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Why ANOVATable does not show the F-Statistic and P value for NonlinearModel

Posted 9 months ago
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Hi, this may be a conceptual question, but if it possible I would like to know why when I use the "ANOVATable" property of a NonlinearModelFit object it does not show the F-Statistic and the corresponding P-Value. The following is the FittedModel object which I am using enter image description here

Thanks in advance for your suggestions.

3 Replies
Posted 4 months ago

As I think you already know when using LinearModelFit the F-statistic and associated P-value show up but I don't know why that isn't included in the "ANOVATable" for NonlinearModelFit. However, the "ANOVATable" gets you the overall model information from which you can construct the F-statistic and associated P-value for the overall model:

data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}};
nlm = NonlinearModelFit[data, Log[a + b x^2], {a, b}, x];
nlm["ANOVATable"]

ANOVATable

anova = nlm["ANOVATableEntries"];
FStatistic = anova[[1, 3]]/anova[[2, 3]]
(* 45.1398 *)
Pvalue = 1 - CDF[FRatioDistribution[anova[[1, 1]], anova[[2, 1]]], FStatistic]
(* 0.00180005 *)

What is probably more interesting is to obtain the t-values and associated P-values for the individual parameters:

nlm["ParameterTable"]

ParameterTable

Hi Jim, thanks for your comment. Yes, I asked myself the same question, I thought that the F statistic was not used for non-linear models but then I realized that it was, and I had to build it from the information in "ANOVATable".

I agree. Yes you can reconstruct it, but why should you have to? Perhaps an ANOVAAssociation property could be added that included this information. Also, in general the various "...Table" properties of the FittedModel and related objects should be augmented by "...Association" properties or "..."Dataset" that describe the statistic using a key value pair.

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