Is there any problem if the R2 of heteroskedasticity-corrected model is very low????? thanks in advance
R SQUARED tells the % explained by the proposed model, i.e. how much does the proposed model explained the data? If the value of R squared is low, it means that the proposed data cannot explain the data or wrong model.
SOLUTION you may explore other types of modeling for your data set and re-run R square. If still low it may mean that you may have misidentified variables. Double check IV and DV against existing literature on the subject.
https://en.m.wikipedia.org/wiki/Coefficient_of_determination
please read this :
Heteroscedasticity in Regression Analysis - Statistics By Jim
I have a problem with this question. The standard heteroconsistent-corrected model (HCSE) corrects the standard errors of model coefficients. It does not change the estimated values of the coefficients. Therefore it does not change the residuals or the R squared. You get the same R squared with the standard OLS estimation.
R squared is not a particularly useful measure of the merit of a model. What is a good value will vary considerably from case to case. A finding of heteroskedasticy can be an indication of model misspecification. Does you model pass other misspecification tests (serial correlation, functional form, model stability, etc.)? If not your data and model are probably not consistent. Your low R squared may be another indication of model misspecification.
Dear Hanan.
A very low R square indicates the variable is not significant.
Regards
Hello -
Heteroscedasticity in regression (in V(y|predicted-y)) is not a bug to be corrected, but a feature to be incorporated into the model. It impacts variance most, yes, but it does impact regression coefficients, which can sometimes be important with highly skewed data, especially with smaller sample sizes. Rather than patch up standard errors, weighted least squares regression can be done, as OLS is just a special case of that.
You might consider the following:
Nature and magnitude of heteroscedasticity of variance of y|y*, for regressions of form y=y*+e,
for finite populations:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as bounded by Ken Brewer,
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity,
and
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates there, in reverse chronological order.
Cheers - Jim
Perhaps I might clarify some of the points that I made in my earlier contribution.
In econometrics, we adjust the variance of the estimates of our regression coefficients using Huber–White standard errors (HCSE or robust standard errors). The problem is that in most cases we are unable to specify the nature of the heteroskedasticity. This method does not change the coefficient estimates, the residuals, or R2. The estimates of the coefficients are still consistent. They may be biased but the bias reduces as sample size increases. The assumption of homoskedasticity simplifies the estimation of the coefficient estimates
If the form of the heteroskedasticity were known one would use weighted least squares. This may be known in other disciplines but it is not, in general, known in econometrics. If it is known then it is best to use some form of appropriately weighted regression.
In econometrics, heteroskedasticity is often an indication of model misspecification.
Hanan Farag -
I wonder if R-squared was calculated correctly in each instance, assuming you modeled heteroscedasticity after first not doing so. R-squared would be defined differently, but I would not use it anyway. See https://data.library.virginia.edu/is-r-squared-useless/.
With enough data you can estimate the coefficient of heteroscedasticity, gamma, or you might have a default gamma value based on application:
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity
and then model it. There is also nonessential heteroscedasticity which comes from model and/or data issues, but Not finding heteroscedasticity can also be a model and/or data issue:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity
https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates there, in reverse chronological order, including one on why you do not want to do an hypothesis test for heteroscedasticity in regression.
Cheers - Jim
It may be that Dr. Frain's experience could be dominated by "nonessential heteroscedasticity" (https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity), where model misspecification, including failure to stratify when necessary, can cause this artificial heteroscedasticity. However, if you can clean that up, then "essential heteroscedasticity" could or should exist based only on its natural occurrence whenever predicted-y values differ, which is generally expected. See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity. In that case, Not having heteroscedasticity can be because of model and/or data issues. See https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR.
Because R-squared is made smaller with a larger sigma, and sigma should become larger with larger predicted-y, R-square cannot be calculated the 'traditional' way, which could relate to the question above.
- Badges
- Science topic
- Similar topics
- Filing