LOESS fit – smoothing settings

[Jean-Yves Le StangParticipant]

Hi DG team and users,

Trying to manage LOESS fit and optimise settings. Searched the web for information on what is the meaning of 1st/2nd slider/radius used as smoothing parameters in the command window . No success – can you help with explanation or web link

Many thanks in advance.

[dgteamModerator]

Have you read this section of the Fit command documentation?

https://community.visualdatatools.com/datagraph/knowledge-base/command-fit/#loess

If the explanation in that article is not clear, let us know.  Thanks!

[Jean-Yves Le StangParticipant]

I use to read the DG manual from the application but it does not explain how to use slider and radius.

The online FIT documentation is perfectly clear, with many thanks.

 

[sandriftParticipant]

FWIW, I also found this documentation a little less than complete on this point.  What is the difference between 1st and 2nd, for example?

[Jean-Yves Le StangParticipant]

“LOESS uses a weighted least squares fit in a specified window. Using the Smoothing menu, chose either 1st or 2nd degree polynomials. The window can be explored using a slider or specified with a an expression.”

For me this means that 1st is related to local 1st degree polynomials (linear regression) and 2nd to local 2nd degree polynomials (quadratic regression). Therefore you have to choose the polynomial degree then set the window width either by slider (“Slider”) either by an expression (“Radius”).

However, still uncertain as to how the regression is “weighted”

Appreciate DG support team comment on this.

[dgteamModerator]

Thanks for clarifying 🙂  That is all correct.

The LOESS Fit in DataGraph uses a cubic drop-off for a weight function. At the edge of the interval the weight is zero. At the center, the weight is 1.

The function is scaled across the x-axis depending on the selected radius for the local fit, where the radius is the distance from the center to the edge of the values included in the local regression.

When the Smoothing is set to specify the radius, the default is 0.3 times the width, where the ‘width’ is the range of the x data.

Using this choice, the total interval used in the local fit is 0.6 of the width. Because of the drop-off of the weight function, you end up with about 0.3 of the width dominating the fit.

To further illustrate, we found an example from the National Institute for Standards and Technology (NIST): https://www.itl.nist.gov/div898/handbook/pmd/section4/pmd423.htm

Here is the NIST example, created using DataGraph:

 

Appreciate you pointing out the missing documentation.  We will be adding these details.

 

[Jean-Yves Le StangParticipant]

Understood with many thanks fort effort and reactivity

[sandriftParticipant]

Thank you.  The more explicit explanation with less terse language is indeed very helpful.

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