Hi Jonathon,

Thank you for your quick and kind reply.

I am sorry if I will write things that you are already familiar with, but I just want you to understand the issue. I will try to make it short:

The linear regression model Y=XB+u allows us to estimate coefficients B (Column estimate in jamovi) and the corresponding standard errors (Column SE in jamovi). This model only works if some assumptions are met, namely that u is homoscedastic (that is, the variance of u is constant).

If u does not have a constant variance (we say, in this case, that there is heteroskedasticity), then the coefficients B remain the same but statistical inference is not consistent (meaning, e.g., that t-tests for individual significance do not work) as the standard errors of the B coefficients are not correctly estimated.

Heteroskedasticity happens in 99.9% of applications in economics, business and international relations, which explains why several statistical software includes tests for this (so does jamovi – we have the well-known Breusch-Pagan test in moretests). In fact, heteroskedasticity is so common that most people in these areas simply use the robust estimator and don’t check it with the appropriate test. Journals in these areas always want us to replicate regression results with the robust estimator, because results without it may not be trusted.

With heteroskedasticity, we need to get the correct values of the standard errors of the coefficients so that we can compute the appropriate statistical significance of any independent variable. This is where the Huber-White estimator enters. Huber and White proposed an estimator to deal with heteroskedasticity, allowing for the correction of the standard errors and, therefore, validating statistical inference. For informal background, check the wikipedia article on this here:

https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors

Several statistical software include this estimator for the standard errors – sadly, I do not work with R, but for instance in Stata it’s the vce(robust) option; in SPSS, you go to Analyze – generalized linear models – estimation and select robust estimator.

Although I don’t understand R, I searched this issue in google and found out that, apparently, R also has (some) functions to calculate the corrected standard errors: e.g., the hccm function – please see:

https://www.rdocumentation.org/packages/car/versions/3.0-10/topics/hccm?fbclid=IwAR3CjuL1RmjQQEdiZZZRAe4flE49S4lqwbcN3sO6RpGEwLZAljuCHGzcY10

Also, here you have the comparison of results with this corrected estimator between the R and Stata procedures:

https://stats.stackexchange.com/questions/117052/replicating-statas-robust-option-in-r?fbclid=IwAR1eoOO3QU4iN1JEqLBPAXFmp61ftq4s9t_Awp_9Cd_XfwxgVaM9Q2OirZg

As jamovi is based on R, I hope this helps.

Please let me know how can I help you to implement this. It would really be wonderful to have this feature in regression analysis (included in moretests, for instance).

Cheers,

Jorge

EDIT: I found a paper that describes how to implement this in R, because it says the functions to use. I suppose it will be helpful. It is here:

https://cran.r-project.org/web/packages/sandwich/vignettes/sandwich.pdf