In nonlinear Langmuir fits of P adsorption with silicon as a treatment, is it appropriate to compare nested models (no dose effect vs. dose effect on Qmax) using a likelihood-ratio test for the global effect, and one-sided Wald tests to assess dose-specific reductions?
Lucas Jónatan Rodrigues da Silva
Yes, the methodological approach involving the comparison of nested nonlinear Langmuir models using a likelihood-ratio test to assess the global effect of treatment (e.g., the presence of a dose effect of silicon on maximum phosphorus adsorption, Qmax) is statistically sound and widely accepted. The likelihood-ratio test allows evaluation of whether including an additional parameter (in this case, the dose effect) significantly improves model fit compared to the baseline model without that effect.
Once a global effect is established, the use of one-sided Wald tests to evaluate dose-specific reductions in Qmax is also valid, provided there is an a priori hypothesis (e.g., that phosphorus adsorption is expected to decrease with increasing silicon dose). One-sided tests offer greater statistical power when the direction of the effect is known in advance, but they should be used carefully and with clear justification.
In summary, the combination of a likelihood-ratio test for assessing overall treatment effects and one-sided Wald tests for dose-specific comparisons provides a robust statistical framework for analyzing treatment effects in nonlinear models such as Langmuir. However, it is important to ensure that all models are correctly specified and that assumptions for test validity and convergence are met.
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