The authors report the sample sizes required to obtain maximum likelihood estimates of parameters in a zero-order model. In the typical formulation of the model, parameter estimation requires about 2000 individuals with five purchases per consumer. The original parameters can be easily transformed, however, into a market share estimate and a polarization index that convey the key information sought from the model. Estimation of the transformed parameters requires smaller samples of about 400 individuals with five purchases per consumer.
Get full access to this article
View all access options for this article.
References
1.
BassFrank M. (1974), “The Theory of Stochastic Preference and Brand Switching,” Journal of Marketing Research, 11 (February), 1–20.
2.
BassFrank M., JeulandAbel, and WrightGordon P. (1976), “Equilibrium Stochastic Choice and Market Penetration Theories: Derivations and Comparisons,” Management Science, 22 (June), 1051–63.
3.
ChatfieldC. and GoodhardtG. J. (1970), “The Beta-Binomial Model for Consumer Purchasing Behavior,” Applied Statistics, 19 (June), 240–50.
4.
HookeRobert and JeevesT. A. (1961), “‘Direct Search’ Solution of Numerical and Statistical Problems,” Journal of the Association of Computing Machinery, 8 (April), 212–29.
5.
KalwaniM. U. (1975), “Zero Order Models: Specification Data Requirements and Estimation,” unpublished Ph.D. dissertation, Graduate School of Business, Columbia University.
6.
KalwaniM. U. and MorrisonDonald G. (1976), “Sample Size and Number of Trials Required for Parameter Estimation in Zero Order Binary Models,” MIT, Sloan School of Management Working Paper No. 885–76.
7.
KalwaniM. U. and MorrisonDonald G. (1977a), “A Parsimonious Description of the Hendry System,” Management Science, 23 (January), 499–509.
8.
KalwaniM. U. and MorrisonDonald G. (1977b), “Estimating the Proportion of ‘Always Buy’ and ‘Never Buy’ Consumers: A Likelihood Ratio Test with Sample Size Implications,” Journal of Marketing Research, 14 (November), 601–6.
9.
KleinmanJoel C. (1973), “Proportions with Extraneous Variance: Single and Independent Samples,” Journal of the American Statistical Association, 68 (March), 46–54.
10.
MassyW. F., MontgomeryD. B., and MorrisonD. G. (1970), Stochastic Models of Buyer Behavior. Cambridge: MIT Press.
11.
ParfittJ. H. and CollinsB. J. K. (1968), “The Use of Consumer Panels for Brand Share Prediction,” Journal of Marketing Research, 6 (November), 405–12.
12.
RaoC. R. (1965), Linear Statistical Inference and Its Applications. New York: John Wiley & Sons, Inc.
13.
SabavalaDarius and MorrisonDonald G. (1977), “A Model of TV Show Loyalty,” Journal of Advertising Research, 17 (December), 35–43.
14.
ShentonL. R. (1950), “Maximum Likelihood and the Efficiency of Fitting by Moments,” Biometrika, 37 (June), 111–116.
15.
ShoemakerRobert and StaelinRichard (1976), “The Effects of Sampling Variation on Sales Forecasts for New Consumer Products,” Journal of Marketing Research, 13 (May) 138–43.
16.
UrbanGlen L. (1969), “SPRINTER Mod I: A Basic New Product Analysis Model,” Proceedings, National Conference of the American Marketing Association, 139–50.
17.
VanMechelen, ClaudeJ. (1975), “Measuring the Sensitivity of SPRINTER Mod I,” Working Paper 75-15, Center for Managerial Economics and Econometrics, University Saint Ignace, University of Antwerp.
