We propose semiparametric procedures for estimation and testing of base-independent equivalence scales. The partial linear index specification permits simultaneous estimation across multiple household types and multiple goods and also the incorporation of continuous and discrete household attributes. Furthermore, asymptotic properties of estimated equivalence scales and tests of base independence are readily obtained. The efficiency gains from the proposed models and estimators are particularly helpful for developing country data where there is often much greater variation in household size and composition. We apply the techniques to South African data and find the results to be broadly consistent with base independence.