mahal {DOS} R Documentation

## Mahalanobis Distance Matrix for Optimal Matching

### Description

Computes a Mahalanobis distance matrix between treated individuals and potential controls. The method is discussed in Chapter 8 of Design of Observational Studies (2010).

### Usage

mahal(z, X)


### Arguments

 z z is a vector that is 1 for a treated individual and 0 for a control. X A matrix of continuous or binary covariates. The number of rows of X must equal the length of z.

### Value

The distance matrix has one row for each treated individual (z=1) and one column for each potential control (z=0). The row and column names of the distance matrix refer to the position in z, 1, 2, ..., length(z).

### Author(s)

Paul R. Rosenbaum

### References

Hansen, B. B. and Klopfer, S. O. (2006). Optimal full matching and related designs via network flows. Journal of computational and Graphical Statistics, 15(3), 609-627. (optmatch package)

Hansen, B. B. (2007). Flexible, optimal matching for observational studies. R News, 7, 18-24. (optmatch package)

Rosenbaum, P. R. (2010). Design of Observational Studies. New York: Springer. The method and example are discussed in Chapter 8.

Rosenbaum, P. R. and Rubin, D. B. (1985). Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician, 39, 33-38.

Rubin, D. B. (1980). Bias reduction using Mahalanobis-metric matching. Biometrics, 36, 293-298.

### Examples

data(costa)
z<-1*(costa$welder=="Y") aa<-1*(costa$race=="A")
smoker=1*(costa$smoker=="Y") age<-costa$age
x<-cbind(age,aa,smoker)
dmat<-mahal(z,x)
# Mahalanobis distances
round(dmat[,1:6],2) # Compare with Table 8.5 in Design of Observational Studies (2010)
# Impose propensity score calipers
prop<-glm(z~age+aa+smoker,family=binomial)\$fitted.values # propensity score
# Mahalanobis distanced penalized for violations of a propensity score caliper.
# This version is used for numerical work.