# Creating a composite rank of restaurants with some missing data

I have monthly sales data of 500 restaurants for one year.

For the same restaurants, I also have customer defection or dissatisfaction rates.

I want to create a composite score that can rank restaurants based on their performance on sales and customer satisfaction. Something similar to customer life-time value, but as my unit is customer and the time series is only 12 months, I am wondering if there is any suitable technique to derive a composite score to rank restaurants.

• What is the aim of this compsite score that two different ranks of the data you have do not solve? – kurast Jun 18 '14 at 14:21
• Because of two reasons. 1.) A restaurant just on strong on financial may not be sustainable if it customers are unhappier. For example, a restaurant could be in food court of high traffic but actually has low customer satisfaction. 2). Both variables together create a single view of the restaurant for ranking purpose. – user3658835 Jun 19 '14 at 0:25
• See the answer here. – Scortchi - Reinstate Monica Jun 20 '14 at 13:56
• Also here. – Scortchi - Reinstate Monica Jun 20 '14 at 14:02

To create a composite rank I suggest two steps. Normalization and combination.

The aim of normalization (also called standardization) is to each of the metrics to the same order of magnitude. I will list some, but there are many more:

1. Linear, or min-max (set min value at 0, max value at 1)
2. Gaussian normalization (subtract the mean, divide by stddev)
3. Inverse tangent normalization

To combine, there are also many methods, I will list some:

1. Linear combination (a.rank1+b.rank2)
2. General polynomial (a.rank1n+b.rank2n)
3. Multiplication (rank1.rank2)

Since you provided no utility function, there is nothing to fit, so I suggest you start with linear normalization and linear combination with equal weights, to visualize the results and see if they serve your purpose.

You see this is all independent of the length of the series, however the combination step is better suited if both lengths are equal. However, if you use Gaussian normalization, you can use zero for all the observations you don't have, and it will not induce any bias to the measure.

• This is very helpful. Unfortunately I am not very familiar with linear combination or general polynomial approach. Can you through some light on these? Which statistical technique would allow me to accomplish this? – user3658835 Jun 23 '14 at 1:54