Realizing the value of extensive replication: A theoretically robust portrayal of double jeopardy

Researchers have spent almost 50 years developing, refining and applying the NBD-Dirichlet in repeat purchase markets, in particular with extensive replication of the Goodhardt, Ehrenberg, and Chatfield (1984) model. Recent research that employs a double jeopardy (DJ) line appears to have progressed with little regard for this body of theory. This paper reviews the varied applications of the NBD-Dirichlet and extends the theory to the portrayal of a double jeopardy line. This DJ line, an x–y plot of brandsʹ penetration versus purchase frequency in a category, is tested against three alternative ways of drawing the line. A linear model for double jeopardy is adequate when used under limited conditions yet the model breaks down with a broad scope of analysis. This meta-analysis of 37 cross-sectional product categories and a 40-period (quarters) longitudinal dataset evaluates the best approximation of the DJ line to empirical data. Jeopardy then appears as an upward sloping curve, rather than a DJ line. The NBD-Dirichlet provides for a theoretically sound, versatile method whose parameters have intuitive meanings regarding seasonality, category acceptance and category loyalty.