A Comparative Study of Some Estimation Methods in Simple Linear Regression Model for Different Sample Sizes in Presence of Outliers

The aim of this study was to compare some estimation methods (LS, M, S, LTS and MM) for estimating the parameters of simple linear regression model in the presence of outlier and different sample size (10, 20, 30, 50 and 100). To compare methods, the effect of chest girth on body weights of Karayaka lambs at weaning period was examined. Chest girth of lambs was used as independent variable and body weight at weaning period was used as dependent variable in the study. Also, it was taken consideration that there were 10-20% outliers of data set for different sample sizes. Mean square error (MSE) and coefficient of determination (R2 ) values were used as criteria to evaluate the estimator performance. Research findings showed that LTS estimator is the best models with minimum MSE and maximum R2 values for different size of sample in the presence of outliers. Thereby, LTS method can be proposed, to predict best-fitted model for relationship between chest girth and body weights of Karayaka lambs at weaning period, to the researches who are studying on small ruminants as an alternative way to estimate the regression parameters in the presence of outliers for different sample size.

PDF

___

Alma ÖG. 2011. Comparison of robust regression methods in linear regression. Int. J. Contemp. Math. Sciences, 6 (9), 409-421. Anonymous. 2013. http://ci.columbia.edu/ci/premba_test/c0331/s7/s7_6.html, Accessed on: 30 July 2013.

Atta M, El khidir OA. 2004. Use of heart girth, wither height and scapuloischial length for prediction of liveweight of Nilotic sheep. Small Ruminant Res, 55 (1): 233-237.

Benyi K. 1997. Estimation of live weight from chest girth in pure and crossbred West African goats. Trop Anim Health Pro, 29 (2): 124-128.

Çankaya S, Eker S, Tahtali Y, Ceyhan A. 2011. Comparison of some estimation methods for parameters of simple regression model in the presence of outliers. 7th National Animal Science Congress, 14-16 September, 2011, Adana, Turkey, p:136-141.

Çankaya S, Kayaalp GT, Sangun L, Tahtali Y, Akar M. 2006. A comparative study of estimation methods for parameters in multiple linear regression model. J Appl Anim Res, 29 (1), 43- 47.

Çankaya S. 2009. A comparative study of some estimation methods for parameters and effects of outliers in simple regression model for research on small ruminants. Trop Anim Health Pro, 41 (1): 35-41.

Chen C. 2002. Robust regression and outlier detection with the robustreg procedure. SUGI Paper, 265-27, 2002.

Faustini M, Colombani C, Vigo D, Communod R, Russo V, Chlapanidas T, Munari E, Morandotti A, Torre ML. 2010.

Dimensional analysis of milk fat globules in sow milk: effects of the lactation stage and fat content and comparison with vaccine milk. Vet Res Comm, 34 (1), 29-32.

Huber PJ. 1973. Robust regression: asymptotics, conjectures and Monte Carlo. Ann. Stat., 1 (5), 799-821.

McKean JW, Sheather SJ, Hettmansperger TP. 1993. The use and interpretation of residuals based on robust estimation. J Am Stat Assoc, 88 (424), 1254-1263.

Miller SJ. 2006. The method of least squares. Mathematics Department Brown University. 1-7.

Montgomery DC, Peck EA, Vining GG. 2012. Introduction to linear regression analysis (Vol. 821). Wiley.

Nsoso SJ, Aganga AA, Moganetsi BP, Tshwenyane SO. 2003. Body weight, body condition score and heart girth in indigenous Tswana goats during the dry and wet seasons in southeast Botswana. Livest Res Rural Dev, 15 (4).

Olive DJ, Hawkins DM. 2003. Robust regression with high coverage. Stat Probabil Lett, 63 (3), 259-266.

Palmer Pol A, Pascual MB, Vázquez PC. 2006. Robust estimators and bootstrap confidence intervals applied to tourism spending. Tourism Manage, 27 (1), 42-50.

Pérez B, Molina I, Peña D. 2013. Outlier detection and robust estimation in linear regression models with fixed group effects. J Stat Comput Sim, (ahead-of-print), 1-18.

Rousseeuw P, Yohai V. 1984. Robust regression by means of Sestimators. In Robust and nonlinear time series analysis, Springer US, 256-272.

Rousseeuw PJ, Leroy A. 1987. Robust regression and outlier detection, John Wiley & Sons, New York.

Rousseeuw PJ. 1984. Least median of squares regression. J Am Stat Assoc, 79 (388), 871-880.

Sarti FM, Castelli L, Bogani D, Panella F. 2009. The measurement of chest girth as an alternative to weight determination in the performance recording of meat sheep. Ital J Anim Sci, 2 (2): 123-129.

SAS Institute Inc. 2009. SAS/STAT ® 9.2, Users Guide, Chapter 74: The ROBUSTREG Procedure, Second Edition, Cary, NC: USA.

SAS Intstitute Inc. 2002. SAS/STAT Software, Version 9. (Cary, NC, USA).

Schumacker RE, Monahan MP, Mount RE. 2002. A comparison of OLS and robust regression using S-PLUS. Multiple Linear Regression Viewpoints, 28, 10-13.

SPSS. 1999. SPSS for Windows (Release 10.0). Standard Version. SPSS, Chicago, IL.

Stromberg AJ. 1993. Computation of high breakdown nonlinear regression parameters. J Am Stat Assoc, 88 (421), 237-244.

Topal M, Macit M. 2004. Prediction of body weight from body measurements in Morkaraman sheep. J Appl Anim Res, 25 (2): 97-100.

Yadav DK, Arora R, Bhatia S, Singh G, Bhar LM. 2011. Robust regression for determining selection criterion of breeding rams. Indian J Small Rumin, 17 (2), 166-169.

Yohai VJ. 1987. High breakdown-point and high efficiency robust estimates for regression. Ann. Stat, 642-656.

Zaman A, Rousseeuw PJ, Orhan M. 2001. Econometric applications of high-breakdown robust regression techniques. Economics Letters, 71 (1), 1-8.