Linear and multiplicative market share models are compared with the attraction specification on the basis of both predictive and descriptive measures. The data used represent 15 brands in three different markets. The results show that linear and multiplicative models with brand-specific parameters estimated by OLS or GLS may perform as well as or better than the attraction specification. The failure of parameter restrictions and ex-post normalization to improve prediction power is explained in terms of the heterogeneity in the estimated parameters. This finding is consistent across brands and models and suggests that the hypothesis of equal response parameters across brands should be tested formally before such restrictions are imposed. The combined results suggest that the attraction model may have considerable intuitive appeal, but that its superiority for descriptive and predictive purposes is not yet established.
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