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Modelling Variance Heterogeneity in Normal Regression Using GLIM

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  • Murray Aitkin

Abstract

This paper describes and presents simple GLIM macros for the modelling of variance heterogeneity in normal regression analysis, using a log‐linear regression model for the variance. The procedure is illustrated with two examples.

Suggested Citation

  • Murray Aitkin, 1987. "Modelling Variance Heterogeneity in Normal Regression Using GLIM," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 332-339, November.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:3:p:332-339
    DOI: 10.2307/2347792
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    1. Jin-Guan Lin & Li-Xing Zhu & Feng-Chang Xie, 2009. "Heteroscedasticity diagnostics for t linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 59-77, June.
    2. N. David Yanez & Richard Kronmal & Jennifer Nelson & Todd Alonzo, 2002. "Analysing change in clinical trials using quasi-likelihoods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1135-1145.
    3. Yeşim Güney & Yetkin Tuaç & Şenay Özdemir & Olcay Arslan, 2021. "Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution," Computational Statistics, Springer, vol. 36(2), pages 805-827, June.
    4. Cheng, Tsung-Chi, 2011. "Robust diagnostics for the heteroscedastic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1845-1866, April.
    5. Jin-Guan Lin & Li-Xing Zhu & Chun-Zheng Cao & Yong Li, 2011. "Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1509-1531, August.
    6. Juli?n Messina & Anna Sanz-de-Galdeano, 2014. "Wage Rigidity and Disinflation in Emerging Countries," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(1), pages 102-133, January.
    7. Liucang Wu & Huiqiong Li, 2012. "Variable selection for joint mean and dispersion models of the inverse Gaussian distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 795-808, August.
    8. Afrânio M.C. Vieira & Roseli A. Leandro & Clarice G.B. Dem�trio & Geert Molenberghs, 2011. "Double generalized linear model for tissue culture proportion data: a Bayesian perspective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1717-1731, September.
    9. Kuhnt, Sonja & Rudak, Nikolaus, 2013. "Simultaneous Optimization of Multiple Responses with the R Package JOP," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i09).
    10. Li, Kim-Hung & Chan, Nai Ng, 2000. "Degeneracy in Heteroscedastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 282-295, August.
    11. Hedeker, Donald & Nordgren, Rachel, 2013. "MIXREGLS: A Program for Mixed-Effects Location Scale Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i12).
    12. George Leckie & Robert French & Chris Charlton & William Browne, 2014. "Modeling Heterogeneous Variance–Covariance Components in Two-Level Models," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 307-332, October.
    13. Liu-Cang Wu & Zhong-Zhan Zhang & Deng-Ke Xu, 2012. "Variable selection in joint mean and variance models of Box--Cox transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2543-2555, August.
    14. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    15. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1624-1631.
    16. Kristy P. Robledo & Ian C. Marschner, 2021. "A new algorithm for fitting semi-parametric variance regression models," Computational Statistics, Springer, vol. 36(4), pages 2313-2335, December.
    17. Luz Marina Rondon & Heleno Bolfarine, 2016. "Bayesian analysis of generalized elliptical semi-parametric models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1508-1524, June.
    18. Tsung-Shan Tsou, 2005. "Inferences of variance function - a parametric robust way," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(8), pages 785-796.
    19. Hui Zheng & Y. Claire Yang & Kenneth C. Land, 2016. "Age-Specific Variation in Adult Mortality Rates in Developed Countries," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 35(1), pages 49-71, February.
    20. Ilmari Juutilainen & Juha Roning, 2010. "How to compare interpretatively different models for the conditional variance function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 983-997.
    21. Jun Zhao & Guan’ao Yan & Yi Zhang, 2022. "Robust estimation and shrinkage in ultrahigh dimensional expectile regression with heavy tails and variance heterogeneity," Statistical Papers, Springer, vol. 63(1), pages 1-28, February.
    22. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    23. Shelley A. Blozis & Ricardo Villarreal & Sweta Thota & Nicholas Imparato, 2019. "Using a two-part mixed-effects model for understanding daily, individual-level media behavior," Journal of Marketing Analytics, Palgrave Macmillan, vol. 7(4), pages 234-250, December.
    24. Donald Hedeker & Robin J. Mermelstein & Hakan Demirtas, 2008. "An Application of a Mixed-Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data," Biometrics, The International Biometric Society, vol. 64(2), pages 627-634, June.

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