Perform the non-constant variance (NCV) score test (deprecated)¶

Source: man/performNCVTest.Rd · Help: ?performNCVTest

The Cook-Weisberg score test for non-constant error variance, the diagnostic returned by car::ncvTest().

Usage¶

performNCVTest(model, data = NULL, var_formula = NULL)

Arguments¶

model: an object of class lm.
data: optional data frame the model was fitted to, in which var_formula is evaluated, as in performCookWeisbergTest. When NULL, the default, the model frame of model is used.
var_formula: optional one-sided formula giving the variance model, evaluated in data (for example ~ x1 + x2). When NULL the fitted values are used. Before 0.15.0 var_formula was the second argument: a formula passed there by position is still read as var_formula, with a warning; that form stops working in 1.0.0.

Value¶

An object of class htest containing the chi-square score statistic, its degrees of freedom and the p-value.

Details¶

Let \(\hat{e}_i\) denote the OLS residuals and \(\hat{\sigma}^2 = \sum_i \hat{e}_i^2 / n\) the maximum-likelihood variance estimate. The test regresses the scaled squared residuals \(u_i = \hat{e}_i^2 / \hat{\sigma}^2\) on the variance regressors \(Z\) and computes half the explained sum of squares of that auxiliary regression. Under homoscedasticity and normal errors the statistic is asymptotically chi-square with degrees of freedom equal to the number of variance regressors.

With var_formula = NULL the fitted values are the sole variance regressor, matching the default of car::ncvTest() and Stata's estat hettest.

Because the divisor 2 is the null variance of \(\hat{e}^2 / \sigma^2\) under normality, the test is sensitive to non-normal errors; performKoenkerTest provides the studentized variant, which is robust to non-normal kurtosis.

Deprecated¶

performNCVTest() is deprecated since 0.14.0: use performCookWeisbergTest, which gained var_formula and is the one entry point for the Cook-Weisberg score test. With a variance formula, performNCVTest(model, var_formula) returns what performCookWeisbergTest(model, var_formula) returns; without one the two return the same statistic, degrees of freedom and p-value, and performCookWeisbergTest() labels the result as the Cook-Weisberg test. The old name still works, returns what it returned and warns.

Weighted fits¶

On a fit with weights the test is computed from the Pearson residuals \(\sqrt{w_i}\, e_i\), so it tests whether the weights are adequate; see the section on weighted fits in performKoenkerTest(), which also covers weights estimated by fitWLS().

Validation¶

Reproduces car::ncvTest() to within 1e-8 for both the default and the var_formula forms; see tests/testthat/test-pass-a-reference.R. Releases before 0.7.0 regressed the absolute residuals on the fitted values and reported a t statistic, which is a Glejser-type test rather than the Cook-Weisberg score test.

References¶

Cook, R. D., & Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika, 70(1), 1–10. doi:10.1093/biomet/70.1.1

Fox, J., & Weisberg, S. (2019). An R Companion to Applied Regression (3rd ed.). SAGE.

Examples¶

 data(mtcars)
 m <- lm(mpg ~ wt + qsec, data = mtcars)
 # Deprecated: use performCookWeisbergTest(m) and
 # performCookWeisbergTest(m, var_formula = ~wt)
 suppressWarnings(performNCVTest(m, var_formula = ~wt))