Inference for Relative Distributions
Estimate and graph relative distribution and density functions for continuous or discrete data.
reldist(y, yo=FALSE, ywgt=FALSE,yowgt=FALSE, show="none", decomp="locadd", location="median", scale="IQR", rpmult=FALSE, z=FALSE, zo=FALSE, smooth = 0.35, quiet = TRUE, cdfplot=FALSE, ci=FALSE, bar="no", add=FALSE, graph=TRUE, type="l", xlab="Reference proportion",ylab="Relative Density",yaxs="r", yolabs=pretty(yo), yolabslabs=NULL, ylabs=pretty(y), ylabslabs=NULL, yolabsloc=0.6, ylabsloc=1, ylim=NULL, cex=0.8, lty=1, binn=5000, aicc=seq(0.0001, 5, length=30), deciles=(0:10)/10, discrete=FALSE, method="Bayes", y0=NULL, control = list(samples = 4000, burnin = 1000), ...)
y: Sample from comparison distribution.
yo: Sample from reference distribution.
discrete: Do y and yo refer to a discrete distribution? If TRUE a discrete estimator is used instead of the default continuous one.
smooth: Degree of smoothness required in the fit. Higher values lead to smoother curves, lower positive values lead to closer fits to the observed data. If it is not specified the value that minimizes GCV is used. If a value less than zero is specified then the value is chosen to minimize a corrected AIC. If discrete=TRUE
it is the minimum number of values to pool in the reference distribution in the probability mass function estimate.
method: Method used to estimate the relative density. The default ("Bayes") uses a density estimator based on Poisson Nonparametric Regression and Bayesian inference developed by Wand and Wu (2022). The option ("bgk") uses a Gaussian kernel density estimator for bounded domain one-dimensional data developed by Botev, Grotowski and Kroese (2010). The option ("gam") uses a local likelihood approach based on smoothed Poisson regression. The option "loclik" uses log-splines. The option "quick" uses the Anscombe transformation to stabilize variances. In versions prior to 1.3 the "quick"
approach was used.
graph: Graph the results on the current device.
bar: Graph the deciles on the current device. Possible values of bar are "no" (no deciles plotted), "yes"
(deciles plotted with the non-parametric fit,
"only"(deciles plotted without non-parametric fit).
add: Add the density to the current plot?
ylim: plotting limit for the vertical axis.
lty: Line type to be used for the density.
xlab: Horizontal label.
ylab: Vertical label.
ylabs: Locations for label to be added to the right axis.
ylabslabs: Labels indicating the original scale for the comparison distribution.
ylabsloc: Distance of labels to right of axis (in lines).
yolabs: locations for labels to be added to the tip axis.
yolabslabs: Labels indicating the original scale for the reference distribution.
yolabsloc: Distance of labels above axis (in lines).
yaxs: Style of vertical axis.
cdfplot: calculate and plot the CDF rather than the density.
quiet: Should the output be returned invisibly?
ci: Plot (pointwise) 95% confidence intervals?
ywgt: Weights on the comparison sample.
yowgt: Weights on the reference sample.
z: Covariate on the comparison sample to be used to adjust it to the reference distribution. Only used if the form of matching specified in
decomp="covariate".
zo: Covariate on the reference sample to be used in the adjustment. to the reference distribution. Only used if the form of matching specified in
decomp="covariate".
show: Type of relative distribution to produce. Possible values are "none" (comparisons to reference), residual
(location-matched reference to reference), effect (comparison to location-matched reference).
decomp: Form of matching to the comparison sample. Possible values are locmult (multiplicatively scale the reference), locadd (additively shift the reference), lsadd
(location/scale additive shift), covariate (covariate adjust the reference (requires z and zo to be specified)).
location: How to measure location. Possible values are "mean" and "median".
scale: How to measure the scale. Possible values are "standev" (standard deviation) and IQR (interquartile range).
rpmult: Only in calculation of polarization indices: multiplicatively scale the reference sample to the comparison sample before comparing the two distributions?
binn: Number of bins used in the smoother.
deciles: The percentiles used for the histogram bins. Typically deciles (i.e., 0.0, 0.1, 0.2,...,0.9, 1.0), but any set can be used (e.g., quintiles, terciles).
aicc: Values of the smoothing parameter to search over in minimizing the corrected AIC. Only used if method="gam" and smooth is less than 0.
type: Type of plot to use. See par().
cex: Character expansion to use in plots. See par().
y0: A test to see if yo was passed. If y0 is passed it prints a warning. If y0 is passed and yo is not passed then y0 is used as the sample from reference distribution.
control: list; A simple list of control options for the STAN HMC computation used when method="Bayes", the default. The two components are samples=4000, the number of samples drawn and burnin=1000, the burn-in used.
...: Additional arguments to the plot functions. See par().
x: Horizontal coordinates for the density (typically percentages).
y: Density at x.
rp: 95% confidence interval for the median relative polarization as lower bound, estimate, upper bound.
rpl: 95% confidence interval for the lower relative polarization as lower bound, estimate, upper bound.
rpu: 95% confidence interval for the upper relative polarization as lower bound, estimate, upper bound.
cdf: x coordinates for the CDF (typically percentages) and y CDF at x.
Most of the code is for the plotting and tinkering. The guts of the method are forming the relative data at the top. The rest is a standard fixed interval density estimation with a few bells and whistles.
# # First load the data. # data(nls, package="reldist") # # A simple example comparing permanent wages of the original to the # recent cohort in the NLS. See H&M (1999) for details. reldist(y=recent$chpermwage,yo=original$chpermwage,method="bgk") # # A more sophisticated version of the same. # reldist(y=recent$chpermwage, yo=original$chpermwage, yowgt=original$wgt, ywgt=recent$wgt, bar=TRUE, smooth=0.1, method="bgk", yolabs=seq(-1, 3, by=0.5), ylim=c(0, 3.0),cex=0.8, ylab="Relative Density", xlab="Proportion of the Original Cohort") # # A CDF version. # reldist(y=recent$chpermwage, yo=original$chpermwage, yowgt=original$wgt, ywgt=recent$wgt, cdfplot=TRUE, smooth=0.4, yolabs=seq(-1,3,by=0.5), ylabs=seq(-1,3,by=0.5), cex=0.8, method="bgk", ylab="proportion of the recent cohort", xlab="proportion of the original cohort")
For more examples see the tech report
Mark S. Handcock and Eric Mark Aldrich Applying Relative Distribution Methods in R
University of Washington CSSS Working Paper No. 27, Available at SSRN: tools:::Rd_expr_doi("10.2139/ssrn.1515775") .
Z. I. Botev, J. F. Grotowski and D. P. Kroese Kernel Density Estimation Via Diffusion
Annals of Statistics, 2010, Volume 38, Number 5, Pages 2916-2957.
M. Wand and J. C. F. Yu Density Estimation via Bayesian Inference Engines
AStA Advances in Statistical Analysis, 2021, tools:::Rd_expr_doi("10.1007/s10182-021-00422-8") .