Is there a way to find suitable ratio for matches to controls (using "ratio" in Matchit package in R or other programs) I am using matchit package in R to find a control set for my treated units and I am testing the model with different ratio to get suitable control set. Is there a way to find suitable ratio and I will use that to find my control set.
 A: There are two considerations in choosing a matching ratio: balance and precision. You want to achieve the best balance in your matched data set; this can be achieved with any ratio, but smaller ratios tend to work better because you're only selecting the best matches, not the second best or third best, etc. Precision depends (in part) on the size of the sample. The size of the treated group is essentially fixed, which means the precision in estimating the counterfactual mean for the treated under treatment is fixed. The issue is in estimating the counterfactual mean for the treated under control, which is what you get from the matched control group. The larger the size of the matched control group, the more precision you have in estimating this counterfactual mean and the treatment effect.
It's impossible to give general advice on balancing precision and balance because the tradeoff involves too many unknowns that are specific to individual data sets. You can make this decision less critical by performing regression in your matched set rather than just performing a t-test, or by prioritizing pair balance and performing a matched pairs analysis. Nonetheless, here's a heuristic that you can use to make your choice:
To find the optimal ratio, try several ratios and choose the one that yields satisfactory balance with the largest sample size. You might define satisfactory balance as standardized mean differences less than .05, for example. Then choose the largest ratio that satisfies this constraint. You should also try full matching and weighting (e.g., using the WeightIt package) and see if you can achieve similar balance with a larger effective sample size. Matching may not always be the best way to maximize precision while maintaining good balance.
