Kammann, E. E., Staudenmayer, J, Zanobetti, A., 2005. SemiPar 1.0 Functions for semiparametric regression. R package. http://cran.r-project.org.
[34]
Wu. H., Zhang. J., 2006. Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed Effects Modeling Approaches, John Wiley & Sons, New Jersey
[35]
Wood S. N., 2006. Generalized Additive Models: An Introduction with R, Chapman & Hall/CRC Press.
[36]
Zeger, S. L., Diggle, P. J., 1994. Semi-parametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics, 50, 689-699.
[37]
Zhang, D., Lin, X., Raz, J., Sowers, M., 1998. Semi-parametric stochastic mixed models for longitudinal data. J. Am. Statist. Ass. 93, 710-719.
Browse journals by subject