IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v169y2006i2p273-288.html
   My bibliography  Save this article

Extending the Box–Cox transformation to the linear mixed model

Author

Listed:
  • Matthew J. Gurka
  • Lloyd J. Edwards
  • Keith E. Muller
  • Lawrence L. Kupper

Abstract

Summary. For a univariate linear model, the Box–Cox method helps to choose a response transformation to ensure the validity of a Gaussian distribution and related assumptions. The desire to extend the method to a linear mixed model raises many vexing questions. Most importantly, how do the distributions of the two sources of randomness (pure error and random effects) interact in determining the validity of assumptions? For an otherwise valid model, we prove that the success of a transformation may be judged solely in terms of how closely the total error follows a Gaussian distribution. Hence the approach avoids the complexity of separately evaluating pure errors and random effects. The extension of the transformation to the mixed model requires an exploration of its potential effect on estimation and inference of the model parameters. Analysis of longitudinal pulmonary function data and Monte Carlo simulations illustrate the methodology discussed.

Suggested Citation

  • Matthew J. Gurka & Lloyd J. Edwards & Keith E. Muller & Lawrence L. Kupper, 2006. "Extending the Box–Cox transformation to the linear mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 273-288, March.
  • Handle: RePEc:bla:jorssa:v:169:y:2006:i:2:p:273-288
    DOI: 10.1111/j.1467-985X.2005.00391.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-985X.2005.00391.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-985X.2005.00391.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Manning, Willard G., 1998. "The logged dependent variable, heteroscedasticity, and the retransformation problem," Journal of Health Economics, Elsevier, vol. 17(3), pages 283-295, June.
    3. Ann Oberg & Marie Davidian, 2000. "Estimating Data Transformations in Nonlinear Mixed Effects Models," Biometrics, The International Biometric Society, vol. 56(1), pages 65-72, March.
    4. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kazushi Maruo & Takaharu Yamabe & Yusuke Yamaguchi, 2017. "Statistical simulation based on right skewed distributions," Computational Statistics, Springer, vol. 32(3), pages 889-907, September.
    2. Patricia Dörr & Jan Pablo Burgard, 2019. "Data-driven transformations and survey-weighting for linear mixed models," Research Papers in Economics 2019-16, University of Trier, Department of Economics.
    3. Natalia Rojas‐Perilla & Sören Pannier & Timo Schmid & Nikos Tzavidis, 2020. "Data‐driven transformations in small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 121-148, January.
    4. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    5. John A. D. Aston & Jeng‐Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317, March.
    6. Ileana Baldi & Eva Pagano & Paola Berchialla & Alessandro Desideri & Alberto Ferrando & Franco Merletti & Dario Gregori, 2013. "Modeling healthcare costs in simultaneous presence of asymmetry, heteroscedasticity and correlation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 298-310, February.
    7. Nora Würz & Timo Schmid & Nikos Tzavidis, 2022. "Estimating regional income indicators under transformations and access to limited population auxiliary information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1679-1706, October.
    8. Shonosuke Sugasawa & Tatsuya Kubokawa, 2015. "Box-Cox Transformed Linear Mixed Models for Positive-Valued and Clustered Data," CIRJE F-Series CIRJE-F-957, CIRJE, Faculty of Economics, University of Tokyo.
    9. Paul Walter & Marcus Groß & Timo Schmid & Nikos Tzavidis, 2021. "Domain prediction with grouped income data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1501-1523, October.
    10. Huapeng Li & Yukun Liu & Riquan Zhang, 2019. "Small area estimation under transformed nested-error regression models," Statistical Papers, Springer, vol. 60(4), pages 1397-1418, August.
    11. Tzavidis, Nikos & Zhang, Li-Chun & Luna Hernandez, Angela & Schmid, Timo & Rojas-Perilla, Natalia, 2016. "From start to finish: A framework for the production of small area official statistics," Discussion Papers 2016/13, Free University Berlin, School of Business & Economics.
    12. Gurka, Matthew J. & Edwards, Lloyd J. & Nylander-French, Leena, 2007. "Testing transformations for the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4297-4307, May.
