RMSE of Weighted Nonlinear Regression

3 次查看（过去 30 天）
wesleynotwise
wesleynotwise 2017-7-18
回答： Mukul Rao 2017-7-21
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?

请先登录，再回答此问题。

回答（1 个）

Mukul Rao
Mukul Rao 2017-7-21
Hi,
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.
A cautionary note on R^2
Please read the bottom left paragraph on page 237 ( Inserted as an image here ).

类别

在 Help Center 和 File Exchange 中查找有关 Linear and Nonlinear Regression 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by