How to establish the effects of a competitor near my store location?

Question

As part of my studies of statistics, market analysis and data analysis, I’m facing the following problem but not sure if the answer I’m proposing it is correct or not. A commercial retail store with “n” number of stores have “p” number of stores without competitor and “q” number of stores with competitor near its ubication, with n=p+q and p>q, wants to measure the effects of the pieces sold of each one of the products when there is a competitor near. To exemplify my problem, I use a very simple data showed in the Table 1.

In the stores without competition product P1 sell 4 pieces, P2 sell 4 pieces and, P3 sell 4 pieces each one equivalent to 33.33% of the total sell.

Stores with competition sell P1 sell 2 pieces, P2 sell 3 pieces and P3 sell 1 piece, equivalent of 33.33%, 50% and, 16.67% respectively.

Using the formula Tot.Pcs.Sell.WC(% Par.Prod.WC- % Par.Prod.WoC), I get the number of pieces necessary to have the same distribution of the stores with competition as the stores without competition.

The overall problem involves information of 3000 products sell in 10000 stores around the globe, but I really need to know If I’m pointing out in the right direction.

Any help, suggestion or topic that I need to review would be very grateful.

Answer 1

I would try first with some "simple" regression model. The stores could have very different characteristics, so lumping them just in two categories "With" or "Without" competitors might not be very helpful. That way of thinking leads to a mixed (or multilevel) model, which could be helpful even if we are not very interested in the individual stores, just to get a better variance model. But as you ask for descriptive statistics, we start with something simpler.

It will help if you have a measure of "size" for each individual store, for example total yearly sales. Then that could be used as a measure of exposure in a poisson (or quasipoisson) model. Here are some posts with examples: Why is Poisson regression used for count data? and Goodness of fit and which model to choose linear regression or Poisson.

Then a very simple poisson model could be fit (as a starting point) with linear predictor somewhat like (in R notation)

sales ~ offset(log(totalsales) + store + product + has_competitor + ... 

or you could fit one model pr. store, leave out the store and has_competitor variables, and then compare the coefficients of product between the competitor categories. For a descriptive analysis I would start with that last analysis! and go from there. Andrew Gelman calls this the secret weapon.

An additional problem with the per-store analysis is that it might well be that the "competitor" status of a store varies by product ... If that is the case you should tell us.