I do not think it is a problem at all; it is interesting - variance heterogeneity is what makes us human!
Bur seriously, the homoscedastic assumption is often being made because people do not know how to explicitly to model it; they are living in the past. It is not something to be got rid off - of course it must not be a technical fault with the specification of the model. I am talking about James's "essential heterogeneity".
To take a single example, have a look at ; I predict that this will become a very big thing - at last:
Article The tyranny of the averages and the indiscriminate use of ri...
Heteroscedasticity is the result of the heterogeneity in the data. It makes the variance of the error terms not constant. This results in unbiased estimator. The variance of the estimator is not the minimum.
Mounir -
If you ignore heteroscedasticity, yes, variance estimates will be impacted. Size of a population member, as measured by an independent variable, or function of them, such as predicted-y, will impact the variance of the prediction error of y for each point.
Heteroscedasticity can be caused by modeling problems, such as an omitted variable, or data that should have been stratified, but it can also be a truly inherent part of the error structure in surveys where member sizes vary, as in an establishment survey. See the following for that:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
Cheers - Jim
I do not think it is a problem at all; it is interesting - variance heterogeneity is what makes us human!
Bur seriously, the homoscedastic assumption is often being made because people do not know how to explicitly to model it; they are living in the past. It is not something to be got rid off - of course it must not be a technical fault with the specification of the model. I am talking about James's "essential heterogeneity".
To take a single example, have a look at ; I predict that this will become a very big thing - at last:
Article The tyranny of the averages and the indiscriminate use of ri...
Following is a related question on "coping," for which most econometrics books may suggest a transformation - dividing by a size measure raised to the coefficient of heteroscedasticity, gamma (where gamma is found in section 2 of my "Essential Heteroscedasticity" paper noted above):
https://www.researchgate.net/post/How_to_cope_with_heteroskedasticity
However, I prefer to avoid transformations, and the interpretation problems they may cause, and just include the (essential) heteroscedasticity in the error structure (where it is naturally found). You can then estimate prediction intervals, around predicted-y values, which vary by population member size.
The response I gave to the above linked question addresses both 'essential' and 'nonessential' heteroscedasticity. (I plan to upload a short research paper on 'nonessential heteroscedasticity' in the not-distant future.)
These papers complement each other:
Essential & Nonessential Heteroscedasticity, respectively:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
&
https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity
The first link was already provided. That is for heteroscedasticity which occurs as a natural part of the error structure, due to the different 'size' of each of the different members of a population. The second link is primarily with regard to "problems" concerning the model and/or data, which may be at least partially resolved. You may want to research the term "model misspecification."
It is customary to check for heteroscedasticity of residuals once you build the linear regression model. The reason is, we want to check if the model thus built is unable to explain some pattern in the response variable Y, that eventually shows up in the residuals. This would result in an inefficient and unstable regression model that could yield bizarre predictions later on.
How to detect heteroscedasticity? and How to rectify?
See link below:
https://datascienceplus.com/how-to-detect-heteroscedasticity-and-rectify-it/
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