Pub Date : 2023-04-03DOI: 10.3389/fams.2023.1151270
Abdulai Kailan Suhuyini, Baba Seidu
Typhoid fever is a potentially fatal illness that is caused by the bacteria Salmonella typhi. In this study, a deterministic mathematical model was formulated to look into transmission dynamics of typhoid fever with treatment and booster vaccination. The reproduction number R0 is calculated using the next-generation matrix approach. Then, a stability analysis on the equilibrium points was performed using Routh–Hurwitz criteria. It was revealed that the disease-free equilibrium point is locally asymptotically stable whenever R0 is less than 1 together with other conditions. We also showed that R0≤1 does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at R0=1. The model parameters in R0 were also subjected to sensitivity analysis, which revealed that the transmission rate, infection through an exposed person, and bacteria are the most influential parameters of the reproduction number R0. Numerical simulations were run to determine the impact of various parameters on the dynamics of typhoid.
{"title":"A mathematical model on the transmission dynamics of typhoid fever with treatment and booster vaccination","authors":"Abdulai Kailan Suhuyini, Baba Seidu","doi":"10.3389/fams.2023.1151270","DOIUrl":"https://doi.org/10.3389/fams.2023.1151270","url":null,"abstract":"Typhoid fever is a potentially fatal illness that is caused by the bacteria Salmonella typhi. In this study, a deterministic mathematical model was formulated to look into transmission dynamics of typhoid fever with treatment and booster vaccination. The reproduction number R0 is calculated using the next-generation matrix approach. Then, a stability analysis on the equilibrium points was performed using Routh–Hurwitz criteria. It was revealed that the disease-free equilibrium point is locally asymptotically stable whenever R0 is less than 1 together with other conditions. We also showed that R0≤1 does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at R0=1. The model parameters in R0 were also subjected to sensitivity analysis, which revealed that the transmission rate, infection through an exposed person, and bacteria are the most influential parameters of the reproduction number R0. Numerical simulations were run to determine the impact of various parameters on the dynamics of typhoid.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42396810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-31DOI: 10.3389/fams.2023.1000785
M. Vinyals, R. Sabbadin, S. Couture, L. Sadou, R. Thomopoulos, Kevin Chapuis, Baptiste Lesquoy, P. Taillandier
In this paper, we tackle innovation diffusion from the perspective of an institution which aims to encourage the adoption of a new product (i.e., an innovation) with mostly social rather than individual benefits. Designing such innovation adoption policies is a very challenging task because of the difficulty to quantify and predict its effect on the behaviors of non-adopters and the exponential size of the space of possible policies. To solve these issues, we propose an approach that uses agent-based modeling to simulate in a credible way the behaviors of possible adopters and (deep) reinforcement learning to efficiently explore the policy search space. An application of our approach is presented for the question of the use of digital technologies in agriculture. Empirical results on this case study validate our scheme and show the potential of our approach to learn effective innovation diffusion policies.
{"title":"Toward AI-designed innovation diffusion policies using agent-based simulations and reinforcement learning: The case of digital tool adoption in agriculture","authors":"M. Vinyals, R. Sabbadin, S. Couture, L. Sadou, R. Thomopoulos, Kevin Chapuis, Baptiste Lesquoy, P. Taillandier","doi":"10.3389/fams.2023.1000785","DOIUrl":"https://doi.org/10.3389/fams.2023.1000785","url":null,"abstract":"In this paper, we tackle innovation diffusion from the perspective of an institution which aims to encourage the adoption of a new product (i.e., an innovation) with mostly social rather than individual benefits. Designing such innovation adoption policies is a very challenging task because of the difficulty to quantify and predict its effect on the behaviors of non-adopters and the exponential size of the space of possible policies. To solve these issues, we propose an approach that uses agent-based modeling to simulate in a credible way the behaviors of possible adopters and (deep) reinforcement learning to efficiently explore the policy search space. An application of our approach is presented for the question of the use of digital technologies in agriculture. Empirical results on this case study validate our scheme and show the potential of our approach to learn effective innovation diffusion policies.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45598758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.3389/fams.2023.1126952
M. Sedghizadeh, M. Van den Berghe, R. Shcherbakov
Microseismicity is expected in potash mining due to the associated rock-mass response. This phenomenon is known, but not fully understood. To assess the safety and efficiency of mining operations, producers must quantitatively discern between normal and abnormal seismic activity. In this work, statistical aspects and clustering of microseismicity from a Saskatchewan, Canada, potash mine are analyzed and quantified. Specifically, the frequency-magnitude statistics display a rich behavior that deviates from the standard Gutenberg-Richter scaling for small magnitudes. To model the magnitude distribution, we consider two additional models, i.e., the tapered Pareto distribution and a mixture of the tapered Pareto and Pareto distributions to fit the bi-modal catalog data. To study the clustering aspects of the observed microseismicity, the nearest-neighbor distance (NND) method is applied. This allowed the identification of potential cluster characteristics in time, space, and magnitude domains. The implemented modeling approaches and obtained results will be used to further advance strategies and protocols for the safe and efficient operation of potash mines.
