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Modeling consumer heterogeneity helps practitioners understand market structures and devise effective marketing strategies. In this research we study finite mixture specifications for modeling consumer heterogeneity where each regression coefficient has its own finite mixture, that is, an attribute finite mixture model. An important challenge of such an approach to modeling heterogeneity lies in its estimation. A proposed Bayesian estimation approach, based on recent advances in reversible jump Markov Chain Monte Carlo (MCMC) methods, can estimate parameters for the attribute-based finite mixture model, assuming that the number of components for each finite mixture is a discrete random variable. An attribute specification has several advantages over traditional, vector-based, finite mixture specifications; specifically, the attribute mixture model offers a more appropriate aggregation of information than the vector specification facilitating estimation. In an extensive simulation study and an empirical application, we show that the attribute model can recover complex heterogeneity structures, making it dominant over traditional (vector) finite mixture regression models and a strong contender compared with mixture-of-normals models for modeling heterogeneity.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2370423