Between Rival Models

The appropriate theoretical distribution (A, B, C) can only be guessed at because the high price and/or time loss attached to each result precludes achievement of the large N necessary to distinguish between rival models,... 

There are several methods for discrimination between rival models. Froment and Hosten (1981), Bischoff and Froment (1991), and Kittrell (1970) summarized them and discussed applications for kinetic models. Here only approximate methods will be presented. 

Mannervik, B. (1981) Design and analysis of kinetic experiment for discrimination between rival models,in Endrenyi, L.(eds.), Kinetic data analysis, Plenum Pub.Co., New York,pp. 

The text reviews the methodology of kinetic analysis for simple as well as complex reactions. Attention is focused on the differential and integral methods of kinetic modelling. The statistical testing of the model and the parameter estimates required by the stochastic character of experimental data is described in detail and illustrated by several practical examples. Sequential experimental design procedures for discrimination between rival models and for obtaining parameter estimates with the greatest attainable precision are developed and applied to real cases. 

A Discrimination Between Rival Models - Design Criteria... 

The curvature of an Arrhenius plot for a phenomenological coefficient can sometimes be used to distinguish between rival models A model in which a phenomenological coefficient is a product, ratio, or ratio of products of individual rate coefficients of steps can in general not be correct if an Arrhenius plot of that coefficients is distinctly curved. 

Atkinson, A. C., and V. V. Fedorov, The design of experiments for discrimination between rival models, Biometrika, 62, 57-70, (1975). 

Still, even with following Wagner s guidelines it may be that many different models fit the data equally well. The situations becomes more complex when variables other than time are included in the model, such as in a population pharmacokinetic analysis. Often then it is of interest to compare a number of different models because the analyst is unclear which model is the more appropriate model when different models fit almost equally to the same data. For example, the Emax model is routinely used to analyze hyperbolic data, but it is not the only model that can be used. A Weibull model can be used with equal success and justification. One method that can be used to discriminate between rival models is to run another experiment, changing the conditions and seeing how the model predictions perform, although this may be unpractical due to time or fiscal constraints. Another alternative is to base model selection on some a priori criterion. 

Statistics can effectively be used to provide a best estimate of the value of a repeatedly measured variable, establish the reliability of such an estimate (confidence interval), estimate parameter values of a model from experimental data, help to discriminate between rival models on the basis of goodness of fit, and guard against acceptance of a model whose superior fit may well be due to chance. It can also help to design experimental data gathering to be most efficient [48], On the other hand, statistics alone cannot be relied upon to identify or verify reaction pathways or mechanisms. 

Another advantage of forced periodic feed experiments, which has not been fully exploited so far, is that the technique could be used for kinetic model discrimination, a technique in which large deviations could be induced into calculated reponses between rival models under consideration. Hawkins has carried out experiments on oxidation of CO for discriminating between several Hougen and Watson rival models. Cutlip et al have compared experimental forced periodic feed CO oxidation experimental transients with simulations using an elementary step model and compared theory with experiment in studies of the variation of the conversion as a function of time period of the forced oscillation. 

An unquestionable discrimination between rival models may be obtained when the physicochemical significance of the parameters is investigated. In the case of fundamental kinetic models, the parameters have a clear physical meaning and, hence, they should not take values outside of a well -defined range corresponding to what is physically reasonable. Rate coefficients, pre-exponential... 

Fig. 11. Structure of a sequential experimental design for discrimination between rivaling models.

Sequential Design for Optimal Discrimination between Rival Models... 

J. Handler, R. Lavie and H. Sheintuch An automated catalytic system for the sequential optimal discrimination between rival models, Chem.Eng.Sci. (1983)979-990 /25/ L.H. Rose, C. Schifferli and D.W.T. Rippin Computer application in the analysis of chemical data and plants, Proc.Chemda-ta Helsinki ( 1977)132-136... 

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