Estimating the Proportion of “Always Buy” and “Never Buy” Consumers: A Likelihood Ratio Test with Sample Size Implications

Abstract

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 by the use of simulated data. The method also is applied to two sets of well-known data. The empirical findings show that although more than 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 provide a superior fit over the no-spike model. The method also applies to advertising reach and frequency models used to estimate or detect the presence of “always read (watch)” and “never read (watch)” individuals.