I'm trying to match potential respondents to a random sample from the target population, and not sure whether any of the usual methods available out-of-the-box in e.g. R are right for the job.
Variables to be included in the distance--or dissimilarity--measure include geographic location (continuous), income class (ordinal) and gender (nominal), and about five others.
I would like a distance measure that works on this type of mixed data, and that has no parameters to be set manually (doesn't require the researcher to make "informed" decisions about the model once the measure is chosen). Ideally it would already be implemented in an existing R or Stata package.
Some distances I've considered so far:
- Propensity scores have the disadvantage of reducing the whole variable space down to a single dimension and can lead to imbalance (King, Gary, and Richard Nielsen. “Why Propensity Scores Should Not Be Used for Matching,” 2019).
- I know YouGov uses a custom weighted Euclidean-type metric for a similar purpose, which involves making judgment calls about each variable's weight (Ansolabehere, Stephen, Brian Schaﬀner, and Sam Luks. “Guide to the 2016 Cooperative Congressional Election Survey,” 2017).
- Mahalanobis distance looks like a good candidate, but in its standard form is only appropriate for numeric data--there exist extensions to it but they look like they would be difficult to implement (e.g. Leon, A.R. de, and K.C. Carrière. “A Generalized Mahalanobis Distance for Mixed Data,” 2005).
Any suggestions would be much appreciated!