binspwc {binsreg}

Data-Driven Pairwise Group Comparison using Binscatter Methods

Description

binspwc implements hypothesis testing procedures for pairwise group comparison of binscatter estimators and plots confidence bands for the difference in binscatter parameters between each pair of groups, following the results in Cattaneo, Crump, Farrell and Feng (2024a) and Cattaneo, Crump, Farrell and Feng (2024b). If the binning scheme is not set by the user, the companion function binsregselect is used to implement binscatter in a data-driven way. Binned scatter plots based on different methods can be constructed using the companion functions binsreg, binsqreg or binsglm. Hypothesis testing for parametric functional forms of and shape restrictions on the regression function of interest can be conducted via the companion function binstest.

Usage

binspwc(y, x, w = NULL, data = NULL, estmethod = "reg",
  family = gaussian(), quantile = NULL, deriv = 0, at = NULL,
  nolink = F, by = NULL, pwc = NULL, testtype = "two-sided",
  lp = Inf, bins = NULL, bynbins = NULL, binspos = "qs",
  pselect = NULL, sselect = NULL, binsmethod = "dpi", nbinsrot = NULL,
  samebinsby = FALSE, randcut = NULL, nsims = 500, simsgrid = 20,
  simsseed = NULL, vce = NULL, cluster = NULL, asyvar = F,
  dfcheck = c(20, 30), masspoints = "on", weights = NULL,
  subset = NULL, numdist = NULL, numclust = NULL, estmethodopt = NULL,
  plot = FALSE, dotsngrid = 0, plotxrange = NULL, plotyrange = NULL,
  colors = NULL, symbols = NULL, level = 95, ...)

Arguments

y

outcome variable. A vector.

x

independent variable of interest. A vector.

w

control variables. A matrix, a vector or a formula.

data

an optional data frame containing variables used in the model.

estmethod

estimation method. The default is estmethod="reg" for tests based on binscatter least squares regression. Other options are "qreg" for quantile regression and "glm" for generalized linear regression. If estmethod="glm", the option family must be specified.

family

a description of the error distribution and link function to be used in the generalized linear model when estmethod="glm". (See family for details of family functions.)

quantile

the quantile to be estimated. A number strictly between 0 and 1.

deriv

derivative order of the regression function for estimation, testing and plotting. The default is deriv=0, which corresponds to the function itself.

at

value of w at which the estimated function is evaluated. The default is at="mean", which corresponds to the mean of w. Other options are: at="median" for the median of w, at="zero" for a vector of zeros. at can also be a vector of the same length as the number of columns of w (if w is a matrix) or a data frame containing the same variables as specified in w (when data is specified). Note that when at="mean" or at="median", all factor variables (if specified) are excluded from the evaluation (set as zero).

nolink

if true, the function within the inverse link function is reported instead of the conditional mean function for the outcome.

by

a vector containing the group indicator for subgroup analysis; both numeric and string variables are supported. When by is specified, binsreg implements estimation and inference for each subgroup separately, but produces a common binned scatter plot. By default, the binning structure is selected for each subgroup separately, but see the option samebinsby below for imposing a common binning structure across subgroups.

pwc

a vector or a logical value. If pwc=c(p,s), a piecewise polynomial of degree p with s smoothness constraints is used for testing the difference between groups. If pwc=T or pwc=NULL (default) is specified, pwc=c(1,1) is used unless the degree p or smoothness s selection is requested via the option pselect or sselect (see more details in the explanation of pselect and sselect).

testtype

type of pairwise comparison test. The default is testtype="two-sided", which corresponds to a two-sided test of the form H0: mu_1(x)=mu_2(x). Other options are: testtype="left" for the one-sided test form H0: mu_1(x)<=mu_2(x) and testtype="right" for the one-sided test of the form H0: mu_1(x)>=mu_2(x).

lp

an Lp metric used for pairwise comparison tests. The default is lp=Inf, which corresponds to the sup-norm of the t-statistic. Other options are lp=q for a positive number q>=1. Note that lp=Inf ("sup-norm") has to be used for one-sided tests (testtype="left" or testtype="right").

