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varin sacha
varin sacha

Reputation: 169

Econometrics : White Test with R

Good morning,

I am trying to realize the white test on my linear model with R. I don't know how to write the R codes to realize the White Test.

Price : house price, in millions dollars

Bdrms : number of bedrooms

Lotsize : size of lot in square feet

Sqrft : size of house in square feet

The linear model is the following :

#Linear Model
LinearModel.1 <- lm(PRICE ~ LOTSIZE + LOTSIZE^2 + SQRFT + BDRMS, data=Dataset)
summary(LinearModel.1)


#Breusch-Pagan Test
library(lmtest)
bptest(LinearModel.1, varformula = NULL, studentize = TRUE, data = Dataset)


#White Test
?????????

Thanks for your answer Kind regards,

Upvotes: 0

Views: 32306

Answers (5)

luchonacho
luchonacho

Reputation: 7167

Test can be implemente using the bptest function from the lmtest package, as follows:

reg <- lm(y~x1+x2) # storing regression
bptest(reg, ~ poly(fitted(reg) , 2))

Notice the above implements the special form of the test, which uses the fitted value of y and its squared value (hence the option poly(fitted(reg) , 2) in bptest) as regressors in the second stage equation. The normal form uses all regressors, their squared values and interactions as elements in the second stage regression, at the cost of losing degrees of freedom. To implement that form you need to replace ~ poly(fitted(reg) , 2) with something like ~ x1*x2 + x1*x3 .... If you have a lot of regressors, it might be easier to use another package.

Upvotes: 1

Thomas Farrar
Thomas Farrar

Reputation: 253

White's Test is now implemented in the white_lm function of skedastic package; see https://www.rdocumentation.org/packages/skedastic/versions/1.0.0/topics/white_lm

Upvotes: 2

Edward
Edward

Reputation: 574

I have written a function to reproduce two methods in R for White's test in hendry2007econometric.

test_white(mod, dat, resi2 ~ x1 + x2 + I(x1^2) + I(x2^2), 3)

where the squared residuals are regressed on all regressors and their squares. The degree of freedom is the number of parameters (let's say k).

test_white(mod, dat, resi2 ~ x1 + x2 + I(x1^2) + I(x2^2) + I(x1 * x2), 6)

where the squared residuals are regressed on all regressors, their squares, and their cross products. The degree of freedom is k * (k + 1) / 2.

test_white <- function(mod, dat, f, df1, prob){
  if(missing(prob)){prob = 0.05}

  dat %<>% mutate(resi2 = mod$residuals^2)

  stat <-
    lm(f, data = dat) %>%
    {summary(.)$r.squared} %>%
    {. * nrow(dat)}

  p_value <- 
    stat %>%
    {1 - pchisq(., df1)}

  results <- tibble(
    whi = "White", stat = stat, df1 = df1, df2 = nrow(dat) - df1,  
    p_value = p_value,prob = prob, if_accept = {p_value <= prob}, 
    if_pass = {p_value >= prob}
  )
  return(results)
}

I think the way @Mike K does is alright, which is actually to test if an lm model based on the scale-location plot is significant. The scale-location plot refers to when you plot diagnostics for an lm object by plot.lm(model, which = 3).

Upvotes: 0

Mike K
Mike K

Reputation: 81

m <- LinearModel.1
data <- Dataset
u2 <- m$residuals^2
y <- fitted(m)
Ru2<- summary(lm(u2 ~ y + I(y^2)))$r.squared
LM <- nrow(data)*Ru2
p.value <- 1-pchisq(LM, 2)
p.value

if p.value < 0.05, then Ho (there is no heteroskedasticity) is rejected at 5% significance level and you conclude that there is heteroskedasticity in your model

Upvotes: 5

Stijn
Stijn

Reputation: 551

The White Test has been implemented in the package "bstats". After installing and loading this package, a White Test is performed on a linear model object by simply typing

white.test(lm0)

See this page for a description and an example.

Upvotes: 4

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