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RMSE of Weighted Nonlinear Regression

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wesleynotwise am 18 Jul. 2017
Beantwortet: Mukul Rao am 21 Jul. 2017
I fit a nonlinear model with weight and without weight. Whilst there is an improvement in R-squared in the weighted model, its RMSE value is, unexpectedly, higher than that of the unweighted model. I did try to run the example code from Matlab click here, and realised that it also has the same 'problem'.
The Stats of Weighted Model, as given in the example:
Root Mean Squared Error: 24
R-Squared: 0.908, Adjusted R-Squared 0.885
The Stats of Unweighted Mode, which I found from the same set of data:
Root Mean Squared Error: 17.1
R-Squared: 0.88, Adjusted R-Squared 0.851
Can anyone explain the reason behind this?

Antworten (1)

Mukul Rao
Mukul Rao am 21 Jul. 2017
I believe the reason is that traditional weighted regression computes R-square based on transformed variables, the better R-square is indicative of weighting addressing the heteroskedastic nature of the data. However, ordinary least squares does give you the best possible RMSE, which is computed based on the original variables.
In fact, this paper talks about the very same issue.
Please read the bottom left paragraph on page 237 ( Inserted as an image here ).


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