On the estimation of reactivity ratios

Patino‐Leal, Hugo; Reilly, Park M.; O’Driscoll, K. F.

doi:10.1002/pol.1980.130180309

Cited by 74 publications

(40 citation statements)

References 8 publications

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“…This is an analogue to the error propagation method discussed by Patino-Leal et al [3] The difference consists of assuming that there is no correlation between observables, which results in the lack of the "covariance" term in Equation (10). The correctly derived error propagation method based on the same amount of information as provided for MML or EVM will lead to nearly identical estimates of reactivity parameters as with the two methods mentioned above.…”

Section: Application Of the MML Methods To Copolymerization Data Procementioning

confidence: 99%

“…[1] Among the different methods proposed, the error-in-variables model (EVM) method has the soundest statistical background. This method, developed by Van der Meer et al [2] and Patino-Leal et al, [3] correctly accounts for the errors in monomer feed and copolymer compositions. EVM minimizes the weighted sum of squares of the distance between measured point and calculated (estimated) value.…”

Section: Introductionmentioning

confidence: 99%

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Use of the Maximum Likelihood Method for Composition Data Analysis in the Radical Copolymerization Terminal Model

Oracz

Kaim

2001

Macromol. Theory Simul.

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A method based on the maximum likelihood principle has been used for the estimation of reactivity ratios in the terminal model of copolymerization from experimental composition data. This method assumes explicitly that all measured variables are subject to errors. If correct estimates of experimental errors are used the best values of parameters are obtained. In addition, this method can also be used for the copolymerization model validation and/or evaluation of the accuracy of the experimental data. The application of the method is illustrated using simulated data disturbed with random errors.

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Section: Application Of the MML Methods To Copolymerization Data Procementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Use of the Maximum Likelihood Method for Composition Data Analysis in the Radical Copolymerization Terminal Model

Oracz

Kaim

2001

Macromol. Theory Simul.

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“…The advance of using a computer allows the use of the integrated copolymer equation such that the systematic error due to factor (2) can be eliminated. Patino-Leal et al 4 and Van der Meer et al 5 gave examples of significant systematic errors due to factor 3. They also described a calculation method to cope adequately with the error structure of the observation^.^ As this method is intricate and difficult to implement, relative to the method based on the differential equation, it seems worthwhile to determine those cases where it yields significantly better results.…”

Section: Hautus Linssen and German (3)mentioning

confidence: 99%

Dependence of computed copolymer reactivity ratios on the calculation method. II. Effects of experimental design and error structure

Hautus

Linssen

German

1984

J. Polym. Sci. Polym. Chem. Ed.

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Two calculation methods for estimating reactivity ratios, one method based on the differential Alfrey‐Mayo equation and one based on the integrated form of this model, are compared with respect to precision and bias. Both methods are characterized by the use of information about the monomer feed composition only and are assumed to be valid up to high conversion. As only monomer feed composition has to be analyzed, several sampling designs are feasible. Two extreme designs can be distinguished. One consists of repetitive sampling of the initial and final monomer feed mixture, whereas the other consists of sequential sampling during the course of the reaction. The influence of both designs of the calculated r‐values is investigated by means of simulation. In the present paper the second calculation method, based on the integrated form, is solved by a nonlinear least squares method considering errors in both variables. This method required additional information about the errorstructure of the data. As this information is mostly of approximate nature, the influence of misspecification of this error structure on the calculated r‐values is also examined.

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“…From a theoretical point of view the most conclusive should be the MML method provided the error estimates are correct and follow the normal distribution. The assumed normal distribution of errors does not allow for comparison with the error-in-variables model (EVM) method [10][11], which is widely used in literature. The reason is that the EVM method makes use of a covariance matrix of errors with built-in correlation between errors.…”

Section: Experimental Partmentioning

confidence: 99%

Statistical approach to model discrimination for the radical copolymerization of methyl methacrylate and styrene from a posteriori data of composition

Kaim

Oracz²

2003

E-Polymers

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Abstract:The multiresponse maximum likelihood (MML) method and statistical tests -the F-test, the t-Student test, and the sign changes test -were compared with respect to their power of discrimination between two kinetic models, the terminal and the penultimate model, for the radical copolymerization of the styrene -methyl methacrylate monomer system in bulk. The results indicate that the investigated statistical methods (except the sign changes test) are suitable for kinetic-model discrimination when they are applied to a posteriori data of copolymer composition. Although the MML method was shown to be more demanding in the error estimation of experimental data, it can serve as a proper tool for kinetic-model discrimination in copolymerization, provided the correct estimates of the ratio between errors in measured copolymer composition data are known. The main steps of the calculating scheme are given.

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On the estimation of reactivity ratios

Cited by 74 publications

References 8 publications

Use of the Maximum Likelihood Method for Composition Data Analysis in the Radical Copolymerization Terminal Model

Use of the Maximum Likelihood Method for Composition Data Analysis in the Radical Copolymerization Terminal Model

Dependence of computed copolymer reactivity ratios on the calculation method. II. Effects of experimental design and error structure

Statistical approach to model discrimination for the radical copolymerization of methyl methacrylate and styrene from a posteriori data of composition

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