bins

A vector. If bins=c(p,s), it sets the piecewise polynomial of degree p with s smoothness constraints for data-driven (IMSE-optimal) selection of the partitioning/binning scheme. The default is bins=c(0,0), which corresponds to the piecewise constant.

bynbins

a vector of the number of bins for partitioning/binning of x, which is applied to the binscatter estimation for each group. If a single number is specified, it is applied to the estimation for all groups. If bynbins=T or bynbins=NULL (default), the number of bins is selected via the companion function binsregselect in a data-driven way whenever possible. Note: If a vector with more than one number is supplied, it is understood as the number of bins applied to binscatter estimation for each subgroup rather than the range for selecting the number of bins.

binspos

position of binning knots. The default is binspos="qs", which corresponds to quantile-spaced binning (canonical binscatter). The other options are "es" for evenly-spaced binning, or a vector for manual specification of the positions of inner knots (which must be within the range of x).

pselect

vector of numbers within which the degree of polynomial p for point estimation is selected. If the selected optimal degree is p, then piecewise polynomials of degree p+1 are used to conduct pairwise group comparison. Note: To implement the degree or smoothness selection, in addition to pselect or sselect, bynbins=# must be specified.

sselect

vector of numbers within which the number of smoothness constraints s for point estimation is selected. If the selected optimal smoothness is s, then piecewise polynomials with s+1 smoothness constraints are used to conduct pairwise group comparison. If not specified, for each value p supplied in the option pselect, only the piecewise polynomial with the maximum smoothness is considered, i.e., s=p.

binsmethod

method for data-driven selection of the number of bins. The default is binsmethod="dpi", which corresponds to the IMSE-optimal direct plug-in rule. The other option is: "rot" for rule of thumb implementation.

nbinsrot

initial number of bins value used to construct the DPI number of bins selector. If not specified, the data-driven ROT selector is used instead.

samebinsby

if true, a common partitioning/binning structure across all subgroups specified by the option by is forced. The knots positions are selected according to the option binspos and using the full sample. If nbins is not specified, then the number of bins is selected via the companion command binsregselect and using the full sample.

randcut

upper bound on a uniformly distributed variable used to draw a subsample for bins/degree/smoothness selection. Observations for which runif()<=# are used. # must be between 0 and 1. By default, max(5000, 0.01n) observations are used if the samples size n>5000.

nsims

number of random draws for hypothesis testing. The default is nsims=500, which corresponds to 500 draws from a standard Gaussian random vector of size [(p+1)*J - (J-1)*s]. Setting at least nsims=2000 is recommended to obtain the final results.

simsgrid

number of evaluation points of an evenly-spaced grid within each bin used for evaluation of the supremum (infimum or Lp metric) operation needed to construct hypothesis testing procedures. The default is simsgrid=20, which corresponds to 20 evenly-spaced evaluation points within each bin for approximating the supremum (infimum or Lp metric) operator. Setting at least simsgrid=50 is recommended to obtain the final results.

simsseed

seed for simulation.

vce

procedure to compute the variance-covariance matrix estimator. For least squares regression and generalized linear regression, the allowed options are the same as that for binsreg or binsqreg. For quantile regression, the allowed options are the same as that for binsqreg.

cluster

cluster ID. Used for compute cluster-robust standard errors.

asyvar

if true, the standard error of the nonparametric component is computed and the uncertainty related to control variables is omitted. Default is asyvar=FALSE, that is, the uncertainty related to control variables is taken into account.

dfcheck

adjustments for minimum effective sample size checks, which take into account number of unique values of x (i.e., number of mass points), number of clusters, and degrees of freedom of the different stat models considered. The default is dfcheck=c(20, 30). See Cattaneo, Crump, Farrell and Feng (2024c) for more details.

masspoints

how mass points in x are handled. Available options:

• "on" all mass point and degrees of freedom checks are implemented. Default.

• "noadjust" mass point checks and the corresponding effective sample size adjustments are omitted.

• "nolocalcheck" within-bin mass point and degrees of freedom checks are omitted.

• "off" "noadjust" and "nolocalcheck" are set simultaneously.

