I don't know when I should use 1:1 matching or 1: to many * .
Also re * how many is 'many'? how do I know how many I need?
Is this based on the number of similar variables having the same propensity scores? Therefore if 3 in the control group have similar propensity scores to 1 in treatment score then it would be 3:1
Not sure if I understood correctly, pls let me know
Hi, the choice of matching methods depends on various technical and substantive considerations including practical ones. For e.g., do you want to lose "sample"?
I really advise reading up on papers by Peter Austin, Elizaeth Stuart, as well as one by my professor Dr. Kainz (Improving Causal Inference: Recommendations for Covariate Selection and Balance in Propensity Score Methods).
It may be good news to you that you should actually use as many methods as possible and choose the one that gives you the best balance in scores (see Kainz). This is not cheating or fishing for results. It is acceptable.
Hi Martinique,
The ultimate goal of your analysis is to estimate appropriate counterfactuals for the observtions who received treatment (treated T) using information on the non-treated units (controls C) in your data. One way to "find" suitable controls is based on propensity score matching, i.e., you compare individuals in the T and C with similar propensity scores (ps) as they should be comparable along observable dimensions (e.g. age, education, health; BUT unobservables might still differ systematically between the two groups biasing the estimated treatement effects).
However, the validity of such comparisons crucially depends on the correct specification of the ps - if you omit key variables that influence the selection into treatment or include covariates that are affected by the treatment itself, then you will end up with biased estimates of the ps which in turn can seriously bias the treatment effects you are after. To overcome these issue, solely include variables that are time invariant (e.g. gender) and were determined/measured before treatment participation when estimating the ps (e.g. Caliendo & Kopeining 2008).
Once you've consistently estimated the ps you need to impose common support, i.e., delete all observations whose ps is smaller than the minimum and larger than the maximum in the opposite group. Only then you arrive at the actual treatment effect estimation step where you compare the outcomes of the T and C with similar ps. As pointed out by Gerard Chung above, there are many matching algorithms and it might be worthwhile to read up on them - however, previous works seems to favor Mahalanobis matching over other matching techniques so I would definitely consider this approach next to your nearest neighbour matching that you seem to be applying (e.g. Baser, 2006).
Re your question: In general, you face a trade-off between bias and variance: including more neighbours to estimate the counterfactuals for the treated might reduce the variance of your treatment effects but increases the bias because you may use controls that are "poor" matches. E.g. if you use 5 nearest neighbours instead of 1 then some of these controls might be quite different than your treated observations (i.e. different propensity score and thus observable characteristics) leading to bias in the estiamted counterfactual.
Hope that helps.
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