Regression Analysis involving Circular Response and Circular Explanatory Variable

S. Bhattacharjee¹ , K.K. Das²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.95-99, Aug-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.9599

Online published on Aug 31, 2018

Copyright © S. Bhattacharjee, K.K. Das . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, two regression models predicting a circular response from a circular predictor are discussed and a new measure for model comparison is introduced. A circular observation is the one which arises in terms of angles. In the first model, the expected value of the response is modeled in terms of Fourier series expansion of the circular predictor whereas the second model consists in minimizing the least circular distance (LCD) between the actual and predicted values of the response. The application of the regression models is exhibited through a data set on wind directions, measured during morning and evening at Silchar Meteorological observatory, Assam, in the Post Monsoon season, wherein the wind direction measured during the evening is modeled as a function of the wind direction measured during the morning. It is found that the wind direction during the evening is not changing significantly with respect to that during the morning. Also, the proposed measure for model comparison shows that the conditional regression model is a better fitting comparison to the LCD regression model.

Key-Words / Index Term :
Regression, circular response, circular predictor, model comparison

References :
[1] J.S. Rao, A. Sengupta, “Topics in Circular Statistics”, World Scientific Publishing Co. Pte. Ltd, Singapore, pp.187-195, 2001.
[2] K.V. Mardia, P.E. Jupp, “Directional Statistics”, John Wiley and Sons Ltd., Chichester, pp.13, 2000.
[3] S.R. Jammalamadaka, U.L. Lund, “The effect of wind direction on ozone levels: a case study”. Environmental and Ecological Statistics, Vol.13, pp.287–298, 2006.
[4] L.P. Rivest, “A decentred predictor for circular–circular regression”. Biometrika, Vol.84, pp.717-726 , 1997.
[5] T.D. Downs, K.V. Mardia, “Circular regression”. Biometrika, Vol.89, pp.683-697, 2002.
[6] S. Kato, K. Shimizu, G.S. Shieh, “A circular-circular regression model”, Statistica Sinica, Vol.18, pp.633-645, 2008.
[7] S.R. Jammalamadaka, Y.R. Sarma, “Circular Regression”. In: Matusita, K. (Ed.), Statistical Sciences and Data Analysis. VSP, Utrecht, pp.109-128, 1993.
[8] U. Lund, “Least circular distance regression for directional data”, Journal of Applied Statistics, Vol.26, Issue.6, pp.723–733, 1999.
[9] N. Fisher, “Statistical Ananlysis of Circular Data”, Cambridge University Press, Cambridge, pp.151, 1993.
[10] S.R. Jammalamadaka, Y.R. Sarma, “A correlation coefficient for angular variables”, Statistical Theory and Data Analysis, Vol.2, pp. 349–364, 1988.
[11] U. Lund, C. Agostinelli, “Circstats: circular statistics, from "topics in circular statistics"”. R package version 0.2–4. Available from http://www.cran.r-project.org/package=circstats, 2012.
[12] U. Lund, C. Agostinelli, “Circular: circular statistics”. R package version 0.4–7, Available from http://www.cran.r-project.org/package=circular, 2013.