Significance and Specification

Practical route to nonparametric significance testing and model-specification testing in np.

Keywords

npsigtest, npcmstest, significance test, model specification test, np tests

The np package includes more than estimators. It also provides nonparametric testing tools for questions that applied users ask all the time:

• is a regressor important,
• does a parametric model look misspecified,
• is a simpler model being rejected by the data?

This page focuses on two especially useful functions:

• npsigtest for nonparametric regression significance testing,
• npcmstest for consistent model specification testing.

If you want minimal downloadable scripts for the two main routes on this page, start with:

• np_significance_quickstart.R
• np_specification_quickstart.R

Significance testing: npsigtest

Once a nonparametric regression model has been fitted, npsigtest provides a nonparametric counterpart to the familiar significance-testing mindset from parametric regression.

library(np)
data(cps71, package = "np")

fit <- npreg(
  logwage ~ age,
  regtype = "ll",
  bwmethod = "cv.aic",
  gradients = TRUE,
  data = cps71
)

npsigtest(fit)

This is useful when you want to know whether a regressor matters without collapsing immediately back to a parametric linear model.

Model specification testing: npcmstest

npcmstest is useful when you have a parametric regression model in hand and want to test whether it looks correctly specified against a nonparametric alternative.

The older wage1 example remains instructive because it starts with a simple linear specification and then asks whether that specification is too restrictive.

library(np)
data(wage1, package = "np")

model_ols <- lm(
  lwage ~ female + married + educ + exper + tenure,
  x = TRUE,
  y = TRUE,
  data = wage1
)

X <- data.frame(
  female = wage1$female,
  married = wage1$married,
  educ = wage1$educ,
  exper = wage1$exper,
  tenure = wage1$tenure
)

test_out <- npcmstest(
  model = model_ols,
  xdat = X,
  ydat = wage1$lwage,
  nmulti = 1
)

summary(test_out)

Practical warning

These tests can be computationally demanding because they may involve both bandwidth selection and bootstrap procedures.

Practical advice:

• begin with a small or illustrative problem,
• do not assume that testing is cheap just because estimation already ran,
• avoid overriding search tolerances casually unless you are deliberately doing a quick exploratory run.

When should I use these?

Question	Function
Is a regressor significant in a nonparametric regression setting?	npsigtest
Does a parametric regression model look misspecified against a nonparametric alternative?	npcmstest

How do these fit with the rest of the site?

• Start with Kernel Primer if you are new to the main estimation workflow.
• See Entropy and Testing for the entropy-based test family.
• See Plotting and Intervals if you want uncertainty summaries and graphical output.

Together, these pages cover the main ways in which np moves beyond “just fit a regression curve”.