Why is fitlm affected by variable scale?

11 vues (au cours des 30 derniers jours)
Harold Matthews
Harold Matthews le 1 Déc 2021
Modifié(e) : Devendra le 13 Avr 2024 à 4:58
Dear all,
My statistics is pretty solid and my understanding is that if you fit a linear regression the scale of the X and Y variables should not affect the resulting p-values. I am running fitlm on some data (see demo and data attached) and changing the scale of the variables by transfiorming them to z-scores has a profound effect on the resulting p values. In the attached (Demo.m) code I fit two models with the same model design on the same data (in the attached 'Data.mat' file). The only difference is that for model 1 the X and Y variables are normalised to z scores and in model 2 they are not. I then scatter the p-values. You can see in the upper left corner that two p values that were not significant for model 1 become signfiocant for model 2.
Sorry I cannot get the demo code embedded in this question, so I have attached it. If anyone has any insights into this that would be great :)
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Devendra
Devendra le 13 Avr 2024 à 4:57
Thank you very much for detailed explanation. I am getting wierd results of fitlm function used in my matlab code. I am attaching the code and input data file and request you to kindly have a look on code and suggest me how to get the correct results.
I would appreciate your kind cooperation.
Deva

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Ive J
Ive J le 1 Déc 2021
Well, the real question would be why not?
You have introduced interaction terms to the model. Two models test different hypotheses (except for the interaction terms). You can find a good explanation here. Clearly, when you remove the interaction terms, all t-stats would be the same for both models.
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Devendra
Devendra le 13 Avr 2024 à 4:54
Modifié(e) : Devendra le 13 Avr 2024 à 4:58
thanks for valuable information.

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Jeff Miller
Jeff Miller le 1 Déc 2021
Your understanding is correct for linear regression but your model is nonlinear because of the interaction terms. Consider:
zX = zscore(X);
corr(X(:,1),zX(:,1))
ans =
1
corr(X(:,1).*X(:,2),zX(:,1).*zX(:,2))
ans =
0.2421

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