A computational approach test for comparing two linear regression models with unequal variances

Year 2021, Volume: 50 Issue: 6, 1756 - 1772, 14.12.2021

Mehmet Yazıcı Fikri Gökpınar , Esra Gökpınar , Meral Ebegil , Yaprak Özdemir

https://doi.org/10.15672/hujms.784623

Cited By: 1

Abstract

In this study, a new testing procedure is proposed to compare two linear regression models based on a computational approach test when the variances are not assumed to be equal. This method is based on restricted maximum likelihood estimators and some simple computational steps. To assess performance of the proposed test, it was compared with some existing tests in terms of power and type I error rate of the test. The simulation study reveals that the proposed test is a better alternative than some existing tests in most considered cases. Besides, an illustration of the proposed test was given by using a sample dataset.

Keywords

Chow Test, Computational Approach Test, Parametric Bootstrap Test, Heteroscedasticity regression models

References

• [1] M.M. Ali and J.L. Silver, Tests for equality between sets of coefficients in two linear regressions under heteroscedasticity, J. Amer. Statist. Assoc. 80 (391), 730-735, 1985.
• [2] C.H. Chang, J.J. Lin and N. Pal, Testing the equality of several gamma means: A parametric bootstrap method with applications, Comput. Statist. 26 (1), 55-76, 2011.
• [3] C.H. Chang and N. Pal, A revisit to the Behren-Fisher Problem: Comparison of five test methods, Comm. Statist. Simulation Comput. 37 (6), 1064-1085, 2008.
• [4] C.H. Chang, N. Pal, W.K. Lim and J. J. Lin, A note on comparing several Poisson means, Comm. Statist. Simulation Comput. 39 (8), 1605-1627, 2010.
• [5] G.C. Chow, Tests of equality between sets of coefficients in two linear regressions, Econometrica 28 (3), 591-605, 1960.
• [6] M.D. Conerly and E.R. Mansfield, An approximate test for comparing heteroscedastic regression models, J. Amer. Statist. Assoc. 83 (403), 811-817, 1988.
• [7] A.C. Davison and D.V. Hinkley, Bootstrap Methods and their Application, Cambridge University Press, 1997.
• [8] T.J. Diciccio, M.A. Martin and S.E. Stern, Simple and accurate one-sided inference from signed roots of likelihood ratios, Canad. J. Statist. 29 (1), 67-76, 2001.
• [9] E.Y. Gokpinar and F. Gokpinar, A test based on the computational approach for equality of means under the unequal variance assumption, Hacet. J. Math. Stat. 41(4), 605-613, 2012.
• [10] E.Y. Gokpinar, E. Polat, F. Gokpinar and S. Gunay, A new computational approach for testing equality of inverse gaussian means under heterogeneity, Hacet. J. Math. Stat. 42 (5), 581-590, 2013.
• [11] F. Gokpinar and E. Gokpinar, Testing the equality of several Log-normal means based on a computational approach, Comm. Statist. Simulation Comput. 46 (3), 1998-2010, 2017.
• [12] S.M. Goldfeld and R.E. Quandt, Asymptotic tests for the constancy of regressions in the heteroscedastic case, Econometric Research Program Research Memorandum, Princeton University 229, 1978.
• [13] S.A. Gupta, Testing the equality between sets of coefficients in two linear regressions when disturbances are unequal, PhD thesis, Purdue University, 1978.
• [14] H. Haghbin, M.R. Mahmoudi and Z. Shishebor, Large sample inference on the ratio of two independent binomial proportions, J. Math. Ext. 5 (1), 87-95, 2015.
• [15] D.J. Hand, F. Daly, A.D. Lunn, K.J. McConway and E. Ostrowski, A Handbook of Small Data Sets, Chapman and Hall, 1994.
• [16] Y. Honda, On tests of equality between sets of coefficients in two linear regressions when disturbance variances are unequal, The Manchester School 50 (2), 116-125, 1982.
• [17] W.A. Jayatissa, Tests of equality between sets of coefficients in two linear regressions when disturbance variances are unequal, Econometrica 45 (5), 1291-1292, 1977.
• [18] K.R. Kadiyala and S. Gupta, Tests for pooling cross-sectional data in the presence of heteroscedasticity, Bulletin of the Institute of Mathematical Statistics 7, 275-276, 1978.
• [19] K. Knight, Mathematical Statistics, Chapman and Hall, 1999. A computational approach test for comparing two linear regression models 17
• [20] M.R. Mahmoudi, J. Behboodian, and M. Maleki, Large sample inference about the ratio of means in two independent populations, J. Stat. Theory Appl. 16 (3), 366-374, 2017.
• [21] M.R. Mahmoudi and M. Mahmoodi, Inferrence on the ratio of variances of two independent populations, J. Math. Ext. 7 (2), 83-91, 2014.
• [22] M.R. Mahmoudi, A.R. Nematollahi and A.R. Soltani, On the detection and estimation of the simple harmonizable processes, Iran. J. Sci. Technol. Trans. A: Sci. 39 (2), 239- 242, 2015.
• [23] E. Moreno, F. Torres and G. Casella, Testing equality of regression coefficients in heteroscedastic normal regression models, J. Statist. Plann. Inference 131 (1), 117- 134, 2005.
• [24] D. Oberhelman and R. Kadiyala, A test for the equality of parameters for separate regression models in the presence of heteroscedasticity, Comm. Statist. Simulation Comput. 36 (1), 99-121, 2007.
• [25] K. Ohtani and T. Toyoda, A Monte Carlo study of the Wald, LM, and LR tests in a heteroscedastic linear model, Comm. Statist. Simulation Comput. 14 (3), 735-746, 1985.
• [26] N. Pal, W.K. Lim and C.H. Ling, A computational approach to statistical inferences, J. Appl. Probab. 2 (1), 13-35, 2007.
• [27] J.J. Pan, M.R. Mahmoudi, D. Baleanu and M. Maleki, On comparing and classifying several independent linear and non-linear regression models with symmetric errors, Symmetry 11 (6), 820, 2019.
• [28] S.M. Sadooghi-Alvandi, A.A. Jafari, and H.A. Mardani-Fard, Comparing several regression models with unequal variances, Comm. Statist. Simulation Comput. 45 (9), 3190-3216, 2016.
• [29] P. Schmidt and R. Sickles, Some further evidence on the use of the Chow test under heteroscedasticity, Econometrica 45 (5), 1293-1298, 1977.
• [30] A. Schworer and D.P. Hovey, NewtonRaphson versus fisher scoring algorithms in calculating maximum likelihood estimates, in: Electronic Proceedings of Undergraduate Mathematics Day, University of Dayton, 1, 111, 2004.
• [31] J.G. Thursby, A comparison of several exact and approximate tests for structural shift under heteroscedasticity, J. Econometrics 53 (1-3), 363-386, 1992.
• [32] JL. Tian, C. Ma and A. Vexler, A parametric bootstrap test for comparing heteroscedastic regression models, Comm. Statist. Simulation Comput. 38 (5), 1026-1036, 2009.
• [33] T. Toyoda,Use of the Chow test under heteroscedasticity, Econometrica 42 (3), 601608, 1974.
• [34] P.A. Watt, Tests of equality between sets of coefficients in two linear regressions when disturbance variances are unequal: Some small properties, The Manchester School 47 (4), 391-396, 1979.
• [35] J. Xu and X. Li, A fiducial p-value approach for comparing heteroscedastic regression models, Comm. Statist. Simulation Comput. 47 (2), 420-431, 2018.