Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model
In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reut...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2020/1837364 |
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| author | Sara Bidah Omar Zakary Mostafa Rachik Hanane Ferjouchia |
| author_facet | Sara Bidah Omar Zakary Mostafa Rachik Hanane Ferjouchia |
| author_sort | Sara Bidah |
| collection | DOAJ |
| description | In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters. |
| format | Article |
| id | doaj-art-b593d2b91fa7415a9b93e02edc23e400 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b593d2b91fa7415a9b93e02edc23e4002025-02-03T01:05:21ZengWileyAbstract and Applied Analysis1085-33751687-04092020-01-01202010.1155/2020/18373641837364Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion ModelSara Bidah0Omar Zakary1Mostafa Rachik2Hanane Ferjouchia3Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences BenM’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences BenM’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences BenM’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences BenM’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoIn this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters.http://dx.doi.org/10.1155/2020/1837364 |
| spellingShingle | Sara Bidah Omar Zakary Mostafa Rachik Hanane Ferjouchia Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model Abstract and Applied Analysis |
| title | Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model |
| title_full | Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model |
| title_fullStr | Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model |
| title_full_unstemmed | Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model |
| title_short | Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model |
| title_sort | mathematical modeling of public opinions parameter estimation sensitivity analysis and model uncertainty using an agree disagree opinion model |
| url | http://dx.doi.org/10.1155/2020/1837364 |
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