An econometric approach to the construction of ecological indices: A case study using the food provision goal of the Ocean Health Index

Ecological indices summarize large sets of complex data to improve performance monitoring, benchmarking, policy analysis, and public communication. Indices, such as the Ocean Health Index, are sensitive to the aggregation method and weighting scheme used in the construction of the index. This analysis investigates the differences in the mathematical properties and aggregate behaviour of eight aggregation methods and weighting schemes, and considers how information about desired index behaviour can be used to make a final choice of the mathematical form for the index. The mathematical properties of these aggregation methods and weighting schemes are compared using the axiomatic approach to index number theory, and a case study of the fisheries sub- goal of the Ocean Health Index. The results show that the exponentially weighted geometric mean with proportional weight, and the weighted arithmetic mean with proportional weight perform the best in terms of their underlying mathematical properties and aggregate behaviour. The results highlight the importance of setting achievable objectives that inform which mathematical properties and aggregate behaviour are most desirable; from this, one can select an appropriate aggregation method for constructing indices that rely on averages.