• "veryfew" forces the function to proceed as if x has only a few number of mass points (i.e., distinct values). In other words, forces the function to proceed as if the mass point and degrees of freedom checks were failed.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. For more details, see lm.

subset

optional rule specifying a subset of observations to be used.

numdist

number of distinct values for selection. Used to speed up computation.

numclust

number of clusters for selection. Used to speed up computation.

estmethodopt

a list of optional arguments used by rq (for quantile regression) or glm (for fitting generalized linear models).

plot

if true, the confidence bands for all pairwise group comparisons (the difference between each pair of groups) are plotted. The degree and smoothness of polynomials used to construct the bands are the same as those specified for testing. The default is plot=F, i.e., no plot is generated.

dotsngrid

number of dots to be added to the plot for confidence bands. Given the choice, these dots are point estimates of the difference between groups evaluated over an evenly-spaced grid within the common support of all groups. The default is dotsngrid=0, i.e., no point estimates are added. Whenever possible, the degree and smoothness of the polynomial for these point estimates are the same as those for selecting the number of bins; otherwise, the degree and smoothness specified for testing are used.

plotxrange

a vector. plotxrange=c(min, max) specifies a range of the x-axis for plotting. Observations outside the range are dropped in the plot.

plotyrange

a vector. plotyrange=c(min, max) specifies a range of the y-axis for plotting. Observations outside the range are dropped in the plot.

colors

an ordered list of colors for plotting the difference between each pair of groups.

symbols

an ordered list of symbols for plotting the difference between each pair of groups.

level

nominal confidence level for confidence band estimation. Default is level=95.

...

optional arguments to control bootstrapping if estmethod="qreg" and vce="boot". See boot.rq.

Value

stat

A matrix. Each row corresponds to the comparison between two groups. The first column is the test statistic. The second and third columns give the corresponding group numbers. The null hypothesis is mu_i(x)<=mu_j(x), mu_i(x)=mu_j(x), or mu_i(x)>=mu_j(x) for group i (given in the second column) and group j (given in the third column). The group number corresponds to the list of group names given by opt$byvals.

pval

A vector of p-values for all pairwise group comparisons.

bins_plot

A ggplot object for confidence bands plot.

data.plot

A list containing data for plotting. Each item is a sublist of data frames for comparison between each pair of groups. Each sublist may contain the following data frames:

• data.dots Data for dots. It contains: pair, the name for the pair of groups; x, evaluation points; diff.fit, point estimates of the group difference;

• data.cb Data for confidence bands. It contains: pair, the name for the pair of groups; x, evaluation points; cb.fit, point estimates of the group difference; cb.se, standard errors; cb.l and cb.r, left and right boundaries of the confidence band.

cval.cb

A vector of critical values for all pairwise group comparisons.

imse.var.rot

Variance constant in IMSE expansion, ROT selection.

imse.bsq.rot

Bias constant in IMSE expansion, ROT selection.

imse.var.dpi

Variance constant in IMSE expansion, DPI selection.

imse.bsq.dpi

Bias constant in IMSE expansion, DPI selection.

opt

A list containing options passed to the function, as well as N.by (total sample size for each group), Ndist.by (number of distinct values in x for each group), Nclust.by (number of clusters for each group), and nbins.by (number of bins for each group), and byvals (number of distinct values in by).

Author(s)

Matias D. Cattaneo, Princeton University, Princeton, NJ. [e-mail].

Richard K. Crump, Federal Reserve Bank of New York, New York, NY. [e-mail].

Max H. Farrell, UC Santa Barbara, Santa Barbara, CA. [e-mail].

Yingjie Feng (maintainer), Tsinghua University, Beijing, China. [e-mail].

References

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2024a: On Binscatter. American Economic Review 114(5): 1488-1514.

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2024b: Nonlinear Binscatter Methods. Working Paper.

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2024c: Binscatter Regressions. Working Paper.

See Also

binsreg, binsqreg, binsglm, binsregselect, binstest.

Examples

 x <- runif(500); y <- sin(x)+rnorm(500); t <- 1*(runif(500)>0.5)
 ## Binned scatterplot
 binspwc(y,x, by=t)