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A statistic for measuring response model performance: Determining the significance of the gains chart
Different statistical measures have been utilized in direct marketing to assess response models. The environment typically consists of large data files and small response rates. Resulting correlations seem surprising small and statistically significant. Frequently, measures, which emphasize goodness of fit are employed to evaluate response models. However, this approach is not useful for assessing financial or behavioral performance. As some have noted (e.g. Roberts and Berger 1993; Leahy 1992: Malthouse 2002: Magliozzi and Berger 1993) even models that don't fit particularly well, still may perform well; thus, traditional measures are not appropriate for assessing performance. In lieu of “goodness of fit” measurements, direct marketers use descriptive statistics. Large files are summarized into small groupings. Category response rates are converted into cumulative gain indices and then exhibited in table and graphic form. Unfortunately, assessment can be ambiguous; there are no inferential tests associated with these statistics, which can be used to address reliability or model equality. This dissertation evaluates and extends the use of the Gini coefficient used by various social scientists (e.g. Giles 2002; Berndt, Fisher and Rajendrababu 2003; Thomas Wang and Fan 2002). The relationship between the Gini index and the gains table is derived. It is then shown how Gini can be used to evaluate performance. A Monte Carlo simulation was conducted to compute distribution properties of Gini, providing a tool for assessing model performance. Using results from the simulation, a regression model was created to estimate the standard deviation of the Gini index. The assumption of normality for the Gini statistic was validated, this making it possible to create confidence intervals for Gini. Theoretical results were validated with two data files acquired from the Direct Marketing Association. A simpler and more efficient approach for calculating the Gini statistic was developed. The empirical distribution of a data file was approximated with a binary power curve. This technique improves computational performance of Gini and the gains table. Finally, a profitability model was presented as a function of the Gini statistic. The function was maximized and a formula representing optimum profitability as a function of Gini was developed.
Greene, Henry J, "A statistic for measuring response model performance: Determining the significance of the gains chart" (2005). Doctoral Dissertations Available from Proquest. AAI3179877.