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Compare two nonlinear models (F-test + AICc)

Compare two nls fits on the same (X, Y) via the extra sum-of-squares F-test (nested models) and AICc-based Akaike weights (any models).

What is Compare two nonlinear models (F-test + AICc)?

Two complementary tests. Extra SS F is the classical likelihood-ratio analogue for nls — valid when one model nests the other (e.g. 4PL nested in 5PL when S = 1). It directly tests whether the more complex model fits significantly better than the simpler one.

AICc + Akaike weights work for non-nested models too. The Akaike weight is the relative probability that each model is the best Kullback-Leibler approximation given the data; weights sum to 1 across the comparison. For 4PL vs Gompertz, where neither nests the other, Akaike weights are the right tool.

When should I use Compare two nonlinear models (F-test + AICc)?

  • Deciding whether to add a parameter (4PL vs 5PL — nested).
  • Comparing competing functional forms (Gompertz vs logistic growth — not nested).
  • Model selection for any nls fit.

What data does it need?

X + Y + two model selections.

What does it report?

Side-by-side # params / df / RSS / σ / AIC / AICc / ΔAICc / Akaike weight / BIC; F-test row when df differ.

How do I interpret the result?

Akaike weight > 0.95 ⇒ overwhelming evidence for one model; 0.5–0.95 ⇒ favoured but not decisive; ≈ 0.5 ⇒ models indistinguishable.

See also

References

  • Burnham & Anderson (2002). Model Selection and Multimodel Inference.