Relative Distribution Methods
* Pennsylvania State University
Mark S. Handcock *, Martina Morris *
We present an outline of relative distribution methods, with an
application to recent changes in the U.S. wage distribution. Relative
distribution methods are a nonparametric statistical framework for
analyzing data in a fully distributional context. The framework combines
the graphical tools of exploratory data analysis with statistical
summaries, decomposition, and inference. The relative distribution is
similar to a density ratio. It is technically defined as the random
variable obtained by transforming a variable from a comparison group by
the cumulative distribution function (CDF) of that variable for a
reference group. This transformation produces a set of observations, the
relative data, that represent the rank of the original comparison value in
terms of the reference group’s CDF. The density and CDF of the relative
data can therefore be used to fully represent and analyze distributional
differences. Analysis can move beyond comparisons of means and variances
to tap the detailed information inherent in distributions. The analytic
framework is general and flexible, as the relative density is decomposable
into the effect of location and shape differences, and into effects that
represent both compositional changes in covariates, and changes in the
covariate-outcome variable relationship.