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When Category-based Indices Encounter Non-independent Categories: Solving the Taxonomy Issue in Resource-based Empirical Studies

Huo, Dong and Motohashi, Kazuyuki (2013): When Category-based Indices Encounter Non-independent Categories: Solving the Taxonomy Issue in Resource-based Empirical Studies. Published in:

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Abstract

Category-based measures such as the cosine index, Herfindahl index, entropy index, Euclidean distance, and Pearson’s correlation coefficient are widely applied in resource-based studies. However, when adopting these indices in empirical studies with respect to the categories of industry, technology, or knowledge, the inherent relatedness between the categories gives rise to a taxonomy issue, as the categories are not naturally inter-independent (as they are supposed to be in the application of the original indices) owing to inaccuracies in classification or categorization. Therefore, category-based indices may fail to produce a valid measurement, and this unmeasured relatedness can result in endogeneity in empirical analyses. To solve this issue, this study proposes new indices that can harness the relatedness information of categories. An example of mathematical constructive proof for the cosine index is given, and the development process provides a rigorous solution framework. In addition, this study thoroughly examines validity such as content validity, convergent validity, discriminant validity, internal consistency, and criterion-related validity. The results reveal that this approach performs as expected in empirical analyses. Finally, the mathematical interpretation and generality of this approach for other category-based indices such as the Herfindahl index, entropy index, Euclidean distance, and Pearson’s correlation coefficient are discussed. Interestingly, other proposed measures from existing literature, such as the concentric index, can also be incorporated into this solution framework.

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