Faq what do the four Fit / Unique Fit stats mean in MCR PARAFAC

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Issue:

What do the four Fit/Unique Fit statistics mean in MCR and PARAFAC models?

Possible Solutions:

MCR and PARAFAC both report the sum-squared (SSQ) captured table with four statistics:

  • Fit (%X)
  • Fit (%Model)
  • Unique Fit (%X)
  • Unique Fit (% Model)

All four of these statistics are all variants of "variance captured" (although strictly speaking, since the data is often not mean-centered with this kind of analysis, it is not variance but just sum squared signal). The first two, Fit (%X) and Fit (% Model), give the sum-squared signal relative to the total signal in the data and to the total amount of signal captured in the model:

Fit (%X) = Ci/CX * 100% 
Fit (%Model) = Ci/Cmodel * 100%

where Ci is the sum-squared signal captured by the ith component, CX is the sum-squared signal in the entirety of the X matrix, and Cmodel is the sum-squared signal captured by the model in total (which is generally < CX because the model doesn't completely describe X). Note that:

Cmodel = C1 + C2 + C3 + ... + Ci 

The second two statistics, Unique Fit (% X) and Unique Fit (% Model), are the same as above except the components are first orthogonalized to each other so that you are seeing the amount of signal that is unique to the given component. Since some components are very similar in their profiles (i.e. they are nearly degenerate), this allows you to see which components are more uniquely contributing to the decomposition of the data. Over-fitting often leads to many degenerate components.


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