Perform the non-constant variance (NCV) score test

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

Usage

performNCVTest(model, var_formula = NULL)

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.

Arguments

model: an object of class lm.
var_formula: optional one-sided formula giving the variance model, evaluated in the model frame of model (for example ~ x1 + x2). When NULL the fitted values are used.

Value

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

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)
 performNCVTest(m)
#> [INFO] Running NCV score test
#> 
#> 	Cook-Weisberg score test for non-constant variance
#> 
#> data:  mpg ~ wt + qsec; variance model: fitted values
#> X-squared = 0.59099, df = 1, p-value = 0.442
#> alternative hypothesis: error variance depends on the variance model
#> 

 # Score test against a specific variance model rather than the fitted values
 performNCVTest(m, var_formula = ~wt)
#> [INFO] Running NCV score test
#> 
#> 	Cook-Weisberg score test for non-constant variance
#> 
#> data:  mpg ~ wt + qsec; variance model: wt
#> X-squared = 0.066469, df = 1, p-value = 0.7965
#> alternative hypothesis: error variance depends on the variance model
#>