I am doing linear regression assumption tests, where Shapiro-Wilk test shows data is normal. Then I tried homoscedasticity test by plotting residual vs predicted plot where I can see a clear pattern (plot is not random) which means data is not homoscedastic, But when use command (estat imtest, white) for Cameron-Trivedi and Breush-Pegan Tests , I get following:
Source | chi2 df p ---------------------+-----------------------------
Heteroskedasticity | 3.62 2 0.1641
Skewness | 0.31 1 0.5800
Kurtosis | 2.49 1 0.1148 ---------------------+-----------------------------
Total | 6.41 4 0.1707
As P value for Heteroskedasticity greater than 0.05, the data is homoscadastic.
Why I get different explanation (which is non-random pattern) from the plot?
Hi Iqbal, what is your sample size? If possible share us your plot.
Hello Seyed Mahdi Amir Jahanshahi sample size is 26. Please see the attachment.
Thanks
Iqbal -
As explained in an update to https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, on August 9, 2019, hypothesis tests for heteroscedasticity are not useful. You need to see the impact on final results, so I suggest you find a reasonable value for the coefficient of heteroscedasticity, and use it. Assuming homoscedasticity, that the coefficient of heteroscedasticity is zero, may be convenient, but it is often a bad assumption, and basically, with the best modeling and no data quality problems, should not be true. See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity.
There are examples in here: https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity. A tool for doing this with your data is found here: https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx.
In complex situations, I think you might find that heteroscedasticity will sometimes breakdown, and OLS might be close enough. But if you use the above, based on graphical residual analyses, you will not need to use hypothesis testing, nor decide what to do after the 'test.'
Cheers - Jim
Iqbal -
Wait. I just saw your graphical residual analysis, and it shows a strong pattern indicating your model does not fit. You need to work on that first.
Jim
Hello James R Knaub , residual vs fitted graph (attached) shows that model does not satisfy homoscedasticity (even though Cameron-Trivedi test in STATA software shows this assumption is satisfied as P > 0.05). I do not have enough reasons to omit problematic data points and I tried a different method to fix the problem such as log transformation etc. Other method I can think of now, is to apply non-parametric linear regression. My question is, can I apply the parametric method even though it is not meeting the homoscedasticity graphical test if the impact in the final result is not substantial?
Thanks
Heteroscedasticity is not what you are seeing on that scatterplot. Model fit is the problem shown there. You can research the term "graphical residual analysis." The Pennsylvania State University (Penn State) often has good material available to all on the internet. You could do a search.
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