I am setting up a quasi-experimental design and I need to compare each treatment account to all potential control accounts within a certain geographic region. I would like measure the distance between a treatment account and each neighboring control account along with their energy usage to help select the most similar pair. Obviously the variables (EW coord, NS coord, and energy usage) are all on different scales, does this mean I have to standardize each variable first? Also, do I need to account for a correlation among variables—-I would think geographic coordinates would get close to zero weight because they orthogonal to each other.

If I choose to use a Mahalanobis distance or some other statistical measure, how would I compute the covariance matrix? I know how to in a typical multivariate setting, but I am looking at a handful of control 3-tuples relative to one treatment 3-tuple. Would I just treat the treatment 3-tuple as the mean vector and use those deviations to compute a covariance matrix?

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    $\begingroup$ Have you thought about trying propensity score matching? $\endgroup$ – Dimitriy V. Masterov Mar 31 '13 at 21:57
  • $\begingroup$ Yes, but the person asking wants me to use a distance measure. I was originally computing the Euclidean distance between points, but it seems the geographic coordinates should get a different weight than total usage. $\endgroup$ – user11281 Mar 31 '13 at 23:47

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