binsregselect {binsreg}

Data-Driven IMSE-Optimal Partitioning/Binning Selection for Binscatter

Description

binsregselect implements data-driven procedures for selecting the number of bins for binscatter estimation. The selected number is optimal in minimizing integrated mean squared error (IMSE).

Usage

binsregselect(y, x, w = NULL, data = NULL, deriv = 0, bins = NULL,
  pselect = NULL, sselect = NULL, binspos = "qs", nbins = NULL,
  binsmethod = "dpi", nbinsrot = NULL, simsgrid = 20, savegrid = F,
  vce = "HC1", useeffn = NULL, randcut = NULL, cluster = NULL,
  dfcheck = c(20, 30), masspoints = "on", weights = NULL,
  subset = NULL, norotnorm = F, numdist = NULL, numclust = NULL)

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.

deriv

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

bins

a vector. bins=c(p,s) set a piecewise polynomial of degree p with s smoothness constraints for data-driven (IMSE-optimal) selection of the partitioning/binning scheme. By default, the function sets bins=c(0,0), which corresponds to piecewise constant (canonical binscatter).

pselect

vector of numbers within which the degree of polynomial p for point estimation is selected. Note: To implement the degree or smoothness selection, in addition to pselect or sselect, nbins=# must be specified.

sselect

vector of numbers within which the number of smoothness constraints s for point estimation is selected. 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.

binspos

position of binning knots. The default is binspos="qs", which corresponds to quantile-spaced binning (canonical binscatter). The other option is binspos="es" for evenly-spaced binning.

nbins

number of bins for degree/smoothness selection. If nbins=T or nbins=NULL (default) is specified, the function selects the number of bins instead, given the specified degree and smoothness. If a vector with more than one number is specified, the command selects the number of bins within this vector.

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.

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 confidence bands and 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.

savegrid

if true, a data frame produced containing grid.

vce

procedure to compute the variance-covariance matrix estimator. Options are

• "const" homoskedastic variance estimator.

• "HC0" heteroskedasticity-robust plug-in residuals variance estimator without weights.

• "HC1" heteroskedasticity-robust plug-in residuals variance estimator with hc1 weights. Default.

• "HC2" heteroskedasticity-robust plug-in residuals variance estimator with hc2 weights.

• "HC3" heteroskedasticity-robust plug-in residuals variance estimator with hc3 weights.

useeffn

effective sample size to be used when computing the (IMSE-optimal) number of bins. This option is useful for extrapolating the optimal number of bins to larger (or smaller) datasets than the one used to compute it.

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.

cluster

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

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 statistical 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.

norotnorm

if true, a uniform density rather than normal density used for ROT selection.

numdist

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

numclust

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

Value

nbinsrot.poly

ROT number of bins, unregularized.

nbinsrot.regul

ROT number of bins, regularized.

nbinsrot.uknot

ROT number of bins, unique knots.

nbinsdpi

DPI number of bins.

nbinsdpi.uknot

DPI number of bins, unique knots.

prot.poly

ROT degree of polynomials, unregularized.

prot.regul

ROT degree of polynomials, regularized.

prot.uknot

ROT degree of polynomials, unique knots.

pdpi

DPI degree of polynomials.

pdpi.uknot

DPI degree of polynomials, unique knots.

srot.poly

ROT number of smoothness constraints, unregularized.

srot.regul

ROT number of smoothness constraints, regularized.

srot.uknot

ROT number of smoothness constraints, unique knots.

sdpi

DPI number of smoothness constraints.

sdpi.uknot

DPI number of smoothness constraints, unique knots.

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.

int.result

Intermediate results, including a matrix of degree and smoothness (deg_mat), the selected numbers of bins (vec.nbinsrot.poly,vec.nbinsrot.regul, vec.nbinsrot.uknot, vec.nbinsdpi, vec.nbinsdpi.uknot), and the bias and variance constants in IMSE (vec.imse.b.rot, vec.imse.v.rot, vec.imse.b.dpi, vec.imse.v.dpi) under each rule (ROT or DPI), corresponding to each pair of degree and smoothness (each row in deg_mat).

opt

A list containing options passed to the function, as well as total sample size n, number of distinct values Ndist in x, and number of clusters Nclust.

data.grid

A data frame containing grid.

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, binstest.

Examples

 x <- runif(500); y <- sin(x)+rnorm(500)
 est <- binsregselect(y,x)
 summary(est)