whitestrap (version 0.0.1)

white_test: This function performs a White's Test for heteroskedasticity (White, H. (1980))

Description

White's test is a statistical test that determines whether the variance of the residuals in a regression model is constant.

Usage

white_test(model)

Arguments

model

An object of class lm

Value

AA list with class white_test containing:

w_stat	The value of the test statistic
p_value	The p-value of the test

Details

The approach followed is the one detailed at Wooldridge, 2012, p. 275. The fitted values from the original model are:

$$\widehat{y_i} = \widehat{\beta_0} + \widehat{\beta_1}x_{i1} + ... + \widehat{\beta_k}x_{ik}$$

Heteroscedasticity could be tested as a linear regression of the squared residuals against the fitted values:

$$\widehat{u^2} = \delta_0 + \delta_1\widehat{y} + \delta_2\widehat{y^2} + error$$

The null hypothesis states that \(\delta_1 = \delta_2 = 0\) (homoskedasticity). The test statistic is defined as:

$$LM = nR^2$$

where \(R^2\) is the R-squared value from the regression of \(u^2\).

References

White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica, 48(4), 817-838.

Wooldridge, Jeffrey M., 1960-. (2012). Introductory econometrics : a modern approach. Mason, Ohio : South-Western Cengage Learning,

See Also

lm

Examples

# NOT RUN {
# Define a dataframe with heteroscedasticity
n <- 100
y <- 1:n
sd <- runif(n, min = 0, max = 4)
error <- rnorm(n, 0, sd*y)
X <- y + error
df <- data.frame(y, X)
# OLS model
fit <- lm(y ~ X, data = df)
# White's test
white_test(fit)
# }