10 October 2019 11 9K Report

What are the various statistical software systems available which will allow you to enter regression weight, w, in weighted least squares (WLS) regression, in addition to SAS?

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Thank you to Guillermo Enrique Ramos for confirming, in another thread/question, that SAS can be used for quadratic linear regression, in addition to straight line linear and multiple regression, to implement weighted least squares in the format y = y* + (e0)(w^(-0.5)), where w is the regression weight as shown in section 2 of "Estimating the Coefficient of Heteroscedasticity," https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity. That is the format for which Ken Brewer made a convincing argument when describing the range of heteroscedasticity one should expect, as discussed in "Essential Heteroscedasticity," https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity.  In section 3 of "Estimating the Coefficient of Heteroscedasticity," one can see that another way of handling heteroscedasticity is sometimes used, but it is not consistent with the Brewer explanation of the root cause of naturally occurring heteroscedasticity.  Perhaps that alternative technique, or something related to it, might be used in some other software systems. 

Here, the two attached images show the format for the regression I think best to use, and the regression weight, w, both presented in terms of the coefficient of heteroscedasticity, gamma.  y* is the WLS prediction.  In most applications, the best practical/obtainable function values for the size measure, z, are the OLS predicted y values.  That is what is suggested for input to the spreadsheet in https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx.

(Note that the method here, using the attached images, is in completely closed form in the case where we have one regressor and a zero intercept, so z = bx, and x can be used for a (relative) size measure.  Otherwise, we first obtain OLS predictions, and then pick a reasonable coefficient of heteroscedasticity, and go back to find the improved WLS predictions.  I think that the other method appears to be more ad hoc.) 

So what other software, in addition to SAS, will allow the input of w for weighted least squares regression?  Is it for linear and multiple linear regression?  Note that such software would then minimize the sum of weighted squared estimated residuals with respect to each regression coefficient, simultaneously, to obtain estimates of regression coefficients.  What about polynomial linear regression?  Multiple regression with interaction terms?  Will it handle those too? 

The other question I wrote regarding polynomial regression is still open, but here I'd like to know about other software for any regression fitting the format in the images attached here. 

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Please see https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression.

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The question then is What other software, besides SAS, will accept regression weight input, w, for WLS regression? 

Thank you. 

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