Regression Spline Significance Test with Mixed Data Types

crssigtest 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 Ma and Racine (2011).

Usage

crssigtest(model = NULL,
           index = NULL,
           boot = TRUE,
           boot.num = 399,
           boot.type = c("residual","reorder"),
           random.seed = 42)

Arguments

Data, Model Inputs And Formula Interface

These arguments identify the fitted model and tested indices.

index: a vector of indices for the columns of model$xz for which the test of significance is to be conducted. Defaults to (1,2,...,$p$) where $p$ is the number of columns in model$xz.
model: a crs model object.

Bootstrap Controls

These arguments control bootstrap execution and reproducibility settings.

boot: a logical value (default TRUE) indicating whether to compute the bootstrap P-value or simply return the asymptotic P-value.
boot.num: an integer value specifying the number of bootstrap replications to use. Defaults to 399.
boot.type: whether to conduct ‘residual’ bootstrapping (iid) or permute (reorder) in place the predictor being tested when imposing the null.
random.seed: an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.

Value

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

index: the vector of indices input
P: the vector of bootstrap P-values for each statistic in F
P.asy: the vector of asymptotic P-values for each statistic in index
F: the vector of pseudo F-statistics F
F.boot: the matrix of bootstrapped pseudo F-statistics generated under the null (one column for each statistic in F)
df1: the vector of numerator degrees of freedom for each statistic in F (based on the smoother matrix)
df2: the vector of denominator degrees of freedom for each statistic in F (based on the smoother matrix)
rss: the vector of restricted sums of squared residuals for each statistic in F
uss: the vector of unrestricted sums of squared residuals for each statistic in F
boot.num: the number of bootstrap replications
boot.type: the boot.type
xnames: the names of the variables in model$xz

References

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

Ma, S. and J.S. Racine, (2011), “Inference for Regression Splines with Categorical and Continuous Predictors,” Working Paper.

Author

Jeffrey S. Racine racinej@mcmaster.ca

Usage Issues

This function should be considered to be in ‘beta status’ until further notice.

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.

Examples

if (FALSE) { # \dontrun{
options(crs.messages=FALSE)
set.seed(42)

n <- 1000
z <- rbinom(n,1,.5)
x1 <- rnorm(n)
x2 <- runif(n,-2,2)
z <- factor(z)
## z is irrelevant
y <- x1 + x2 + rnorm(n)

model <- crs(y~x1+x2+z,complexity="degree",segments=c(1,1))
summary(model)

model.sigtest <- crssigtest(model)
summary(model.sigtest)
} # }