Some Comments on Designs for Cox's Mixture Polynomial

Cornell, John A.

doi:10.1080/00401706.1975.10489267

Cited by 29 publications

(12 citation statements)

References 9 publications

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“…The standard state of 0.33333 was relatively arbitrarily chosen. Had the standard state been chosen to be the center point of the experimental data, the equilibrium constants would be more similar for the two methods (Cornell, 1975; see electronic supplemental material section in Appendix A). Within the composition region of the experimental data, the fit from the Rational and Multiresponse methods are relatively comparable.…”

Section: Resultsmentioning

confidence: 98%

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A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

Reynolds¹

2009

Geoderma

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Section: Resultsmentioning

confidence: 98%

“…ln K eq ) is an extrapolation. This large difference in prediction of the dependent variable at the standard composition when it is outside of the range of the experimental data is a well known statistical property of the Cox mixture models (Cornell, 1975). The standard state of 0.33333 was relatively arbitrarily chosen.…”

Section: Resultsmentioning

confidence: 99%

A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

Reynolds¹

2009

Geoderma

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“…In this case, experimental designs that have been proposed in the literature are the simplex lattice design (Scheff6, 1958), the simplex centroid design (Scheff6, 1963), the symmetric simplex design (Murty and Das, 1968), the simplex screening design (Snee and Marquardt, 1976) and axial designs (Cornell, 1975). While some of these designs are D-optimal and would be strong candidates for studying nutrient systems, most were developed in the chemical or other industries and were based on rather pragmatic and empirical grounds.…”

Section: Experimentation Over the Whole Simplexmentioning

confidence: 99%

“…For these designs specific mixture models were developed and are based on the incorporation of the mixture constraints (Eq. 1 and 2) resulting in polynomial or other model forms: Scheff6 canonical polynomials (Scheff6, 1958;1963), Cox's mixture models (Cornell, 1975;Cox, 1971) mixture models with inverse terms and adaptations of some theoretical model to the mixture situation (Gorman and Cornell, 1985). and/or upper bounds (x i ~< U/< 1).…”

Section: Experimentation Over the Whole Simplexmentioning

confidence: 99%

Design and analysis of mixture systems: Applications in hydroponic, plant nutrition research

Schrevens

Cornell

1993

Plant Soil

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This study demonstrates that nutrient solutions can be defined as 'mixture systems'. A general methodology for design and analysis of mixture optimization experiments is developed. The emphasis is centered on multivariate investigation of the zone of optimal solution properties as a function of the ion composition and the total ionic strength of the solution. The study of the effects of ion interaction on well-defined solution properties is also possible by this multivariate approach. This work is a valuable tool in mineral nutritional research, because for the first time the chemical feasibility conditions of such solution, combined with additional chemical, physiological or economical constraints, form the foundation of the statistical experimental design theory, which makes the optimization of complex mixtures of ions in relation to well-defined response variables possible.

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“…For mixture models, commonly used designs include the simplex lattice design (Scheffé, 1958), the simplex centroid (Scheffé, 1963), the symmetric simplex design (Murty and Das, 1968) and the axial designs (Cornell, 1975). Their design points are mainly on the boundary: vertices, edges, or faces of design simplex.…”

Section: Introductionmentioning

confidence: 99%

Extensions of D-optimal minimal designs for symmetric mixture models

Raghavarao

Chervoneva

2016

Communications in Statistics - Theory and Methods

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The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé's linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. In This Paper, Extensions Of The D-Optimal Minimal Designs Are Developed For A General Mixture Model To Allow Additional Interior Points In The Design Space To Enable Prediction Of The Entire Response Surface Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations.

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Some Comments on Designs for Cox's Mixture Polynomial

Cited by 29 publications

References 9 publications

A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

Design and analysis of mixture systems: Applications in hydroponic, plant nutrition research

Extensions of D-optimal minimal designs for symmetric mixture models

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