Trying to use the white test in r

Question

I am doing a regression on the influence on marketing spending.

I have already tested for heteroskedasticity with the Breusch-Pagan Test and found that the test came out positive.

Based on the template that I have from a book, one should now also check with the White test whether heteroskedasticity is present.

I tried using packages like: white_lm, white.htest and white.test but all seem to not be working any longer (can't use library for them).

Therefore I tried setting the test up by myself.

The formula for the White test should look something like this (as mentioned in the book):

bptest(eqbp, varformula = ~ log(LOTSIZE) + log(SQRFT) + BDRMS +
I(log(LOTSIZE))^2 + I(log(SQRFT))^2 + I(BDRMS)^2 + I(log(LOTSIZE)*log(SQRFT)) + I(log(LOTSIZE)*BDRMS) + I(log(SQRFT)*BDRMS), data=HPRICE1)

My regression looks like this:

lm.01.3 <-lm(log(marketingspending) ~ log(intr) + log(sale_py_at_py) 
             + log(R_at_py) + log(p_con) + log(txt) + factor(Dummy_SIC)
             , data=r1)

I "implemented" my regression to the white test format:

install.packages(c("AER"))
library(AER)
bptest(lm.01.3, varformula = ~ log(intr) + log(sale_py_at_py) + log(R_at_py) 
       + log(p_con) + log(txt) + factor(Dummy_SIC)
       + I(log(intr))^2 + I(log(sale_py_at_py))^2 + I(log(R_at_py))^2 
        + I(log(p_con))^2 + I(log(txt))^2 + I(factor(Dummy_SIC))^2
        + I(log(intr)*log(sale_py_at_py)) + I(log(intr)*log(R_at_py))
        + I(log(intr)*log(p_con)) + I(log(intr)*log(txt)) 
        + I(log(sale_py_at_py)*log(R_at_py)) 
        + I(log(sale_py_at_py)*log(p_con))
         + I(log(sale_py_at_py)*log(txt))
         + I(log(R_at_py)*log(p_con)) + I(log(R_at_py)*log(txt))
         + I(log(p_con)*log(txt)) + I(log(intr)*factor(Dummy_SIC))
         + I(log(sale_py_at_py)*factor(Dummy_SIC))
         + I(log(R_at_py)*factor(Dummy_SIC)) 
         + I(log(p_con)*factor(Dummy_SIC)) 
          + I(log(txt)*factor(Dummy_SIC)), data = r1)

But now it tells me the error:

> Error in lm.fit(X, y) : 0 (non-NA) cases

Does that mean the I can't use the White test? Or perhaps use it like this?:

bptest(lm.01.3, varformula = ~ log(intr) + log(sale_py_at_py) + log(R_at_py) 
       + log(p_con) + log(txt) + factor(Dummy_SIC)
       + I(log(intr))^2 + I(log(sale_py_at_py))^2 + I(log(R_at_py))^2 
       + I(log(p_con))^2 + I(log(txt))^2
       + I(log(intr)*log(sale_py_at_py)) + I(log(intr)*log(R_at_py))
       + I(log(intr)*log(p_con)) + I(log(intr)*log(txt)) 
       + I(log(sale_py_at_py)*log(R_at_py)) 
       + I(log(sale_py_at_py)*log(p_con))
       + I(log(sale_py_at_py)*log(txt))
       + I(log(R_at_py)*log(p_con)) + I(log(R_at_py)*log(txt))
       + I(log(p_con)*log(txt)) 
        , data = r1)

Or would that have a different meaning/interpretation?

If I can't use the White test is there another test that uses the same approach as the White test? Because the book that I rely on tells me that I need to do the Breusch-Pagan test and the White test.

score 0 · Accepted Answer · answered Feb 10 '22 at 13:24

0

Here is an implementation of the White test that works for me, at the time of writing (along with some manual calculations to illustrate the $nR^2$ format of the test statistic).

library(skedastic)

mtcars_lm <- lm(mpg ~ wt + hp, data = mtcars)
summary(mtcars_lm) # i.e. weight and horsepower bad for mileage

# canned
white_lm(mtcars_lm, interactions = TRUE, statonly = T)

# handmade
n <- dim(mtcars)[1]
u.hat.squared <- resid(mtcars_lm)^2
aux.reg <- lm(u.hat.squared~poly(cbind(wt,hp), 2), data = mtcars)

summary(aux.reg) # fyi, to show polynomials

(white.stat <- n*summary(aux.reg)$r.squared)


n*(1-sum(resid(aux.reg)^2)/sum((u.hat.squared-mean(u.hat.squared))^2))

k <- 5
rssr <- sum((u.hat.squared-mean(u.hat.squared))^2)
ussr <- sum(resid(aux.reg)^2)
(rssr-ussr)/rssr*n # white stat
(rssr-ussr)/rssr  # r-squared

Some things that also strike me in your post:

Why use White if you have already done Breusch-Pagan? Both serve the same purpose.

I do not think you use I correctly when generating the square of the log. Try the following for illustration:

set.seed(1)
y <- rnorm(19)
x <- runif(19)

lm(y~I(log(x)^2))
lm(y~I(log(x))^2)
lm(y~I(log(x)))

answered Feb 10 '22 at 13:24

Christoph Hanck

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Thank you very much. I don't know why but now the package is working hahaha. What does it mean that you use "interactions = TRUE, statonly = T"?. And could you do me a favour and post the output of your white_lm code please? – New_to_r Feb 10 '22 at 13:45
Try writing `?white_lm` to access the documentation of the command. It means I also regress the squared residuals on the squared regressors and interactions, and that I only report the test statistic and not p-values etc. Why not just copy & paste the code and play with it yourself? That is generally instructive! – Christoph Hanck Feb 10 '22 at 13:47
Fair enough. Just one last question because I am not sure if I did the part with my manual function: Did I use interaction? And I am sorry that I can't the arrow up because of my lvl :/ – New_to_r Feb 10 '22 at 17:32
Yes, terms like `I(log(intr)*log(sale_py_at_py))` are the interactions, i.e. products of regressors. With `poly` you get all these terms automatically though, and need not specify them by hand. – Christoph Hanck Feb 10 '22 at 17:33
1

Man you are the best!!! Wish you all the best :* – New_to_r Feb 10 '22 at 17:48

Trying to use the white test in r

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