qqstats function

QQ Summary Statistics

This function calculates a set of summary statistics for the QQ plot of two samples of data. The summaries are useful for determining if the two samples are from the same distribution. If standardize==TRUE, the empirical CDF is used instead of the empirical-QQ plot. The later retains the scale of the variable.

qqstats(x, y, standardize=TRUE, summary.func)

Arguments

• x: The first sample.
• y: The second sample.
• standardize: A logical flag for whether the statistics should be standardized by the empirical cumulative distribution functions of the two samples.
• summary.func: A user provided function to summarize the difference between the two distributions. The function should expect a vector of the differences as an argument and return summary statistic. For example, the quantile function is a legal function to pass in.

Returns

• meandiff: The mean difference between the QQ plots of the two samples.

• mediandiff: The median difference between the QQ plots of the two samples.

• maxdiff: The maximum difference between the QQ plots of the two samples.

• summarydiff: If the user provides a summary.func, the user requested summary difference is returned.

• summary.func: If the user provides a summary.func, the function is returned.

Author(s)

Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu , https://www.jsekhon.com.

References

Sekhon, Jasjeet S. 2011. "Multivariate and Propensity Score Matching Software with Automated Balance Optimization.'' Journal of Statistical Software 42(7): 1-52. tools:::Rd_expr_doi("10.18637/jss.v042.i07")

Diamond, Alexis and Jasjeet S. Sekhon. Forthcoming. "Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies.'' Review of Economics and Statistics. https://www.jsekhon.com

See Also

Also see ks.boot, balanceUV, Match, GenMatch, MatchBalance, GerberGreenImai, lalonde

Examples

#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
#

data(lalonde)

#
# Estimate the propensity model
#
glm1  <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
             hisp + married + nodegr + re74  + I(re74^2) + re75 + I(re75^2) +
             u74 + u75, family=binomial, data=lalonde)

#
#save data objects
#
X  <- glm1$fitted
Y  <- lalonde$re78
Tr  <- lalonde$treat

#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr  <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)

#
# Do we have balance on 1975 income after matching?
#
qqout  <- qqstats(lalonde$re75[rr$index.treated], lalonde$re75[rr$index.control])
print(qqout)