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Marketing Models

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MKT 6362 Project Reports 1. Problem statement
The data provided (Ketchupsas) is a subset of the data used by Kamakura and Russell (1989). It is household panel data on choices of ketchup brand as a function of price and promotion. We need to know how prices and display influence a family’s choice on specific brand of ketchup, comparing three brands (Heinz, Hunts, Del Monte) with others. The most effective element should be chosen so that we could give suggestions on how to make them more attractive to customers.
The following questions should be answered in order to provide proper suggestions. * Evaluate the influence of different prices and promotions to choice * Study the price elastic of different brand * Conclude the analysis and provide some advice for different brands

2. Data and Methodology a) Data Description
The data we have are panel data with 2000 observations. It includes customers’ preference of ketchups along with price and the promotion statue of three key brands. b) Methodology
With such a dataset, the first analysis would be descriptive analysis. As we would like to know about difference between promotion and non-promotion, a chi-square test (t-test) could help to identify. Since we are interested in preference, the multinomial logistic is prefect for it. Considered it is a panel data, mixed effect should also be considered. We would also like to study the behavior of customer switch (which means a customer changes his preference), a regression would also be used. 3. Analysis and result c) Descriptive analysis
Basically, there are 2000 observations from 250 different customers in the data.
Shown as chart 1 in appendix, in general, customers have about 2/3 of chances to choose Heinz, 17% for Hunts, 10% for Del Monte and the rest for others.
The price for the four brands is shown as chart 2 and on average, Heinz is sold at $4.06, Hunts at $3.45, Del Monte at $3.81 and others at $3.39.
In total, Heinz runs 197 times promotions, Hunts does 143 times, Del Monte does only 62 times and others does 27 times.
From these results, we can see that Heinz enjoys its leader position with a highest price; Hunts positions itself at lower price and takes the second place; Del Monte, though ranks in the third place, sells at the middle price. Other brands have the lowest price but have smallest share. d) Chi-square test
We would like to know if the promotion helps to sell the product, so we do a chi-square test in each brands.
The results are following tables: Heinz Display | Heinz | Hunts | Del Monte | Others | No | 64.17% | 16.92% | 11.54% | 7.38% | Yes | 82.23% | 15.23% | 1.02% | 1.52% |
We can see that Heinz’s promotion mainly attracts customers originally in Del Monte and Others – the possible to choose other than Heinz and Hunts drops to about 2.5%. Hunts Display | Heinz | Hunts | Del Monte | Others | No | 67.26% | 15.08% | 10.93% | 6.73% | Yes | 48.95% | 38.46% | 4.9% | 7.69% |
We can learn from the above table that Hunts’ promotion does quite well to steal the share from two main competitor brands. Del Monte Display* | Heinz | Hunts | Del Monte | Others | No | 65.84% | 16.92% | 10.42% | 6.81% | Yes | 69.35% | 12.90% | 12.90% | 6.45% |
* Chi-square 0.6561, not significant
As the chi-square turns out to be not significant, we cannot tell the influence of Del Monte’s promotion.
From above analysis, we can say that Heinz and Hunts both have an effective promotion, but they are a little bit different – Heinz mainly seizes shares from Del Monte and other brands, while Hunts mainly get from other two competitor. Del Monte seems do poorly in promotions – there is not significant different from no promotions. e) Multinomial Logistic regression
In chi-square, we only investigate the influence of promotions separately. Here, we would like to put them together and see how price and promotion influence the customers’ decision.
We take the choice of Heinz, Hunts and Del Monte as 1, 2 and 3, and set choice of others as reference category.
The Result for Multinomial Logistic regression is as below tables.
From the table 1 analysis of effect, we can know that in general prices are all significant variables and only promotions of Heinz and Hunts are significant.
However, if we take a closer look at different choices (results in appendix table 3), we could realize that different choice are influenced by different factors: Table 1 Analysis of Effects | Effect | PrDelMonte | PrHeinz | PrHunts | PrOther | DsHeinz | DsHunts | DF | 3 | 3 | 3 | 3 | 3 | 3 | Chi-Square | 138.826 | 143.6892 | 7.813 | 70.5533 | 13.3599 | 40.623 | Pr > ChiSq | <.0001 | <.0001 | 0.05 | <.0001 | 0.0039 | <.0001 |
To Heinz, the price of Hunts has a weak significantly negative influence but the price of others has a strong significantly positive influence; the promotion of itself would have a positive effect while Hunts’ would have a negative one.