    13. Jiang, Jiakun & Lin, Huazhen & Zhong, Qingzhi & Li, Yi, 2022. "Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Hiroshi Ishijima & Akira Maeda, 2015. "Real Estate Pricing Models: Theory, Evidence, and Implementation," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(4), pages 369-396, November.
    15. Villandré Luc & Hutcheon Jennifer A & Perez Trejo Maria Esther & Abenhaim Haim & Jacobsen Geir & Platt Robert W, 2011. "Modeling Fetal Weight for Gestational Age: A Comparison of a Flexible Multi-level Spline-based Model with Other Approaches," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-26, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patrick Richard & Regine Walker & Pierre Alexandre, 2018. "The burden of out of pocket costs and medical debt faced by households with chronic health conditions in the United States," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-13, June.
    2. Trottmann, Maria & Zweifel, Peter & Beck, Konstantin, 2012. "Supply-side and demand-side cost sharing in deregulated social health insurance: Which is more effective?," Journal of Health Economics, Elsevier, vol. 31(1), pages 231-242.
    3. Buntin, Melinda Beeuwkes & Zaslavsky, Alan M., 2004. "Too much ado about two-part models and transformation?: Comparing methods of modeling Medicare expenditures," Journal of Health Economics, Elsevier, vol. 23(3), pages 525-542, May.
    4. Keith Davis & Timothy Bell & Jacqueline Miller & Derek Misurski & Bela Bapat, 2011. "Hospital costs, length of stay and mortality associated with childhood, adolescent and young Adult meningococcal disease in the US," Applied Health Economics and Health Policy, Springer, vol. 9(3), pages 197-207, May.
    5. Jones, A.M, 2010. "Models For Health Care," Health, Econometrics and Data Group (HEDG) Working Papers 10/01, HEDG, c/o Department of Economics, University of York.
    6. Caballer-Tarazona, Vicent & Guadalajara-Olmeda, Natividad & Vivas-Consuelo, David, 2019. "Predicting healthcare expenditure by multimorbidity groups," Health Policy, Elsevier, vol. 123(4), pages 427-434.
    7. Barry T. Hirsch & Edward J. Schumacher, 2012. "Underpaid or Overpaid? Wage Analysis for Nurses Using Job and Worker Attributes," Southern Economic Journal, John Wiley & Sons, vol. 78(4), pages 1096-1119, April.
    8. Toni Mora & Joan Gil & Antoni Sicras-Mainar, 2012. "The Influence of BMI, Obesity and Overweight on Medical Costs: A Panel Data Approach," Working Papers 2012-08, FEDEA.
    9. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    10. Toni Mora & Joan Gil & Antoni Sicras-Mainar, 2015. "The influence of obesity and overweight on medical costs: a panel data perspective," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 16(2), pages 161-173, March.
    11. Marcel Bilger & Willard G. Manning, 2015. "Measuring Overfitting In Nonlinear Models: A New Method And An Application To Health Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 24(1), pages 75-85, January.
    12. Jay Dev Dubey, 2021. "Measuring Income Elasticity of Healthcare-Seeking Behavior in India: A Conditional Quantile Regression Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(4), pages 767-793, December.
    13. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    14. Avi Dor & Partha Deb & Michael Grossman & Gregory Cooper & Siran Koroukian & Fang Xu, 2013. "Impact of Mortality-Based Performance Measures on Hospital Pricing: the Case of Colon Cancer Surgeries," NBER Working Papers 19447, National Bureau of Economic Research, Inc.
    15. Kaushik Ghosh & Irina Bondarenko & Kassandra L Messer & Susan T Stewart & Trivellore Raghunathan & Allison B Rosen & David M Cutler, 2020. "Attributing medical spending to conditions: A comparison of methods," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-17, August.
    16. Ying Qiu & Alex Fu & Gordon Liu & Dale Christensen, 2010. "Healthcare costs of atypical antipsychotic use for patients with bipolar disorder in a medicaid programme," Applied Health Economics and Health Policy, Springer, vol. 8(3), pages 167-177, May.
    17. Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-10, January.
    18. Galina Besstremyannaya, 2012. "Estimating income equity in social health insurance system," Working Papers w0172, Center for Economic and Financial Research (CEFIR).
    19. Inmaculada Martínez-Zarzoso, 2013. "The log of gravity revisited," Applied Economics, Taylor & Francis Journals, vol. 45(3), pages 311-327, January.
    20. Mary A. Burke & Ali Ozdagli, 2013. "Household inflation expectations and consumer spending: evidence from panel data," Working Papers 13-25, Federal Reserve Bank of Boston.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssa:v:169:y:2006:i:2:p:273-288. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.