Estimating the Proportion of "always Buy" and "never Buy" Consumers: a Likelihood Ratio Test with Sample Size Implications

The likelihood ratio test is presented as a natural method to test for the presence of "always buy" and "never buy" consumers. The purchase sequence lengths and sample sizes required to estimate the proportions of these buyers are determined through the use of simulated data. Our method was then applied to two sets of well known data first analyzed by Aaker [1] and Montgomery [8]. The empirical findings show that although over half of the consumers never bought a given brand, the specific addition of a spike at p=0 to provide for "never buy" consumers did not form a superior fit over the no-spike model.