| BOX-COX TRANSFORMATIONS IN THE ANALYSIS OF COMPOSITIONAL DATA |
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| 作者姓名： | WILLIAM S.RAYENS CIDAMBI SRINIVASAN |
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| 作者单位： | WILLIAM S.RAYENS CIDAMBI SRINIVASAN Department of Statistics，University of Kentucky，Lexington，KY 40506，U.S.A. |
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| 摘 要： | The statistical analysis of compositional data is of fundamental importance to practitioners in generaland to chemists in particular.The existing methodology is principally due to Aitchison,who effectivelyuses two transformations,a ratio followed by the logarithmic,to create a useful,coherent theory thatin principle allows the plethora of normal-based multivariate techniques to be used on the transformeddata.This paper suggests that the well-known class of Box-Cox transformations can be employed inplace of the logarithmic to significantly improve the existing methodology.This is supported in part byshowing that one of the most basic problems that Aitchison managed to overcome,namely thespecification of an interpretable covariance structure for compositional data,can be resolved,or nearlyresolved,once the ratio transformation has been applied.Hence the resolution is not directly dependenton the logarithmic transformation.It is then verified that access to the general Box-Cox family will allowa more accurate use of the normal-based multivariate techniques,simply because better fits to normalitycan be achieved.Finally,maximum likelihood estimation and some associated asymptotics are employedto construct confidence intervals for ratios of the true,unknown compositional constituents.Heretoforethis had not been done even in the context of the logarithmic transformation.Applications to real dataare presented.
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BOX-COX TRANSFORMATIONS IN THE ANALYSIS OF COMPOSITIONAL DATA |
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| WILLIAM S.RAYENS CIDAMBI SRINIVASAN.BOX-COX TRANSFORMATIONS IN THE ANALYSIS OF COMPOSITIONAL DATA[J].Journal of Geographical Sciences,1991(3). |
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| Authors: | WILLIAM SRAYENS CIDAMBI SRINIVASAN |
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| Institution: | WILLIAM S.RAYENS CIDAMBI SRINIVASAN Department of Statistics,University of Kentucky,Lexington,KY,U.S.A. |
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| Abstract: | The statistical analysis of compositional data is of fundamental importance to practitioners in general and to chemists in particular.The existing methodology is principally due to Aitchison,who effectively uses two transformations,a ratio followed by the logarithmic,to create a useful,coherent theory that in principle allows the plethora of normal-based multivariate techniques to be used on the transformed data.This paper suggests that the well-known class of Box-Cox transformations can be employed in place of the logarithmic to significantly improve the existing methodology.This is supported in part by showing that one of the most basic problems that Aitchison managed to overcome,namely the specification of an interpretable covariance structure for compositional data,can be resolved,or nearly resolved,once the ratio transformation has been applied.Hence the resolution is not directly dependent on the logarithmic transformation.It is then verified that access to the general Box-Cox family will allow a more accurate use of the normal-based multivariate techniques,simply because better fits to normality can be achieved.Finally,maximum likelihood estimation and some associated asymptotics are employed to construct confidence intervals for ratios of the true,unknown compositional constituents.Heretofore this had not been done even in the context of the logarithmic transformation.Applications to real data are presented. |
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| Keywords: | Unit-sum constraint Mixing proportions Ratio data |
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