Dear experts,
I would appreciate if you help me to find a hint for my question.
Consider a routine example of having a dependent (y) and several independent (X's) variables. The variable y is recovery rate. Based on experience, we know that the X1 is the most important predictor and the greater the value of X1, the more recovery rate we have.
Is it reasonable we assign weights to the observations according to their value of X1 before fitting any models? if yes, do you know any references to support this idea? (For either the linear regression or machine learning methods)
P.S: I have found some book chapters and articles but their ideas behind assigning weights to the observations are as follows;
(1) to achieve more precise estimates by correcting for heteroskedasticity
(2) to achieve consistent estimates by correcting for endogenous sampling
(3) to identify average partial effects in the presence of unmodeled heterogeneity of effects.
Yes this situation leads to non constant variance a violation of the linear model requirements. The fix is weighted regression. See Kutner et al, Applied linear statisical models as a reference. Best, David Booth
I think that heteroscedasticity here is something important that must be considered in the analysis and should not be "worked-around" with weights in models that actually assume a homegeneous variance.
Why not use a Weibull-or Gamma-model, what is usually the right tool to model rates, and what would (presumanbly) neatly explain (and require) the heteroscedasticity.
Jochen Wilhelm , Thank you very much for your answer. I will try your suggestions to see whether they lead to reasonable results.
To calculate the average of data set by applying importance(specific value) on each value of variable.
David Eugene Booth
Thank you for the answer and introduced reference.
Warm regards,
Saeed
Saeed -
Maybe I'm missing something, but it seems to me that the 'importance' that you are looking at might be what is captured in the regression coefficients themselves.
Heteroscedasticity is basically a consequence of 'size,' which encompasses all predictors. That 'essential' heteroscedasticity is impacted by model specification and data issues, but basically I don't see weighting observations by predictors the way it is described in your question, as a way to address your concerns. (See papers under https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression.)
You might consider the meaning of the regression coefficients and see if that satisfies the weighting you are thinking about.
Cheers - Jim
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