To Hunts, the price of itself and Del Monte both have a negative influence but Heinz’s would have a positive influence; both promotions of Heinz and Hunts would have a positive influence.
To Del Monte, the price of itself would have a negative influence but Heinz’s and others’ would have a positive one. Promotion has no influence at all.
Thus, the relations would be as below table. Price | Heinz | Hunts | Del Monte | Heinz | NA | - | + | Hunts | - | + | NA | Del Monte | NA | - | - |
+: Positive effect -: negative effect Promotion | Heinz | Hunts | Del Monte | Heinz | + | + | NA | Hunts | - | + | NA | Del Monte | NA | NA | NA |
+: Positive effect -: negative effect f) Mixed-logit regression
As this is a set of panel data, we would like to consider a mixed-logit regression here.
The result is provided by professor and in appendix table 4.
We can see that the odds to choose Hunts, Del Monte and others are 3.59, 3.51 and 4.63 times less than choose Heinz. So we can basically see that Del Monte have stronger customer loyalty.
Price increasing have a negative effect regardless of brand but the promotion have a positive effect. g) Switch study
We are also interested in the reason that a customer change his preference.
There are 609 switches in the dataset, we pick them out and create a new dataset called switch. We calculate the difference of price and display between before and after switch. Then, we do a multinomial regression to see which significant influence factors are.
Similar to table 2 analysis of effect, we can say that changes in prices and promotions of Heinz and Hunts are significant variables. Table 2 Analysis of Effects | Effect | dprheinz | dprhunts | dprdelmonte | dprother | ddsheinz | ddshunts | DF | 11 | 11 | 11 | 11 | 11 | 11 | Chi-Square | 95.976 | 38.706 | 70.8453 | 54.0722 | 21.9262 | 32.7742 | Pr > ChiSq | <.0001 | <.0001 | <.0001 | <.0001 | 0.025 | 0.0006 |
*Diff = previous – current
If we take some time checking the results in appendix table 5, we could have some interesting conclusions: 1. Customer would switch from Heinz to Hunts because Del Monte increases the price. 2. Customer would switch from Heinz to Del Monte because Brands except Hunts increase their price or Del Monte drops its price. 3. Customer would switch from Hunts to Heinz because Heinz or other brand drops its price, or Del Monte increases its price. 4. Customer would switch from Hunts to Del Monte because Heinz drops its price. 5. Customer would switch from Del Monte to Heinz because Heinz drops its price or Del Monte increase its price. 6. Customer would switch from Del Monte to Hunts when Heinz and Hunts drop the price, or Del Monte increase the price.
From these results, we can see that the price influence of three brands is quite complex. But basically it would be like Heinz and Del Monte benefit from a higher price, while Hunts benefit from lower price. h) Other possible methods not used i. Clustering
As there are only 250 customers and only 2 variables (price and promotion), clustering seems may not be a good fit here. ii. Discount
Since we don’t have the tag price for different brands, so we can hardly study the influence of discount. If we take the mode price as regular price, it would just be the price divided by a fixed number, so that don’t change the result. 4. Conclusion and recommendation
Generally, we would have both price and promotion recommendation for all three brands. i) Price
In our analysis above, we can see that higher price would lead to a lower purchase possibility. However, price strategy would differ to different brands.
Heinz should try to keep its price high. It seems that price drop would not help the switch and customers are not so sensitive to its high price.
Hunts should keep its price far away Heinz and Del Monte if possible. Lower price would help it to keep its customers and attract switchers from other brands.
Del Monte should pay attention to both other brands price. It should carefully stay in the middle to prevent losing customers. j) Promotion
In most of our study, only Heinz and Hunt’s promotions show significant influence on customers. That means Del Monte should pay attention to its promotions – avoid doing any promotions or try to figure out what’s going on.
