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A quantile approach to the power transformed location–scale model


  • Grace Hong, Hyokyoung


The burgeoning growth of health care spending has become a major concern to policy makers, making the modeling of health care expenditure valuable in their decision-making processes. The challenges of health care expenditure analysis are two-fold: the exceptional skewness of its distribution as the top 5% of the population accounted for almost half of all spending and its heteroscedasticity. To address these concerns, the quantile regression model with power transformation has been employed, but at a price of the model complexity and analysis cost. In this article, we introduce a simpler quantile approach to the analysis of expenditure data by employing the location–scale model with an unknown link function to accommodate the heteroscedastic data with non-ignorable outliers. Specifically, in our approach a link function does not depend on quantiles; yet, it effectively fits the data as the slope coefficient depends on the quantiles. This parsimonious feature of our model helps us conduct a more intuitive and easily understood analysis for the whole distribution with fewer computational steps. Thus, it can be more widely applicable in practice. Additionally, simulation studies are conducted to investigate the model performance compared to other competing models. Analysis of the 2007 Medical Expenditure Panel Survey data using our model shows that aging and self-rated health tend to drive up costs. However, uninsured persons do not contribute to the high health cost. These findings suggest that careful monitoring of elderly’s health status and a more aggressive preventive medicare system may contribute to slow down the explosion of medical costs.

Suggested Citation

  • Grace Hong, Hyokyoung, 2013. "A quantile approach to the power transformed location–scale model," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 50-62.
  • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:50-62
    DOI: 10.1016/j.csda.2013.01.022

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    References listed on IDEAS

    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Hong, Hyokyoung Grace & He, Xuming, 2010. "Prediction of Functional Status for the Elderly Based on a New Ordinal Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 930-941.
    3. Jose A. F. Machado & Jose Mata, 2000. "Box-Cox quantile regression and the distribution of firm sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(3), pages 253-274.
    4. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    5. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
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