A number of methods have been developed to link single-period arithmetic attribution results, including the Cariño logarithmic method, the Frongello methods, the Menchero method and some Ad Hoc methods. We point out an omitted but necessary property, the associative property, which renders the Menchero and the Ad Hoc methods invalid. We present evidence that non-associative methods violate another necessary property which we refer to as “sign preservation.” These distinct but related properties provide strong support for the use of the Cariño and Frongello methods, which often produce similar results.

The Associative Property of Attribution Linking