To Heinz and Hunts, they both do a good job in promotions. But Heinz should try to avoid doing promotion at the same time of Hunts. 5. Appendix
Chart 1

Chart 2
Price history
Table 3 Analysis of Maximum Likelihood Estimates | Parameter | CHOICE | DF | Estimate | Standard
Error | Wald
Chi-Square | Pr > ChiSq | Intercept | 1 | 1 | 0.00657 | 0.8832 | 0.0001 | 0.9941 | Intercept | 2 | 1 | -5.2385 | 1.0573 | 24.5488 | <.0001 | Intercept | 3 | 1 | -3.5276 | 1.1961 | 8.6979 | 0.0032 | PrDelMonte | 1 | 1 | 0.0132 | 0.1463 | 0.0081 | 0.9283 | PrDelMonte | 2 | 1 | -0.4074 | 0.1770 | 5.2990 | 0.0213 | PrDelMonte | 3 | 1 | -1.9016 | 0.2127 | 79.9132 | <.0001 | PrHeinz | 1 | 1 | -0.0573 | 0.1706 | 0.1129 | 0.7369 | PrHeinz | 2 | 1 | 1.0267 | 0.1940 | 28.0150 | <.0001 | PrHeinz | 3 | 1 | 1.3765 | 0.2180 | 39.8713 | <.0001 | PrHunts | 1 | 1 | -0.3457 | 0.1828 | 3.5768 | 0.0586 | PrHunts | 2 | 1 | -0.6394 | 0.2369 | 7.2857 | 0.0070 | PrHunts | 3 | 1 | -0.2762 | 0.2795 | 0.9762 | 0.3231 | PrOther | 1 | 1 | 1.2073 | 0.2255 | 28.6560 | <.0001 | PrOther | 2 | 1 | 1.7211 | 0.2369 | 52.7896 | <.0001 | PrOther | 3 | 1 | 1.7874 | 0.2409 | 55.0365 | <.0001 | DsHeinz | 1 | 1 | 1.7370 | 0.5963 | 8.4851 | 0.0036 | DsHeinz | 2 | 1 | 1.3741 | 0.6382 | 4.6359 | 0.0313 | DsHeinz | 3 | 1 | 0.3532 | 0.9437 | 0.1401 | 0.7082 | DsHunts | 1 | 1 | -0.6282 | 0.3546 | 3.1393 | 0.0764 | DsHunts | 2 | 1 | 0.7957 | 0.3977 | 4.0031 | 0.0454 | DsHunts | 3 | 1 | -0.3725 | 0.5691 | 0.4285 | 0.5127 |
Table 4 choice Coef. Std. Err. z P>z [95% Conf. Interval] | | | | | | | | | Mean | | | | | | dum2 -3.585467 .2339942 -15.32 0.000 -4.044087 -3.126847 | dum3 -3.51375 .1959407 -17.93 0.000 -3.897786 -3.129713 | dum4 -4.637378 .3011845 -15.40 0.000 -5.227689 -4.047068 | price -1.594272 .1126503 -14.15 0.000 -1.815063 -1.373482 | display 1.281216 .1970816 6.50 0.000 .8949433 1.667489 | | | | | | | | SD | | | | | | dum2 1.98003 .1770353 11.18 0.000 1.633047 2.327013 | dum3 1.218536 .1966712 6.20 0.000 .8330678 1.604005 | dum4 -2.043621 .2639204 -7.74 0.000 -2.560895 -1.526346 | price 1.11771 .0977155 11.44 0.000 .9261909 1.309229 | display .2745045 .3841121 0.71 0.475 -.4783413 1.02735 |

Table 5 Parameter | switch | DF | Estimate | Standard
Error | Wald
Chi-Square | Pr > ChiSq | Intercept | 1 | 1 | 2.5792 | 0.4726 | 29.7850 | <.0001 | Intercept | 2 | 1 | 1.7432 | 0.4930 | 12.5016 | 0.0004 | Intercept | 3 | 1 | 2.0545 | 0.4912 | 17.4929 | <.0001 | Intercept | 4 | 1 | 2.4357 | 0.4839 | 25.3393 | <.0001 | Intercept | 5 | 1 | 0.8392 | 0.5583 | 2.2598 | 0.1328 | Intercept | 6 | 1 | -0.3039 | 0.6846 | 0.1971 | 0.6571 | Intercept | 7 | 1 | 1.2616 | 0.5252 | 5.7716 | 0.0163 | Intercept | 8 | 1 | 0.9395 | 0.5526 | 2.8901 | 0.0891 | Intercept | 9 | 1 | -0.8495 | 0.7751 | 1.2013 | 0.2731 | Intercept | 10 | 1 | 2.0381 | 0.4923 | 17.1394 | <.0001 | Intercept | 11 | 1 | 0.1860 | 0.6143 | 0.0917 | 0.7621 | dprheinz | 1 | 1 | 0.4921 | 0.3018 | 2.6591 | 0.1030 | dprheinz | 2 | 1 | 0.3789 | 0.3178 | 1.4216 | 0.2331 | dprheinz | 3 | 1 | 1.3589 | 0.3743 | 13.1779 | 0.0003 | dprheinz | 4 | 1 | 2.1673 | 0.3595 | 36.3351 | <.0001 | dprheinz | 5 | 1 | 1.9230 | 0.4245 | 20.5221 | <.0001 | dprheinz | 6 | 1 | 2.2710 | 0.4701 | 23.3421 | <.0001 | dprheinz | 7 | 1 | 2.6477 | 0.3818 | 48.1034 | <.0001 | dprheinz | 8 | 1 | 1.0293 | 0.4249 | 5.8681 | 0.0154 | dprheinz | 9 | 1 | 3.0672 | 0.5055 | 36.8091 | <.0001 | dprheinz | 10 | 1 | 1.2594 | 0.3551 | 12.5778 | 0.0004 | dprheinz | 11 | 1 | 0.4146 | 0.4104 | 1.0206 | 0.3124 | dprhunts | 1 | 1 | 0.8260 | 0.6106 | 1.8300 | 0.1761 | dprhunts | 2 | 1 | 0.4743 | 0.6265 | 0.5731 | 0.4490 | dprhunts | 3 | 1 | 0.2697 | 0.6801 | 0.1572 | 0.6917 | dprhunts | 4 | 1 | -0.6990 | 0.6477 | 1.1647 | 0.2805 | dprhunts | 5 | 1 | -0.3445 | 0.7571 | 0.2070 | 0.6491 | dprhunts | 6 | 1 | -0.4272 | 0.7596 | 0.3164 | 0.5738 | dprhunts | 7 | 1 | 0.3540 | 0.6755 | 0.2746 | 0.6002 | dprhunts | 8 | 1 | 1.8668 | 0.7522 | 6.1597 | 0.0131 | dprhunts | 9 | 1 | -0.3255 | 0.7916 | 0.1691 | 0.6809 | dprhunts | 10 | 1 | 1.1854 | 0.6723 | 3.1087 | 0.0779 | dprhunts | 11 | 1 | 0.4286 | 0.8483 | 0.2553 | 0.6134 | dprdelmonte | 1 | 1 | -0.8714 | 0.3350 | 6.7663 | 0.0093 | dprdelmonte | 2 | 1 | -0.1349 | 0.3421 | 0.1554 | 0.6934 | dprdelmonte | 3 | 1 | -1.1739 | 0.3882 | 9.1449 | 0.0025 | dprdelmonte | 4 | 1 | -1.1696 | 0.3687 | 10.0648 | 0.0015 | dprdelmonte | 5 | 1 | -0.5389 | 0.4620 | 1.3607 | 0.2434 | dprdelmonte | 6 | 1 | -1.7072 | 0.4913 | 12.0728 | 0.0005 | dprdelmonte | 7 | 1 | -2.1933 | 0.3931 | 31.1337 | <.0001 | dprdelmonte | 8 | 1 | -2.0369 | 0.4430 | 21.1423 | <.0001 | dprdelmonte | 9 | 1 | -2.1289 | 0.4823 | 19.4799 | <.0001 | dprdelmonte | 10 | 1 | -0.6709 | 0.3731 | 3.2334 | 0.0722 | dprdelmonte | 11 | 1 | -0.7830 | 0.4762 | 2.7031 | 0.1002 | dprother | 1 | 1 | -0.0199 | 0.2200 | 0.0082 | 0.9278 | dprother | 2 | 1 | 0.0265 | 0.2321 | 0.0131 | 0.9090 | dprother | 3 | 1 | 1.0845 | 0.3038 | 12.7427 | 0.0004 | dprother | 4 | 1 | 1.3661 | 0.2813 | 23.5919 | <.0001 | dprother | 5 | 1 | 0.3122 | 0.2878 | 1.1767 | 0.2780 | dprother | 6 | 1 | 1.5401 | 0.3192 | 23.2804 | <.0001 | dprother | 7 | 1 | 1.2960 | 0.2889 | 20.1210 | <.0001 | dprother | 8 | 1 | 1.1491 | 0.3256 | 12.4552 | 0.0004 | dprother | 9 | 1 | 1.2927 | 0.3443 | 14.0979 | 0.0002 | dprother | 10 | 1 | 0.4638 | 0.2861 | 2.6283 | 0.1050 | dprother | 11 | 1 | -0.1458 | 0.2631 | 0.3070 | 0.5795 | ddsheinz | 1 | 1 | 0.5469 | 0.6953 | 0.6187 | 0.4315 | ddsheinz | 2 | 1 | 0.5920 | 0.7124 | 0.6906 | 0.4060 | ddsheinz | 3 | 1 | 0.7407 | 0.8309 | 0.7947 | 0.3727 | ddsheinz | 4 | 1 | -0.8420 | 0.7936 | 1.1256 | 0.2887 | ddsheinz | 5 | 1 | -0.0693 | 0.9758 | 0.0050 | 0.9434 | ddsheinz | 6 | 1 | 0.3289 | 1.0407 | 0.0999 | 0.7520 | ddsheinz | 7 | 1 | -1.2391 | 0.8281 | 2.2387 | 0.1346 | ddsheinz | 8 | 1 | 0.4676 | 0.9276 | 0.2542 | 0.6142 | ddsheinz | 9 | 1 | -0.1714 | 1.0957 | 0.0245 | 0.8757 | ddsheinz | 10 | 1 | -1.0036 | 0.7936 | 1.5991 | 0.2060 | ddsheinz | 11 | 1 | -0.0499 | 0.9755 | 0.0026 | 0.9592 | ddshunts | 1 | 1 | -1.3287 | 0.8731 | 2.3160 | 0.1281 | ddshunts | 2 | 1 | -0.5058 | 0.8944 | 0.3198 | 0.5717 | ddshunts | 3 | 1 | -0.7384 | 0.9682 | 0.5817 | 0.4456 | ddshunts | 4 | 1 | 1.2142 | 0.9268 | 1.7163 | 0.1902 | ddshunts | 5 | 1 | 1.3660 | 1.0449 | 1.7089 | 0.1911 | ddshunts | 6 | 1 | 2.2366 | 1.0998 | 4.1360 | 0.0420 | ddshunts | 7 | 1 | 0.4036 | 0.9735 | 0.1719 | 0.6784 | ddshunts | 8 | 1 | -0.9016 | 1.0224 | 0.7776 | 0.3779 | ddshunts | 9 | 1 | -0.3774 | 1.1489 | 0.1079 | 0.7426 | ddshunts | 10 | 1 | 0.4001 | 0.9301 | 0.1850 | 0.6671 | ddshunts | 11 | 1 | -1.2758 | 1.1382 | 1.2565 | 0.2623 | ddsdelmonte | 1 | 1 | 0.2808 | 1.0353 | 0.0736 | 0.7862 | ddsdelmonte | 2 | 1 | 0.9783 | 1.0872 | 0.8098 | 0.3682 | ddsdelmonte | 3 | 1 | 1.0909 | 1.1985 | 0.8286 | 0.3627 | ddsdelmonte | 4 | 1 | -0.2185 | 1.1723 | 0.0347 | 0.8521 | ddsdelmonte | 5 | 1 | -1.1989 | 1.3811 | 0.7536 | 0.3853 | ddsdelmonte | 6 | 1 | -0.5901 | 1.7547 | 0.1131 | 0.7366 | ddsdelmonte | 7 | 1 | 0.5186 | 1.2356 | 0.1762 | 0.6747 | ddsdelmonte | 8 | 1 | -0.6153 | 1.6234 | 0.1436 | 0.7047 | ddsdelmonte | 9 | 1 | 0.8192 | 1.5227 | 0.2894 | 0.5906 | ddsdelmonte | 10 | 1 | 0.1460 | 1.2001 | 0.0148 | 0.9032 | ddsdelmonte | 11 | 1 | 0.8350 | 1.8135 | 0.2120 | 0.6452 | ddsother | 1 | 1 | 1.0900 | 2.1740 | 0.2514 | 0.6161 | ddsother | 2 | 1 | 0.2761 | 2.2882 | 0.0146 | 0.9040 | ddsother | 3 | 1 | -2.3877 | 2.1879 | 1.1909 | 0.2751 | ddsother | 4 | 1 | 0.6251 | 2.2709 | 0.0758 | 0.7831 | ddsother | 5 | 1 | 0.1029 | 2.9718 | 0.0012 | 0.9724 | ddsother | 6 | 1 | 0.1285 | 3.5838 | 0.0013 | 0.9714 | ddsother | 7 | 1 | -2.4739 | 2.2435 | 1.2159 | 0.2702 | ddsother | 8 | 1 | -0.1036 | 2.8146 | 0.0014 | 0.9706 | ddsother | 9 | 1 | -2.3553 | 2.4455 | 0.9276 | 0.3355 | ddsother | 10 | 1 | 1.3999 | 2.2984 | 0.3710 | 0.5425 | ddsother | 11 | 1 | 0.5563 | 3.1783 | 0.0306 | 0.8611 |

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