binstest implements binscatter-based hypothesis testing procedures for parametric functional
forms of and nonparametric shape restrictions on the regression function of interest, following the results
in Cattaneo, Crump, Farrell and Feng (2021a).
If the binning scheme is not set by the user,
the companion function binsregselect is used to implement binscatter in a
data-driven way and inference procedures are based on robust bias correction.
Binned scatter plots based on different methods can be constructed using the companion functions binsreg,
binsqreg or binsglm.
binstest(y, x, w = NULL, data = NULL, estmethod = "reg",
family = gaussian(), quantile = NULL, deriv = 0, at = NULL,
nolink = F, testmodel = c(3, 3), testmodelparfit = NULL,
testmodelpoly = NULL, testshape = c(3, 3), testshapel = NULL,
testshaper = NULL, testshape2 = NULL, lp = Inf, bins = c(2, 2),
nbins = NULL, binspos = "qs", binsmethod = "dpi", nbinsrot = NULL,
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, ...)testshapeLResults for testshapel, including: testvalL, null boundary values;
stat.shapeL, test statistics; and pval.shapeL, p-value.
testshapeRResults for testshaper, including: testvalR, null boundary values;
stat.shapeR, test statistics; and pval.shapeR, p-value.
testshape2Results for testshape2, including: testval2, null boundary values;
stat.shape2, test statistics; and pval.shape2, p-value.
testpolyResults for testmodelpoly, including: testpoly, the degree of global polynomial;
stat.poly, test statistic; pval.poly, p-value.
testmodelResults for testmodelparfit, including: stat.model, test statistics;
pval.model, p-values.
optA list containing options passed to the function, as well as total sample size n,
number of distinct values Ndist in x, number of clusters Nclust, and
number of bins nbins.
outcome variable. A vector.
independent variable of interest. A vector.
control variables. A matrix, a vector or a formula.
an optional data frame containing variables used in the model.
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.
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.)
the quantile to be estimated. A number strictly between 0 and 1.
derivative order of the regression function for estimation, testing and plotting.
The default is deriv=0, which corresponds to the function itself.
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).
if true, the function within the inverse link function is reported instead of the conditional mean function for the outcome.
a vector. testmodel=c(p,s) sets a piecewise polynomial of degree p with s
smoothness constraints for parametric model specification testing. The default is
testmodel=c(3,3), which corresponds to a cubic B-spline estimate of the regression
function of interest for testing against the fitting from a parametric model specification.
a data frame or matrix which contains the evaluation grid and fitted values of the model(s) to be tested against. The column contains a series of evaluation points at which the binscatter model and the parametric model of interest are compared with each other. Each parametric model is represented by other columns, which must contain the fitted values at the corresponding evaluation points.
degree of a global polynomial model to be tested against.
a vector. testshape=c(p,s) sets a piecewise polynomial of degree p with s
smoothness constraints for nonparametric shape restriction testing. The default is
testshape=c(3,3), which corresponds to a cubic B-spline estimate of the regression
function of interest for one-sided or two-sided testing.
a vector of null boundary values for hypothesis testing. Each number a in the vector
corresponds to one boundary of a one-sided hypothesis test to the left of the form
H0: sup_x mu(x)<=a.
a vector of null boundary values for hypothesis testing. Each number a in the vector
corresponds to one boundary of a one-sided hypothesis test to the right of the form
H0: inf_x mu(x)>=a.
a vector of null boundary values for hypothesis testing. Each number a in the vector
corresponds to one boundary of a two-sided hypothesis test ofthe form
H0: sup_x |mu(x)-a|=0.
an Lp metric used for (two-sided) parametric model specification testing and/or shape restriction testing. The default is lp=Inf, which
corresponds to the sup-norm of the t-statistic. Other options are lp=q for a positive integer q.
A vector. Degree and smoothness for bin selection. The default is bins=c(2,2), which corresponds to a quadratic spline estimate.
number of bins for partitioning/binning of x. If not specified, the number of bins is
selected via the companion function binsregselect in a data-driven, optimal way whenever possible.
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).
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.
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.
upper bound on a uniformly distributed variable used to draw a subsample for bins selection.
Observations for which runif()<=# are used. # must be between 0 and 1.
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].
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.
seed for simulation.
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 ID. Used for compute cluster-robust standard errors.
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.
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 (2021b) for more details.
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.
an optional vector of weights to be used in the fitting process. Should be NULL or
a numeric vector. For more details, see lm.
optional rule specifying a subset of observations to be used.
Number of distinct for selection. Used to speed up computation.
Number of clusters for selection. Used to speed up computation.
optional arguments to control bootstrapping if estmethod="qreg" and vce="boot". See boot.rq.
Matias D. Cattaneo, Princeton University, Princeton, NJ. cattaneo@princeton.edu.
Richard K. Crump, Federal Reserve Bank of New York, New York, NY. richard.crump@ny.frb.org.
Max H. Farrell, University of Chicago, Chicago, IL. max.farrell@chicagobooth.edu.
Yingjie Feng (maintainer), Tsinghua University, Beijing, China. fengyingjiepku@gmail.com.
Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2021a: On Binscatter. Working Paper.
Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2021b: Binscatter Regressions. Working Paper.
binsreg, binsqreg, binsglm, binsregselect.
x <- runif(500); y <- sin(x)+rnorm(500)
est <- binstest(y,x, testmodelpoly=1)
summary(est)
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