Interpreting Heteroskedasticity Tests

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ashab
Posts: 2
Joined: Thu Apr 08, 2021 6:56 am

Interpreting Heteroskedasticity Tests

Post by ashab »

Hi there,

I've used heteroskedasticity tests via the moretests add-on. But I'm having trouble finding any literature on interpreting/reporting the results. See attached.
HETEROSKEDASTICITY.png
HETEROSKEDASTICITY.png (17.65 KiB) Viewed 10593 times
Can anyone please help? I'm a stats beginner, so would appreciate some expert advice!

Thanks,
Asha
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jonathon
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Joined: Fri Jan 27, 2017 10:04 am

Re: Interpreting Heteroskedasticity Tests

Post by jonathon »

i don't know much about these unfortunately, but hopefully someone else will chime in.

cheers
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MAgojam
Posts: 421
Joined: Thu Jun 08, 2017 2:33 pm
Location: Parma (Italy)

Re: Interpreting Heteroskedasticity Tests

Post by MAgojam »

Hi, @ashab.

Unfortunately, a problem that often occurs in regression is known as heteroskedasticity, where there is a systematic change in the variance of residuals over a range of measured values.
One test we can use to determine if heteroskedasticity is present, is the Breusch-Pagan test which produces a Chi-square test statistic and a corresponding p-value.

The jamovi moretest module uses the R lmtest package (Maintainer: Achim Zeileis) which makes three tests for heteroskedasticity available.
The Breusch-Pagan test with bptest(), the Goldfeld-Quandt test gqtest() and the Harrison-McCabe test hmctest().

The Breusch-Pagan test fits a linear regression model to the residuals of a linear regression model (the same explanatory variables are taken as the main regression model by default) and rejects if too much variance is explained by the additional explanatory variables.
Under null hypothesis the Breusch-Pagan test statistic follows a chi-square distribution with the degrees of freedom of the parameters (the number of regressors without the constant in the model).

The jamovi output printout for Breusch-Pagan is a Koenker studentized version of the test statistic.
If the p-value is below a certain threshold (e.g. common choices are .01, .05), there is sufficient evidence to state that it is present heteroskedasticity.
If the null hypothesis of the Breusch-Pagan test is not rejected, heteroscedasticity is not present and the original regression output can be interpreted.

However, if you reject the null hypothesis of the Breusch-Pagan test, this means that heteroskedasticity is present in the data.
In this case, the standard errors displayed in the regression output table they are not reliable.

There are several ways to solve this problem, including:
Try to perform a transformation on the response variable. For example, use his log. Generally, taking the log of the response variable can be an effective way to eliminate heteroscedasticity.
Another common transformation is to use the square root of the response variable.
Also use weighted regression, where a choice of appropriate weights can eliminate the problem of heteroscedasticity.
Or finally (what I prefer) to use robust standard errors.
Robust standard errors are more "robust" to the problem heteroscedasticity because they tend to provide a measure more accurate than the true standard error of a regression coefficient.
In the FORUM if you search there are posts for Heteroskedasticity and robust standard error.

References
T.S. Breusch & A.R. Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287–1294
R. Koenker (1981), A Note on Studentizing a Test for Heteroscedasticity. Journal of Econometrics 17, 107–112.



Cheers,
Maurizio
nikv
Posts: 4
Joined: Sat Oct 02, 2021 10:17 am

Re: Interpreting Heteroskedasticity Tests

Post by nikv »

Hi
Thanks for your valuable reply @MAgjojam.
Although it's been a while since your reply, I wonder if you have any thoughts on interpreting conflicting results from tests as shown in the attachment?
(the data is actually from Field (2009) - a simple, linear regression of Adverts and Album Sales)
Attachments
Heterosk.png
Heterosk.png (8.17 KiB) Viewed 5146 times
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MAgojam
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Location: Parma (Italy)

Re: Interpreting Heteroskedasticity Tests

Post by MAgojam »

Hey @nikv,
tests look at different ways in which heteroskedasticity can manifest itself and, therefore, a given dataset may "appear" heteroskedastic for one test and not so for another.
In general, I would say that different widely used tests are to be expected to give different responses at times.
I am attaching an .OMV file that maybe helps you and let's look (Breusch-Pagan vs. Goldfeld-Quandt), the BP examines if the quadratic residuals can be explained by the observed regressors, while the GQ test is based on the divided sample exercise.
BP_vs_GQ_data.omv
(11.95 KiB) Downloaded 195 times
Thus, it is conceivable that the first test detected heteroskedasticity from the relation to a variable that did not act as a division variable in the second, which GQ was therefore unable to detect.
Sorry I was quick, but lately I've been running a bit ...

Could it be of interest to you to take a look here?
https://www.scirp.org/pdf/ojs_2020060215231036.pdf

Cheers,
Maurizio
nikv
Posts: 4
Joined: Sat Oct 02, 2021 10:17 am

Re: Interpreting Heteroskedasticity Tests

Post by nikv »

Hi Maurizio

Thanks a lot for a very interesting reply. The article was certainly interesting, although it requires a lot of study to comprened (at least for me). Also, I think your reply with the .omv file show the beauty of Jamovi's abaility to share data, analysis etc in one file. Absolutely brilliant @jonathon

Cheers,
Nils
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