{"title":"Statistical and clustering analysis of microseismicity from a Saskatchewan potash mine","authors":"M. Sedghizadeh, M. Van den Berghe, R. Shcherbakov","doi":"10.3389/fams.2023.1126952","DOIUrl":"https://doi.org/10.3389/fams.2023.1126952","url":null,"abstract":"Microseismicity is expected in potash mining due to the associated rock-mass response. This phenomenon is known, but not fully understood. To assess the safety and efficiency of mining operations, producers must quantitatively discern between normal and abnormal seismic activity. In this work, statistical aspects and clustering of microseismicity from a Saskatchewan, Canada, potash mine are analyzed and quantified. Specifically, the frequency-magnitude statistics display a rich behavior that deviates from the standard Gutenberg-Richter scaling for small magnitudes. To model the magnitude distribution, we consider two additional models, i.e., the tapered Pareto distribution and a mixture of the tapered Pareto and Pareto distributions to fit the bi-modal catalog data. To study the clustering aspects of the observed microseismicity, the nearest-neighbor distance (NND) method is applied. This allowed the identification of potential cluster characteristics in time, space, and magnitude domains. The implemented modeling approaches and obtained results will be used to further advance strategies and protocols for the safe and efficient operation of potash mines.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45981691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.3389/fams.2023.1083410
M. Cadena, M. Méndez
Here we assess countries' management of the coronavirus 2019 (COVID-19) pandemic using the reliability measure P(X ≤ Y). In this management, all kind of strategies as interventions deployed by governments as well individuals' initiatives to prevent, mitigate, and reduce the contagion of this disease are taken into account. Also, typical customs practiced locally and influencing contagion are included. Regarding a number of countries and rates associated to deaths and incidence, orderings of countries about such management are established, by using the measure of reliability indicated above. In this way, countries are distinguished from each other depending on how they managed this pandemic. This kind of analysis may be extended to the management of other diseases.
{"title":"Ordering countries when managing COVID-19","authors":"M. Cadena, M. Méndez","doi":"10.3389/fams.2023.1083410","DOIUrl":"https://doi.org/10.3389/fams.2023.1083410","url":null,"abstract":"Here we assess countries' management of the coronavirus 2019 (COVID-19) pandemic using the reliability measure P(X ≤ Y). In this management, all kind of strategies as interventions deployed by governments as well individuals' initiatives to prevent, mitigate, and reduce the contagion of this disease are taken into account. Also, typical customs practiced locally and influencing contagion are included. Regarding a number of countries and rates associated to deaths and incidence, orderings of countries about such management are established, by using the measure of reliability indicated above. In this way, countries are distinguished from each other depending on how they managed this pandemic. This kind of analysis may be extended to the management of other diseases.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42367612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.3389/fams.2023.1086240
Stefanie Hittmeyer, B. Krauskopf, H. Osinga, Katsutoshi Shinohara
Introduction The extension of the Smale horseshoe construction for diffeomorphisms in the plane to those in spaces of at least dimension three may result in a hyperbolic invariant set referred to as a blender. The defining property of a blender is that it has a stable or unstable invariant manifold that appears to have a dimension larger than expected. In this study, we consider a Hénon-like family in ℝ3, which is the only explicitly given example of a system known to feature a blender in a certain range of a parameter (corresponding to an expansion or contraction rate). More specifically, as part of its hyperbolic set, this family has a pair of saddle fixed points with one-dimensional stable or unstable manifolds. When there is a blender, the closure of these manifolds cannot be avoided by one-dimensional curves coming from an appropriate direction. This property has been checked for the Hénon-like family by the method of computing extremely long pieces of global one-dimensional manifolds to determine the parameter range over which a blender exists. Methods In this study, we take the complimentary and local point of view of constructing an actual three-dimensional box (a parallelopiped) that acts as an outer cover of the hyperbolic set. The successive forward or backward images of this box form a nested sequence of sub-boxes that contains the hyperbolic set, as well as its respective local invariant manifold. Results This constitutes a three-dimensional horseshoe that, in contrast to the idealized affine construction, is quite general and features sub-boxes with curved edges. The initial box is defined in a parameter-dependent way, and this allows us to characterize properties of the hyperbolic set intuitively. Discussion In particular, we trace relevant edges of sub-boxes as a function of the parameter to provide additional geometric insight into when the hyperbolic set may or may not be a blender.
