R: Kernel Regression Significance Test with Mixed Data Types

npsigtest {np}

R Documentation

Kernel Regression Significance Test with Mixed Data Types

Description

npsigtest implements a consistent test of significance of an explanatory variable in a nonparametric regression setting that is analogous to a simple t-test in a parametric regression setting. The test is based on Racine, Hart, and Li (2006) and Racine (1997).

Usage

npsigtest(bws, ...)

## S3 method for class 'formula'
npsigtest(bws, data = NULL, ...)

## S3 method for class 'call'
npsigtest(bws, ...)

## S3 method for class 'npregression'
npsigtest(bws, ...)

## Default S3 method:
npsigtest(bws, xdat, ydat, ...)

## S3 method for class 'rbandwidth'
npsigtest(bws,
          xdat = stop("data xdat missing"),
          ydat = stop("data ydat missing"),
          boot.num = 399,
          boot.method = c("iid","wild","wild-rademacher"),
          boot.type = c("I","II"),
          index = seq(1,ncol(xdat)),
          random.seed = 42,
          ...)

Arguments

`bws`	a bandwidth specification. This can be set as a `rbandwidth` object returned from a previous invocation, or as a vector of bandwidths, with each element `i` corresponding to the bandwidth for column `i` in `xdat`. In either case, the bandwidth supplied will serve as a starting point in the numerical search for optimal bandwidths when using `boot.type="II"`. If specified as a vector, then additional arguments will need to be supplied as necessary to specify the bandwidth type, kernel types, selection methods, and so on.
`data`	an optional data frame, list or environment (or object coercible to a data frame by `as.data.frame`) containing the variables in the model. If not found in data, the variables are taken from `environment(bws)`, typically the environment from which `npregbw` was called.
`xdat`	a `p`-variate data frame of explanatory data (training data) used to calculate the regression estimators.
`ydat`	a one (1) dimensional numeric or integer vector of dependent data, each element `i` corresponding to each observation (row) `i` of `xdat`.
`boot.method`	a character string used to specify the bootstrap method. `iid` will generate independent identically distributed draws. `wild` will use a wild bootstrap. `wild-rademacher` will use a wild bootstrap with Rademacher variables. Defaults to `iid`.
`boot.num`	an integer value specifying the number of bootstrap replications to use. Defaults to `399`.
`boot.type`	a character string specifying whether to use a ‘Bootstrap I’ or ‘Bootstrap II’ method (see Racine, Hart, and Li (2006) for details). The ‘Bootstrap II’ method re-runs cross-validation for each bootstrap replication and uses the new cross-validated bandwidth for variable `i` and the original ones for the remaining variables. Defaults to `boot.type="I"`.
`index`	a vector of indices for the columns of `xdat` for which the test of significance is to be conducted. Defaults to (1,2,...,`p`) where `p` is the number of columns in `xdat`.
`random.seed`	an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.
`...`	additional arguments supplied to specify the bandwidth type, kernel types, selection methods, and so on, detailed below.

Value

npsigtest returns an object of type sigtest. summary supports sigtest objects. It has the following components:

`In`	the vector of statistics `In`
`P`	the vector of P-values for each statistic in `In`
`In.bootstrap`	contains a matrix of the bootstrap replications of the vector `In`, each column corresponding to replications associated with explanatory variables in `xdat` indexed by `index` (e.g., if you selected `index = c(1,4)` then In.bootstrap will have two columns, the first being the bootstrap replications of `In` associated with variable `1`, the second with variable `4`).

Usage Issues

If you are using data of mixed types, then it is advisable to use the data.frame function to construct your input data and not cbind, since cbind will typically not work as intended on mixed data types and will coerce the data to the same type.

Caution: bootstrap methods are, by their nature, computationally intensive. This can be frustrating for users possessing large datasets. For exploratory purposes, you may wish to override the default number of bootstrap replications, say, setting them to boot.num=99 A version of this package using the Rmpi wrapper is under development that allows one to deploy this software in a clustered computing environment to facilitate computation involving large datasets.

Author(s)

Tristen Hayfield hayfield@mpia.de, Jeffrey S. Racine racinej@mcmaster.ca

References

Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.

Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.

Racine, J.S., J. Hart, and Q. Li (2006), “Testing the significance of categorical predictor variables in nonparametric regression models,” Econometric Reviews, 25, 523-544.

Racine, J.S. (1997), “Consistent significance testing for nonparametric regression,” Journal of Business and Economic Statistics 15, 369-379.

Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.

Examples

## Not run: 
# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we simulate 100 draws
# from a DGP in which z, the first column of X, is an irrelevant
# discrete variable

set.seed(12345)

n <- 100

z <- rbinom(n,1,.5)
x1 <- rnorm(n)
x2 <- runif(n,-2,2)

y <- x1 + x2 + rnorm(n)

# Next, we must compute bandwidths for our regression model. In this
# case we conduct local linear regression. Note - this may take a few
# minutes depending on the speed of your computer...

bw <- npregbw(formula=y~factor(z)+x1+x2,regtype="ll",bwmethod="cv.aic")

# We then compute a vector of tests corresponding to the columns of
# X. Note - this may take a few minutes depending on the speed of your
# computer... we have to generate the null distribution of the statistic
# for each variable whose significance is being tested using 399
# bootstrap replications for each...

npsigtest(bws=bw)

# If you wished, you could conduct the test for, say, variables 1 and 3
# only, as in

npsigtest(bws=bw,index=c(1,3))

# EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we simulate 100
# draws from a DGP in which z, the first column of X, is an irrelevant
# discrete variable

set.seed(12345)

n <- 100

z <- rbinom(n,1,.5)
x1 <- rnorm(n)
x2 <- runif(n,-2,2)

X <- data.frame(factor(z),x1,x2)

y <- x1 + x2 + rnorm(n)

# Next, we must compute bandwidths for our regression model. In this
# case we conduct local linear regression. Note - this may take a few
# minutes depending on the speed of your computer...

bw <- npregbw(xdat=X,ydat=y,regtype="ll",bwmethod="cv.aic")

# We then compute a vector of tests corresponding to the columns of
# X. Note - this may take a few minutes depending on the speed of your
# computer... we have to generate the null distribution of the statistic
# for each variable whose significance is being tested using 399
# bootstrap replications for each...

npsigtest(bws=bw)

# If you wished, you could conduct the test for, say, variables 1 and 3
# only, as in

npsigtest(bws=bw,index=c(1,3))

## End(Not run)

[Package np version 0.50-1 Index]