Estimating Dirichlet Market Statistics From Survey Data A Replication

Transcription

1 Estimating Dirichlet Market Statistics From Survey Data A Replication Malcolm Wright Massey University Anne Sharp Byron Sharp Marketing Science Centre, University of South Australia Abstract The development of the NBD-Dirichlet model of purchase incidence and brand choice is one of the greatest achievements of marketing science. However, its applications have been somewhat limited by the requirement for panel data to estimate the model. Consequently Wright, Kearns, Sharp, and Sharp (1998) developed a survey-based approach to satisfying the data requirements of the NBD-Dirichlet model, validating their surveybased estimates against previously recorded panel observations for the same respondents. While their results were good, a concern remained that this may have been due to conditioning of respondents by their previous participation in the panel. This paper reports a replication of Wright et al s (1998) original study which addresses this issue by reversing the order of data collection; that is Juster estimators were applied before the panel data was collected. The analysis was partly confounded by unexpected promotional activity during the collection of the panel data, but once this is taken into account, the results clearly support Wright et al s (1998) original study. Introduction Some of the most well established empirical generalisations in marketing are those associated with the NBD- Dirichlet model of purchase incidence and brand choice. This model and the generalisations associated with it have been widely tested and supported in marketing (Uncles, Ehrenberg and Hammond 1995) having been observed for over 30 years across North American, Asian, European, and Australasian markets. Unfortunately estimation of the NBD-Dirichlet model usually requires panel data which can be time consuming and expensive to collect, and which in some circumstances may not be available at all. Wright, Kearns, Sharp and Sharp (1998) developed and tested a survey-based approach to meeting the data requirements of the NBD-Dirichlet model. Using the Juster scale, estimators were developed for market share, penetration, and repeat purchase frequency (the inputs of the NBD-Dirichlet model) which could be applied in a single shot survey. The performance of these estimators was empirically assessed in three product categories (supermarkets, retail fuel, and department stores) by comparing the results of a single shot survey with those of a panel run in the same markets six months earlier. The Juster estimators were found to perform well, suggesting that the data requirements of the NBD-Dirichlet model could be satisfied with a single shot survey. More generally, the accuracy of the Juster estimators suggested that the long established problems of getting accurate market statistics from survey data (Parfitt 1967, Wind and Lerner 1979) may have been solved. However, one major criticism of Wright et al (1998) is that the respondents could have been conditioned by their participation in the panel to provide more accurate estimates of their purchasing behaviour than would otherwise have been the case. Consequently, this paper reports a replication of Wright et al s (1998) original study in which the order of data collection was reversed; that is Juster estimators were applied before the panel data was collected. Data and Method Data was gathered for the Juster estimators as part of the recruitment questionnaire for a diary panel of New Zealand car drivers. The verbal probability scale, a spoken analogue of the Juster scale was used (Brennan, Esslemont, and Hini 1995), and the behaviour examined was purchases from the various retail fuel brands over the next four weeks. Of the 1103 respondents who were interviewed during the panel recruitment process, 592 continuously reported their retail fuel purchases for the full 10 weeks of data collection, which commenced two weeks after recruitment. The recruitment datafile was matched to the panel datafile of the 592 continuous reporters. Five responses were not useable, leaving 587 respondents with matched Juster estimators and panel purchase records. 1466