{"title":"Boxing-in of a blender in a Hénon-like family","authors":"Stefanie Hittmeyer, B. Krauskopf, H. Osinga, Katsutoshi Shinohara","doi":"10.3389/fams.2023.1086240","DOIUrl":"https://doi.org/10.3389/fams.2023.1086240","url":null,"abstract":"Introduction The extension of the Smale horseshoe construction for diffeomorphisms in the plane to those in spaces of at least dimension three may result in a hyperbolic invariant set referred to as a blender. The defining property of a blender is that it has a stable or unstable invariant manifold that appears to have a dimension larger than expected. In this study, we consider a Hénon-like family in ℝ3, which is the only explicitly given example of a system known to feature a blender in a certain range of a parameter (corresponding to an expansion or contraction rate). More specifically, as part of its hyperbolic set, this family has a pair of saddle fixed points with one-dimensional stable or unstable manifolds. When there is a blender, the closure of these manifolds cannot be avoided by one-dimensional curves coming from an appropriate direction. This property has been checked for the Hénon-like family by the method of computing extremely long pieces of global one-dimensional manifolds to determine the parameter range over which a blender exists. Methods In this study, we take the complimentary and local point of view of constructing an actual three-dimensional box (a parallelopiped) that acts as an outer cover of the hyperbolic set. The successive forward or backward images of this box form a nested sequence of sub-boxes that contains the hyperbolic set, as well as its respective local invariant manifold. Results This constitutes a three-dimensional horseshoe that, in contrast to the idealized affine construction, is quite general and features sub-boxes with curved edges. The initial box is defined in a parameter-dependent way, and this allows us to characterize properties of the hyperbolic set intuitively. Discussion In particular, we trace relevant edges of sub-boxes as a function of the parameter to provide additional geometric insight into when the hyperbolic set may or may not be a blender.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47336905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.3389/fams.2023.1072447
Qusain Haider, A. Hassan, S. M. Eldin
This article aims to describe the simulation studies of the hepatitis B virus non-linear system using supervised neural networks procedures supported by Levenberg-Marquardt back propagation methodology. The proposed strategy has five distinct quantities: susceptible X(t), symptomatic infections Y(t), chronic infections W(t), recovered population R(t), and a population that has received vaccinations Z(t). The reference data set for all three distinct cases has been obtained utilizing the ND-Solver and Adams method in Mathematica software. The outcomes have been validated with performance plots for all cases. To check the accuracy and effectiveness of proposed methodology mean square error has are presented. State transition, and regression plots are illustrated to elaborated the testing, training, and validation methodology. Additionally, absolute errors for different components of hepatitis B virus model are demonstrated to depict the error occurring during distinct cases. Whereas the data assigned to training is 81%, and 9% for each testing and validation. The mean square error for all three cases is 10−12 this show the accuracy and correctness of proposed methodology.
