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

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.

Value

AA list with class white_test containing:

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

# 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)

Bootstrapped version of the White's test (Jeong, J., Lee, K. (1999))

Description

This is a versioned White's test based on a bootstrap procedure that can improve the performance of White’s test, specially in small samples. It was proposed by Jeong, J., Lee, K. (1999) (see references for further details).

Usage

white_test_boot(model, bootstraps = 1000)

Arguments

Details

The bootstrapped error term is defined by:

\widehat{u_i} = \sigma^2 * t_i^{*} (i = 1,...N)

where t_i^{*} follows a distribution satisfying E(t) = 0 and var(t) = I.

In particular, the selected distribution of t can be found at the bottom of page 196 at Handbook of Computational Econometrics (2009).

Value

A list with class white_test containing:

References

Jeong, J., & Lee, K. (1999). Bootstrapped White’s test for heteroskedasticity in regression models. Economics Letters, 63(3), 261-267.

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,

Examples

# 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_boot(fit)