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ARS Home » Pacific West Area » Corvallis, Oregon » Forage Seed and Cereal Research Unit » Research » Publications at this Location » Publication #287781
Title: What is a good index? Problems with statistically based indicators and the Malmquist index as alternative

Author
item Whittaker, Gerald
item LAUTENBACH, SVEN - Helmholtz Centre
item VOLK, MARTIN - Helmholtz Centre

Submitted to: Environmental Modelling & Software
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/31/2012
Publication Date: 8/6/2014
Citation: Whittaker, G.W., Lautenbach, S., Volk, M. 2014. What is a good index? Problems with statistically based indicators and the Malmquist index as alternative. Environmental Modelling & Software. 925-932.

Interpretive Summary: Conventional multivariate statistical methods have been used for decades to calculate environmental indicators. These methods generally work fine if they are used in a situation where the method can be tailored to the data. But there is some skepticism that the methods might fail where the data do not have "nice" properties in a statistical sense. The aim of the paper is to demonstrate some of the shortcomings of some of the popular methods and to identify how the Malmquist index might be used as an alternative. The paper presents the results of an exhaustive review in the field of environment, hydrology and water quality which identified the most commonly used approaches. We then compare the most popular method, principal component analysis with the Malmquist index, using a synthetic data set with known properties. We found that the Malmquist index approach always produced good results. On the same data set, the statistical method failed and gave results that are not usable, or worse, misleading. This result calls into question many of the results reported for the calculation of an index in geoscience applications.

Technical Abstract: Conventional multivariate statistical methods have been used for decades to calculate environmental indicators. These methods generally work fine if they are used in a situation where the method can be tailored to the data. But there is some skepticism that the methods might fail in the context of skewed data distributions or spatial auto-correlation. Further, the indicators developed by statistical approaches cannot be used to compare different regions or time periods that had not been covered by the input data. The aim of the paper is to demonstrate some of the shortcomings and to identify how the Malmquist index might be used as an alternative. The paper presents the results of an exhaustive review in the field of environment, hydrology and water quality which identified the most commonly used approaches. Then principal component analysis as representative of these approaches and the Malmquist index are challenged with simulated time series data to demonstrate the failure of statistical methods in two of the most common problems faced in construction of a water quality index.