{"title":"Artificial neural network scheme to solve the hepatitis B virus model","authors":"Qusain Haider, A. Hassan, S. M. Eldin","doi":"10.3389/fams.2023.1072447","DOIUrl":"https://doi.org/10.3389/fams.2023.1072447","url":null,"abstract":"This article aims to describe the simulation studies of the hepatitis B virus non-linear system using supervised neural networks procedures supported by Levenberg-Marquardt back propagation methodology. The proposed strategy has five distinct quantities: susceptible X(t), symptomatic infections Y(t), chronic infections W(t), recovered population R(t), and a population that has received vaccinations Z(t). The reference data set for all three distinct cases has been obtained utilizing the ND-Solver and Adams method in Mathematica software. The outcomes have been validated with performance plots for all cases. To check the accuracy and effectiveness of proposed methodology mean square error has are presented. State transition, and regression plots are illustrated to elaborated the testing, training, and validation methodology. Additionally, absolute errors for different components of hepatitis B virus model are demonstrated to depict the error occurring during distinct cases. Whereas the data assigned to training is 81%, and 9% for each testing and validation. The mean square error for all three cases is 10−12 this show the accuracy and correctness of proposed methodology.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48261986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-29DOI: 10.3389/fams.2023.1150921
Keisuke Otaki, Akihisa Okada, Hiroaki Yoshida
The aim of this study was to explore the information disclosure (ID) problem, which involves selecting pairs of two sides before matching toward user-oriented optimization. This problem is known to be useful for mobility-on-demand (MoD) platforms because drivers' choice behaviors are appropriately modeled, but solving the problem is still under development, although heuristic solvers have been proposed. We develop new branch-and-bound-based (BnB) solvers and a new heuristic solver based on a quadratic unconstrained binary optimization (QUBO) formulation. Our numerical experiments show that the QUBO-based solver indeed works within the limit of available bits, and the BnB solver performs slightly better than existing heuristic ones.
{"title":"Experimental study on the information disclosure problem: Branch-and-bound and QUBO solver","authors":"Keisuke Otaki, Akihisa Okada, Hiroaki Yoshida","doi":"10.3389/fams.2023.1150921","DOIUrl":"https://doi.org/10.3389/fams.2023.1150921","url":null,"abstract":"The aim of this study was to explore the information disclosure (ID) problem, which involves selecting pairs of two sides before matching toward user-oriented optimization. This problem is known to be useful for mobility-on-demand (MoD) platforms because drivers' choice behaviors are appropriately modeled, but solving the problem is still under development, although heuristic solvers have been proposed. We develop new branch-and-bound-based (BnB) solvers and a new heuristic solver based on a quadratic unconstrained binary optimization (QUBO) formulation. Our numerical experiments show that the QUBO-based solver indeed works within the limit of available bits, and the BnB solver performs slightly better than existing heuristic ones.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41817817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-29DOI: 10.3389/fams.2023.1082928
Ángel J. Zamora-Ramírez, M. Santillán
There is growing evidence that mitochondrial dynamics play a role in mitochondrial function quality control. Recent studies have discovered that physical activity can aid in maintaining a healthy mitochondrial population and may even counteract the mitochondrial damage caused by obesity by modifying mitochondrial dynamics processes like mitogenesis, fission, and mitophagy. However, the underlying mechanisms and how they influence the various processes of mitochondrial dynamics have not been completely clarified. This study seeks to make an initial effort to fill this gap by utilizing mathematical modeling to investigate how modifications to the processes involved in mitochondrial dynamics can aid in preserving a healthy mitochondrial population under conditions of accelerated damage. We found by analyzing the model stationary behavior that fission and mitophagy are strictly required for a healthy mitochondrial population, that increasing the rate of mitochondrial damage has a negative impact on the population of functional mitochondria, and that such damage can be mitigated to some extent by increasing fission and/or mitophagy rates. These findings are finally discussed in the context of the benefits of physical activity for mitochondrial population health in obese individuals.
