# After matching: How do I interpret the value of the type ‘distance’ (=Propensity score) in the balance measures table of the r-package cobalt bal.tab?

I have used the R-package ‘MatchIt’ to perform (1) a nearest neighbour propensity score matching (NNM) based on the Framingham Heart Study and (2) for comparison, an optimal PS matching (OM) for the same PS model.

PS model: BPMeds ~ age + male + education + BMI + diabetes + prevalentHyp

For the balance diagnostics I used the bal.tab function of the R-Package ‘Cobalt’ and get the following results:


Balance Measures
distance     Distance  0.0276  0.1188  1.7333  0.1172  0.1172  -0.0003 Balanced, <0.1
age           Contin. 49.3479 56.0721  0.8821 56.0000 56.0182   0.0024 Balanced, <0.1
male           Binary  0.4483  0.2973 -0.1510  0.3091  0.3000  -0.0091 Balanced, <0.1
education     Contin.  1.9828  1.9009 -0.0812  1.9000  1.8909  -0.0090 Balanced, <0.1
BMI           Contin. 25.7068 28.2104  0.4770 28.2804 28.1248  -0.0296 Balanced, <0.1
diabetes       Binary  0.0257  0.0721  0.0464  0.0636  0.0636   0.0000 Balanced, <0.1
prevalentHyp   Binary  0.2901  1.0000  0.7099  1.0000  1.0000   0.0000 Balanced, <0.1

Balance tally for mean differences
count
Balanced, <0.1         7
Not Balanced, >0.1     0

Variable with the greatest mean difference
BMI  -0.0296 Balanced, <0.1

Sample sizes
Control Treated
All          3547     111
Matched       110     110
Unmatched    3437       1

bal.tab(m.framingham_**OM**, continuous = "std", binary = "raw", disp = c("means"), un = TRUE, stats = c("m"),+ thresholds = c(m = .10))
Balance Measures
distance     Distance  0.0276  0.1188  1.7333  0.1184  0.1188   0.0085 Balanced, <0.1
age           Contin. 49.3479 56.0721  0.8821 56.5135 56.0721  -0.0579 Balanced, <0.1
male           Binary  0.4483  0.2973 -0.1510  0.3423  0.2973  -0.0450 Balanced, <0.1
education     Contin.  1.9828  1.9009 -0.0812  1.9820  1.9009  -0.0804 Balanced, <0.1
BMI           Contin. 25.7068 28.2104  0.4770 27.8785 28.2104   0.0632 Balanced, <0.1
diabetes       Binary  0.0257  0.0721  0.0464  0.0721  0.0721   0.0000 Balanced, <0.1
prevalentHyp   Binary  0.2901  1.0000  0.7099  1.0000  1.0000   0.0000 Balanced, <0.1

Balance tally for mean differences
count
Balanced, <0.1         7
Not Balanced, >0.1     0

Variable with the greatest mean difference
education  -0.0804 Balanced, <0.1

Sample sizes
Control Treated
All          3547     111
Matched       111     111
Unmatched    3436       0

1. How do I interpret the value of the type ‘distance’ (=Propensity score) in the first line of the balance measures table of the r-package cobalt bal.tab?
2. Can I use distance to make a statement about which matching method fits better (comparing two modells/methods of matching NNM vs OM)?

I just found the following description about distance, but no interpretation (https://ngreifer.github.io/cobalt/reference/bal.tab.matchit.html): distance an optional formula or data frame containing distance valuesdistance(e.g., propensity scores) or a character vector containing theirnames. If a formula or variable names are specified, bal.tab() will look in the argument to data , if specified. The distancemeasure (e.g., propensity score) generated by matchit() is automatically included and named "distance".

distance refers to the propensity score. This is explained in the MatchIt documentation. Balance on the propensity score is generally uncorrelated with bias in the treatment effect estimate; what matters is balance on the covariates. Your first specification yields better balance on the covariates than the second, so I would go with the first.