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Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale

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  • Ricardo Ramírez-Aldana
  • Lizbeth Naranjo

Abstract

Random intercept models are linear mixed models (LMM) including error and intercept random effects. Sometimes heteroscedasticity is included and the response variable is transformed into a logarithmic scale, while inference is required in the original scale; thus, the response variable has a log-normal distribution. Hence, correction terms should be included to predict the response in the original scale. These terms multiply the exponentiated predicted response variable, which subestimates the real values. We derive the correction terms, simulations and real data about the income of elderly are presented to show the importance of using them to obtain more accurate predictions. Generalizations for any LMM are also presented.

Suggested Citation

  • Ricardo Ramírez-Aldana & Lizbeth Naranjo, 2021. "Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-21, April.
  • Handle: RePEc:plo:pone00:0249910
    DOI: 10.1371/journal.pone.0249910
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    References listed on IDEAS

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    1. Luigi Ermini & David F. Hendry, 2008. "Log Income vs. Linear Income: An Application of the Encompassing Principle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 807-827, December.
    2. Elbers, Chris & Lanjouw, Jean O. & Lanjouw, Peter, 2002. "Micro-level estimation of welfare," Policy Research Working Paper Series 2911, The World Bank.
    3. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    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.
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    Cited by:

    1. Xu, Yujie & Wang, Yinan, 2023. "Has financial development made income more equal? – From the perspective of regional development imbalance," International Review of Financial Analysis, Elsevier, vol. 90(C).

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