{"title":"Effects of fission and mitophagy on mitochondrial functionality under accelerated damage conditions: A mathematical modeling approach","authors":"Ángel J. Zamora-Ramírez, M. Santillán","doi":"10.3389/fams.2023.1082928","DOIUrl":"https://doi.org/10.3389/fams.2023.1082928","url":null,"abstract":"There is growing evidence that mitochondrial dynamics play a role in mitochondrial function quality control. Recent studies have discovered that physical activity can aid in maintaining a healthy mitochondrial population and may even counteract the mitochondrial damage caused by obesity by modifying mitochondrial dynamics processes like mitogenesis, fission, and mitophagy. However, the underlying mechanisms and how they influence the various processes of mitochondrial dynamics have not been completely clarified. This study seeks to make an initial effort to fill this gap by utilizing mathematical modeling to investigate how modifications to the processes involved in mitochondrial dynamics can aid in preserving a healthy mitochondrial population under conditions of accelerated damage. We found by analyzing the model stationary behavior that fission and mitophagy are strictly required for a healthy mitochondrial population, that increasing the rate of mitochondrial damage has a negative impact on the population of functional mitochondria, and that such damage can be mitigated to some extent by increasing fission and/or mitophagy rates. These findings are finally discussed in the context of the benefits of physical activity for mitochondrial population health in obese individuals.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"61 9‐10","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41268229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-28DOI: 10.3389/fams.2023.1095769
K. Schweizer, C. DiStefano, B. French
A transformational measurement model for structural equation modeling (SEM) of asymmetric non-normal data is proposed. This measurement model aligns with the expectation-maximization (EM) algorithm of the maximum likelihood estimation (MLE) method, creating adaptability to data that deviate from normality. Distinctive properties of the connection of the measurement model and EM algorithm are maintenance of the normality assumption, which is at the core of EM algorithm, and applicability to asymmetric non-normality of observed data mediated by distortion coefficients. An evaluation using a mixture of normal and severely asymmetric non-normal data analyzed by MLE for asymmetric non-normal data (MLE for ASN) demonstrated efficiency of the model. Comparisons with robust DWLS and WLS yielded better fit results under MLE for ASN estimation.
提出了一种非对称非正态数据结构方程建模的转换测量模型。该测量模型与最大似然估计（MLE）方法的期望最大化（EM）算法一致，创造了对偏离正态性的数据的适应性。测量模型和EM算法的连接的显著特性是保持正态性假设，这是EM算法的核心，以及适用于由失真系数介导的观测数据的不对称非正态性。MLE对非对称非正态数据（MLE for ASN）进行分析，使用正态和严重非正态的混合数据进行评估，证明了该模型的有效性。与鲁棒DWLS和WLS的比较在用于ASN估计的MLE下产生了更好的拟合结果。
{"title":"A maximum likelihood approach for asymmetric non-normal data using a transformational measurement model","authors":"K. Schweizer, C. DiStefano, B. French","doi":"10.3389/fams.2023.1095769","DOIUrl":"https://doi.org/10.3389/fams.2023.1095769","url":null,"abstract":"A transformational measurement model for structural equation modeling (SEM) of asymmetric non-normal data is proposed. This measurement model aligns with the expectation-maximization (EM) algorithm of the maximum likelihood estimation (MLE) method, creating adaptability to data that deviate from normality. Distinctive properties of the connection of the measurement model and EM algorithm are maintenance of the normality assumption, which is at the core of EM algorithm, and applicability to asymmetric non-normality of observed data mediated by distortion coefficients. An evaluation using a mixture of normal and severely asymmetric non-normal data analyzed by MLE for asymmetric non-normal data (MLE for ASN) demonstrated efficiency of the model. Comparisons with robust DWLS and WLS yielded better fit results under MLE for ASN estimation.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42470882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-27DOI: 10.3389/fams.2023.1169164
S. Sanders, J. Ehrlich, James W. Boudreau
This study establishes sufficient conditions for observing instances of Simpson's (data aggregation) Paradox under rank sum scoring (RSS), as used, e.g., in the Wilcoxon-Mann-Whitney (WMW) rank sum test. The WMW test is a primary nonparametric statistical test in FDA drug product evaluation and other prominent medical settings. Using computational nonparametric statistical methods, we also establish the relative frequency with which paradox-generating Simpson Reversals occur under RSS when an initial data sequence is pooled with its ordinal replicate. For each 2-sample, n-element per sample or 2 x n case of RSS considered, strict Reversals occurred for between 0% and 1.74% of data poolings across the whole sample space, roughly similar to that observed for 2 x 2 x 2 contingency tables and considerably less than that observed for path models. The Reversal rate conditional on observed initial sequence is highly variable. Despite a mode at 0%, this rate exceeds 20% for some initial sequences. Our empirical application identifies clusters of Simpson Reversal susceptibility for publicly-released mobile phone radiofrequency exposure data. Simpson Reversals under RSS are not simply a theoretical concern but can reverse nonparametric or parametric biostatistical results even in vitally important public health settings. Conceptually, Paradox incidence can be viewed as a robustness check on a given WMW statistical test result. When an instance of Paradox occurs, results constituting this instance are found to be data-scale dependent. Given that the rate of Reversal can vary substantially by initial sequence, the practice of calculating this rate conditional on observed initial sequence represents a potentially important robustness check upon a result.
