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Principles of parametric estimation in modeling language competition.

ABSTRACT: It is generally difficult to define reasonable parameters and interpret their values in mathematical models of social phenomena. Rather than directly fitting abstract parameters against empirical data, we should define some concrete parameters to denote the sociocultural factors relevant for particular phenomena, and compute the values of these parameters based upon the corresponding empirical data. Taking the example of modeling studies of language competition, we propose a language diffusion principle and two language inheritance principles to compute two critical parameters, namely the impacts and inheritance rates of competing languages, in our language competition model derived from the Lotka-Volterra competition model in evolutionary biology. These principles assign explicit sociolinguistic meanings to those parameters and calculate their values from the relevant data of population censuses and language surveys. Using four examples of language competition, we illustrate that our language competition model with thus-estimated parameter values can reliably replicate and predict the dynamics of language competition, and it is especially useful in cases lacking direct competition data.

SUBMITTER: Zhang M

PROVIDER: S-EPMC3683775 | biostudies-literature | 2013 Jun

REPOSITORIES: biostudies-literature

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Principles of parametric estimation in modeling language competition.

Zhang Menghan M Gong Tao T

Proceedings of the National Academy of Sciences of the United States of America 20130528 24

It is generally difficult to define reasonable parameters and interpret their values in mathematical models of social phenomena. Rather than directly fitting abstract parameters against empirical data, we should define some concrete parameters to denote the sociocultural factors relevant for particular phenomena, and compute the values of these parameters based upon the corresponding empirical data. Taking the example of modeling studies of language competition, we propose a language diffusion p ...[more]

PMID: 23716678

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Project description:Quantitative characterization of disease progression using longitudinal data can provide long-term predictions for the pathological stages of individuals. This work studies the robust modeling of Alzheimer's disease progression using parametric methods. The proposed method linearly maps the individual's age to a disease progression score (DPS) and jointly fits constrained generalized logistic functions to the longitudinal dynamics of biomarkers as functions of the DPS using M-estimation. Robustness of the estimates is quantified using bootstrapping via Monte Carlo resampling, and the estimated inflection points of the fitted functions are used to temporally order the modeled biomarkers in the disease course. Kernel density estimation is applied to the obtained DPSs for clinical status classification using a Bayesian classifier. Different M-estimators and logistic functions, including a novel type proposed in this study, called modified Stannard, are evaluated on the data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) for robust modeling of volumetric magnetic resonance imaging (MRI) and positron emission tomography (PET) biomarkers, cerebrospinal fluid (CSF) measurements, as well as cognitive tests. The results show that the modified Stannard function fitted using the logistic loss achieves the best modeling performance with an average normalized mean absolute error (NMAE) of 0.991 across all biomarkers and bootstraps. Applied to the ADNI test set, this model achieves a multiclass area under the ROC curve (AUC) of 0.934 in clinical status classification. The obtained results for the proposed model outperform almost all state-of-the-art results in predicting biomarker values and classifying clinical status. Finally, the experiments show that the proposed model, trained using abundant ADNI data, generalizes well to data from the National Alzheimer's Coordinating Center (NACC) with an average NMAE of 1.182 and a multiclass AUC of 0.929.

Dataset Information

Principles of parametric estimation in modeling language competition.

Publications

Principles of parametric estimation in modeling language competition.

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