2 Four-weekly estimates of market share, penetration and purchase frequency were calculated in a spreadsheet package using the Juster estimators (see Appendix One). The matched panel observations were input into the BUYER software (Uncles 1989) to calculate market shares, penetrations, and purchase frequencies for comparison with the Juster estimates. History Effects During the data collection some potentially confounding history effects came into play. One of the Retail Fuel brands () was known to be launching a loyalty program at the time of panel recruitment, but this was not expected to have a major effect (Sharp and Sharp 1997). However, after the Juster estimators has been applied, another brand () unexpectedly announced a series of 150 year anniversary promotions, which peaked with a 5c per litre discount in the first four weeks of the panel, and was followed by other promotions. The 5c per litre discount was an unprecedented promotion in a market regarded by the key players as highly promotion sensitive. Another chain,, ran some defensive sales promotions in response to these activities, while the fourth major chain () deliberately did nothing. Results Table 1 compares the fit of the Juster estimates to the panel observations of market share, while Table 2 makes similar comparison for penetration and purchase frequency. In both tables two sets of observations are presented. Panel 1 consists of the first four weeks of observations, which have a close temporal correspondence to the Juster estimates; Panel 2 consists of the final four weeks which are the ones least affected by promotional activities. Two steps have been taken to simplify presentation. First, all results have been multiplied by 100. Second, fit statistics (Mean Absolute Deviation, Mean Absolute Percentage Error, and correlation) are recorded against the panel observations, although strictly speaking they apply to the fit of the Juster estimates and not the panel observations. Table 1 shows that the fit of the Juster estimates of market share is excellent for and and poor for and. While the estimates for and are of roughly the right magnitude, the order is reversed; this is a serious discrepancy. However, the fit of the Juster market share estimates for and improves somewhat when compared to Panel 2, suggesting that the poor fit against Panel 1 may have been a temporary phenomenon. It may be that the Juster estimates were accurate at the time of the recruitment survey, but that the brands relative positions were affected by the unexpected promotional activities. Table 1: Market Share Estimates Juster Panel 1 Panel * 27 * * 27 * Average MAD 4 3 MAPE 17% 13% Correlation *deviation >3 Table 2 is a more complex table, so discussion of its results will be broken down into three areas; category statistics, brand penetration estimates, and brand purchase frequency estimates. 1467

3 Table 2: Penetration and Purchase Frequency Estimates B and b j W and w j Juster Panel 1 Panel 2 Juster Panel 1 Panel 2 Any * 44 * * 30 * 96 * 43 * * 28 * * * 3.5 * * * 2.7 Average Brand MAD MAPE 17% 13% 9% 7% Correlation *deviation >3 for B, b j, >0.3 for W, w j. The category statistics show an acceptable level of fit. While category penetration and purchase frequency are under-estimated, the magnitude of these underestimates is not great; 5% for penetration and 12% for purchase frequency. Given the extensive promotional activity that occurred at the time of the panel, it does seem reasonable to expect some increases in penetration and purchase frequency over the levels estimated in the recruitment survey. The brand penetration estimates are mostly of the same order and magnitude as the panel observations, but do show a consistent underestimation of 7 points in Panel 1 and 6 points in Panel 2. This underestimation may be partly ascribed to the promotional activity, but it is important to note that Wright et al (1998) also found consistent underestimates of brand penetration. The worst error is for, whose penetration is much close to s in the panel observations than is expected from the Juster estimates. Despite this, all fit statistics are reasonable, and all fit statistics improve from Panel 1 (most affected by the promotional activity) to Panel 2 (less affected by the promotional activity). The brand purchase frequency estimates are considerably worse than those found by Wright et al (1998). While the Juster estimates and panel observations are of similar order and magnitude, and show low MADs and MAPEs, the order is different, and the correlations are poor. This is because s purchase frequency is much higher than estimated, while s is much lower. Are these differences due to the promotional activity? Certainly we might expect that s major price promotion may have boosted s purchase frequency at the expense of who, unlike the other brands in the market, did nothing. Again, the fit statistics do improve from Panel 1 (most affected by the promotional activity) to Panel 2 (less affected by the promotional activity). Given the marketing activity undertaken during the panel, some deviations must be expected, and as was the only brand to do nothing in this period, is seems highly likely that this brand would suffer most. However, the overall correlation remains unimpressive for Panel 2. It is very important to try to identify the effects of the promotions undertaken during the panel. If the errors in Tables 1 and 2 are not due to the promotions, the conclusion must be that Wright et al s (1998) results are not replicable (at least in this study). On the other hand, if these errors are due to the promotions, then Wright et al s (1998) method can be credited with having accurately identified pre-promotion brand performance. The best way to attempt to examine promotional effects in more detail is to consider weekly rather than 4- weekly brand performance. Figure 1 does this for market share. The results are striking; the relative positions of and were reversed between week one and week two of the panel. This provides strong evidence that the Juster estimates were accurate, and the errors were introduced by the reversal of market position at the start of the panel. 1468