这项研究为在秩和得分（RSS）下观察Simpson（数据聚合）悖论的实例建立了充分的条件，例如在Wilcoxon-Mann-Whitney（WMW）秩和检验中使用。WMW检验是美国食品药品监督管理局药品评估和其他重要医疗环境中的主要非参数统计检验。使用计算非参数统计方法，我们还建立了当初始数据序列与其有序复制合并时，在RSS下产生悖论的Simpson反转发生的相对频率。对于每个2个样本、每个样本n个元素或所考虑的RSS的2 x n种情况，在整个样本空间中，0%至1.74%的数据池发生了严格的反转，与2 x 2 x 2列联表观察到的情况大致相似，但远低于路径模型观察到的情况。以观察到的初始序列为条件的逆转率变化很大。尽管模式为0%，但对于一些初始序列，该比率超过20%。我们的经验应用程序确定了公开发布的手机射频暴露数据的Simpson逆转易感性集群。RSS下的Simpson反转不仅仅是一个理论问题，甚至在至关重要的公共卫生环境中也可以反转非参数或参数生物统计学结果。从概念上讲，Paradox发生率可以被视为对给定WMW统计测试结果的稳健性检查。当Paradox的一个实例发生时，组成该实例的结果被发现是数据规模相关的。鉴于逆转率可能因初始序列而异，以观察到的初始序列为条件计算逆转率的做法代表了对结果的潜在重要稳健性检查。
{"title":"Simpson's aggregation paradox in nonparametric statistical analysis: Theory, computation, and susceptibility in public health data","authors":"S. Sanders, J. Ehrlich, James W. Boudreau","doi":"10.3389/fams.2023.1169164","DOIUrl":"https://doi.org/10.3389/fams.2023.1169164","url":null,"abstract":"This study establishes sufficient conditions for observing instances of Simpson's (data aggregation) Paradox under rank sum scoring (RSS), as used, e.g., in the Wilcoxon-Mann-Whitney (WMW) rank sum test. The WMW test is a primary nonparametric statistical test in FDA drug product evaluation and other prominent medical settings. Using computational nonparametric statistical methods, we also establish the relative frequency with which paradox-generating Simpson Reversals occur under RSS when an initial data sequence is pooled with its ordinal replicate. For each 2-sample, n-element per sample or 2 x n case of RSS considered, strict Reversals occurred for between 0% and 1.74% of data poolings across the whole sample space, roughly similar to that observed for 2 x 2 x 2 contingency tables and considerably less than that observed for path models. The Reversal rate conditional on observed initial sequence is highly variable. Despite a mode at 0%, this rate exceeds 20% for some initial sequences. Our empirical application identifies clusters of Simpson Reversal susceptibility for publicly-released mobile phone radiofrequency exposure data. Simpson Reversals under RSS are not simply a theoretical concern but can reverse nonparametric or parametric biostatistical results even in vitally important public health settings. Conceptually, Paradox incidence can be viewed as a robustness check on a given WMW statistical test result. When an instance of Paradox occurs, results constituting this instance are found to be data-scale dependent. Given that the rate of Reversal can vary substantially by initial sequence, the practice of calculating this rate conditional on observed initial sequence represents a potentially important robustness check upon a result.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49187274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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