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Kinetic model selection and the Hill model in geochemistry
Turner, B. D.; Henley, B. J.; Sleap, S. B. & Sloan, S. W.
Abstract
This study introduces the Hill model for modelling
sorption kinetics and illustrates its efficacy using
formal model selection procedures. Although the coeffi-
cient of determination (R2) value can be used to ensure
goodness-of-fit of a particular model to a set of data, a
measure that incorporates the number of model parameters,
such as the Bayesian information criterion, law of iterated
logarithm criterion, Akaike information criterion, and the
extra sum-of-squares F-test is necessary to undertake reliable
model selection. This study undertook a formal model
selection procedure based on these criteria, in combination
with the coefficient of determination, for a range of candidate
kinetics sorption models [the pseudo-second order
(PSO), the intra-particle diffusion (IPD), Power, Elovich,
and the four and five parameter Hill models]. It was found
that the model order that statistically best described the
data was Hill 5>Hill 4>pseudo-second order>Elovich>Power>IPD as given by the evidence ratios,
information criterion weights and Bayes factors. The extra
sum-of-squares F-test, only applicable to nested models,
confirms the best fit order as Hill 5[Hill 4[PSO models.
Two new parameters (T and kHill) have also been
defined that give the Hill models a mechanistic meaning
directly comparable to the well-defined parameters of the
pseudo-second-order model, namely, the pseudo-secondorder
rate constant kpso and the instantaneous sorption
coefficient hpso. In the field of geochemistry the use of the
four and five parameter Hill models for describing sorption
kinetics has been overlooked with many studies favouring
the PSO model. It is strongly recommended that the Hill
model be considered more widely as a general predictive
tool in geochemistry.
Keywords
Hill model; Pseudo-second order; Adsorption; Kinetics; Model selection; AIC
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