# How to create a "similarity index" on a set of variables

I have a set of 12 variables that describe the dwelling characteristics. 10 of them are dummies (i.e questions like "does the dwelling have a bath?" or "is there crime in the area?"), while one is a 4-level categorical variable determining the kind of accommodation and the last one reports the total number of room in the accommodation. What I would like to do is to create a "similarity" index for the accommodation of each household. The aim is to use this index to impute the reported monthly gross rent paid by tenants to the occupiers-owner household with accommodation with same characteristics of the tenants. Therefore, having the characteristics of the houses for both tenants and owners, how can I create this sort of "similarity index"? Is it sufficient rely on clustering methods or a Jaccard coefficients shall be used on dummies variables only and using "if else" conditions for matching the other two remaining variables?

Thank you

• See [diversity indexes](en.wikipedia.org/wiki/… (econ, ecology, etc.) and similarity indexes (detecting cheating on exams). Perhaps google both. One of the simplest is Simpson index (see link) $\lambda = \sum_{i=1}^R p_i^2 \le 1/R,$ where $R$ nr of categories/types and $p_i$ are proportions of each. [Under sampling w/ repl, $\lambda$ can be interpreted as probability two sampled individuals are in same category.] Oct 31, 2019 at 17:14
• Since you don't describe any rent information in your data, what hope have you of discovering any combination of the variables ("similarity index") that bears any relationship to rent whatsoever? cc @BruceET
– whuber
Oct 31, 2019 at 20:22
• Having all information about paid rent and dwelling characteristics, the aim is to assign to the owner with same dwelling characteristics of the renter their paid rent. The question is how to use these 12 variables to synthesize them in an index that describe how similar are dwelling of owner and tenants. I will check how to implement the Simpson index in R Nov 1, 2019 at 9:44

## 1 Answer

To solve this problem, I simply realize that is sufficient to run an hedonic regression. This means I regress the paid rent on dwelling and location characteristics for the "market" tenants only and then compute the linear predictions for the owner and "non-market" tenants.