by **MAgojam** » Fri Apr 16, 2021 3:59 pm

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