Kindly elaborate other ways of solving Heteroscedasticity problem in Multiple Linear Regression Model. If possible, assist me with published empirical literature on the same. Thank you.
Olila, D.O.
First choice is transform the serie into a ratio, dividing by other serie....
Almost any book of econometrics has a chapter about the Heteroscedasticity, and ways to deal with it.
Regards,
Random coefficient models allow you to model the heteroscedasticity explicitly as a function of predictor variables - you can do this before or after a transform of the response variable. The predictor variables can be continuous or categorical.
see ttps://www.researchgate.net/publication/23538539_Modelling_Complexity_Analysing_between_Individual_and_between_Place_Variation
and
https://www.researchgate.net/publication/260771330_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_1_updated_June_2015_Volume_2_is_also_on_RGate
Article Modelling complexity: Analysing between-individual and betwe...
Book Developing multilevel models for analysing contextuality, he...
Remember that in general heteroscedasticity will not bias your regression coefficients, but may affect your standard errors. Weighted least squares could be adopted to provide higher weight to those observations that have less variability.
Of course, using logarithms or percentage changes would, in general, remove HS, but this would at the same time change the specification from an additional relation of the independent variables to a multiplicative (or higher) one. Therefore, it could be non-feasible, if (your) theory says that the effects should be additive (or subtractive). In this case, I would not care about HS, but you could, I think, use "fully" detrended data in the sense that you divide the deviations from the trend through the trend values.
Of course, one cannot use these percentage deviations from trend directly in a regression, because that would mean a a change in specification. One has to transform them back to absolute values by multiplying them by the average of the original series (I thin it could also be the first or last or one of the other values) to get something like detrended, non-heteroskedastic series of absolute differences.
I have tried to apply this approach to simulated heteroskedastic time series, but the results with the detrended data were similar, but mostly not better than regressions with the original (simulated) data. Therefore, not caring about HS is not a bad proposal, because HS does not lead to biased estimates. I know there are methods to hnadle HS, but I think in practice it is not worth the trouble.
There are two reasons for modeling the heterogeneity explicitly
1) to get better estimates of the standard errors
2) because heterogeneity may of itself be substantively interesting - this can often be an important question.
The former treats heteroscedasticity as a mere nuisance - for many of the things that interest me, viewpoint 2 is important. Take climate change - we now know that the average is going up but is the system becoming more heterogeneous over time? This is a fundamental research question worthy of direct answering. You are not trying to solve the problem of heteroscedasticity but find out its nature.
To solve heteroscedasticity in MLR, 3 solutions exist that I am aware:
1) Box Cox transformation
2) transformation of the predictand : try sqrt(y) or 1/y
3) try weighted regression
Ref. Weisberg Regression analysis John Wiley and Sons
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