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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: multi-dimensional chi-squared? |

Date |
Wed, 21 Jul 2010 12:18:22 -0400 |

Judy <judith.chevalier@yale.edu>: There is almost certainly dependence over time--these products take turns being on sale, right? And I presume you have a more elaborate theory to test; e.g. http://www.jstor.org/stable/2006734 or http://scholar.google.com/scholar?cites=9915702171871712194 for some relevant theory (i.e. is there a first mover in this sale price game?) You might consider reformulating this as a logit or alternative binary regression using your panel data, where each obs is a product in a time period, and you have dummies on the RHS for one, two, or three other products on sale (the excluded group-- zero --corresponds to the "one product tends to be on sale at a time" hypothesis, so the joint test on the three dummies is the one you want, I think). Then you can start thinking about the correlated error structure (including the ineluctable serial correlation), mixed and random effects, etc. Ideally, I think you would want some instruments, maybe demand shifters, as well, depending on your theory. Maybe that means going to a -ivprobit- or -gmm- model, or using a triangular simultaneous equation if there is a first mover. On Tue, Jul 20, 2010 at 10:13 PM, Steven Samuels <sjhsamuels@earthlink.net> wrote: > Download -mgof-, Goodness-of-fit tests for multinomial data, from SSC > > There are assumptions behind -mgof-. One is that there is no dependence of > the counts in different weeks (This is different from assuming that the > decision to put an item on sale each week was independent of the decision > for the other items that week.) . A second is that the probabilities were > constant from week-to-week. Without more information on how the data were > generated, it's difficult to say more. > > Steve > > On Jul 20, 2010, at 10:54 AM, Chevalier, Judy wrote: > > > Hello. I am fairly new to this listserve. I have a question about how one > my think about constructing a test statistic and then how to program it in > STATA. I may be missing a good way to think about it. I will present this > in the context of an economics/marketing dataset, though it may have a close > analog in other domains. > > Consider a dataset with multiple products (let's call them 4 different > brands of peanut butter to be concrete) observed over multiple weeks. I > have coded whether each product for each week is at its regular price or on > sale. I am interested in the question of whether one and only one product > being on sale in a given week occurs more frequently than would be predicted > if the product sales were independent of one another. So, I have (easily > calculated) the frequency with which: > > 0 items are on sale > 1 item is on sale > 2 items are on sale > 3 items are on sale > All 4 items are on sale. > > Also, given the overall frequency that each item is on sale, I have also > easily calculated the predicted probability (under the null hypothesis of > independence) that 0 items would be on sale, 1 item would be on sale, 2 > items would be on sale, 3 items would be on sale, etc. > > I can see that 1 item is on sale more frequently in the data than would be > predicted under the null hypothesis of independence, and, of course, the > other categories are somewhat less frequent than would be predicted under > the null. However, I am stymied as to how to construct an appropriate test > statistic. I can test for the independence of the sales for each item, > pairwise, easily, using Stata, but I can't quite manage the right test > statistic nor how to compute it in Stata. I will actually repeat this test > for some other samples--- the products will be different, the number of > products will be different, but the hypothesis will be the same-- that 1 and > only 1 product is on sale more often than would be predicted under the null > of independence. > > If you have gotten this far-thanks for reading! > > Judy * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: multi-dimensional chi-squared?***From:*"Chevalier, Judy" <judith.chevalier@yale.edu>

**Re: st: RE: multi-dimensional chi-squared?***From:*Steven Samuels <sjhsamuels@earthlink.net>

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