4 Figure 1: Market Share for the First Four Weeks of the Panel 35% 30% 25% 20% 15% 10% 5% 0% Weeks If the panel shares for the first week are substituted into Table 1, the results are a MAD of 2, a MAPE of 9%, and a correlation of These are excellent results, and a considerable improvement over the original comparisons. Exact comparisons cannot be made for penetration and purchase frequency, as the Juster estimates are 4 weekly and the more detailed panel observations are weekly. However, the order of and s penetration does reverse during the first two weeks of panel observations, similar to what is seen in Figure 1. The purchase frequencies for these two brands are similar in the first week, but subsequently diverge with s increasing and s declining, again similar to what is seen in Figure 1. Conclusion Wright et al s (1998) method initially provides an excellent fit for and and a poor fit for and. However, once the effects of promotional activity are taken into account, it can be seen that the Juster estimates were accurate for all brands at the start of the panel. This provides provide further support for the use of Wright et al s (1998) method of satisfying the data requirements of the NBD-Dirichlet model. Appendix One - The Estimators Wright et al (1998) provide detail on the Juster scale and on the development of the Juster estimators. In this paper we merely report the relevant estimators. b j = (( i p ij ) / n) (1) where b j = penetration for brand j; p ij = probability that individual i will purchase from (or visit) brand j (equal to the Juster score divided by 10). B = ( i ( 1 - (Π j (1 - p ij ) ) / n ) (2) where B = penetration for the product category. Average purchase frequency for brand j (w j ) equals brand volume divided by the number of buyers of the brand. Average purchase frequency for the category (W) can be estimated as the sum of the individual brand volumes divided by the number of buyers of the category. w j = ( i (p ij * v ij )) / ( n * b j ) (3) W = ( i j ( p ij * v ij )) / ( n * B ) (4) 1469

5 where v ij = the most likely number of purchases (or visits) by individual i from brand j. Volume and average purchase frequency are thus based on purchase occasions rather than purchase quantities, but the same simplifying assumption is made in the application of the NBD-Dirichlet model. Note also that the denominators of (3) and (4) are different. These estimators are applied first to all brands of interest, and then to an other brand which represents the aggregate of all other minor brands in the market. The other brand is only required for the calculation of B and W, and is not otherwise reported. From these the market share of the brand can also be calculated. ms j = (( b j * w j ) / ( B * W )) (5) where ms j = the share of brand j in the category in the relevant period. References Brennan, Mike; Esslemont, Don and Hini, Dean (1995), Obtaining Purchase Predictions via Telephone Interviews, Journal of the Market Research Society, Vol. 37, No. 3, pp Parfitt, John (1967), A Comparison of Purchase Recall with Diary Panel Records, Journal of Advertising Research, Vol. 7, pp Sharp, Byron and Sharp, Anne (1997), Loyalty programs and their impact on repeat-purchase loyalty patterns, International Journal of Research in Marketing, Vol. 14, pp Uncles, Mark (1989), Buyer Behaviour Software: A Manual for Version 89.1, London Business School, Centre for Marketing and Communication. Uncles, Mark; Ehrenberg, Andrew, and Hammond, Kathy (1995) Patterns of Buyer Behavior: Regularities, Models, and Extensions, Marketing Science, Vol. 14, No. 3, Part 2, pp. G61-G70. Wind, Yoram and Lerner, David (1979), On the Measurement of Purchase Data: Surveys versus Purchase Diaries, Journal of Marketing Research, Vol. 16, pp Wright, Malcolm; Kearns, Zane; Sharp, Anne and Sharp, Byron (1998), Predicting Repeat Purchase from a Single Shot Survey, Proceedings of the 27 th EMAC Conference, Vol. 5, pp