Mixture Regression Model Research Articles

Weighted fast-trimmed likelihood estimator for mixture regression models

The fast-trimmed likelihood estimate is a robust method to estimate the parameters of a mixture regression model. However, this method is vulnerable to the presence of bad leverage points, which are outliers in the direction of independent variables. To address this issue, we propose the weighted fast-trimmed likelihood estimate to mitigate the impact of leverage points. The proposed method applies the weights of the minimum covariance determinant to the rows suspected of containing leverage points. Notably, both real data and simulation studies were considered to determine the efficiency of the proposed method compared to the previous methods. The results reveal that the weighted fast-trimmed estimate method is more robust and reliable than the fast-trimmed likelihood estimate and the expectation–maximization (EM) methods, particularly in cases with small sample sizes.

Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance

Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.

Investigating ingredient influence on reconstitution of powdered cocoa beverage via constrained mixture design

Reconstitution of a powdered cocoa beverage (PCB) produced by wet-mixing and oven-drying were studied. Sixteen PCB samples with different proportions of core ingredients, namely cocoa (5–25 %), skimmed milk (10–50 %), hydrolysed cereal extract (15–60 %), sucrose (0–30 %) and palm olein (0–15 %), were generated via a constrained mixture design. PCB samples had varying physical properties which included bulk porosity (57.3–74.8 %), particle surface hydrophilicity (contact angle = 60.0–94.5°) and glass transition temperature (51.2–86.3 °C). Consequently, PCB samples differed in reconstitution properties like wetting time (11–>300 s), reconstitution time (14–141 s) and soluble content (51.3–86.8 %). Subsequently, mixture regression models were developed to varying success (adjusted R2 = 70–97 %) for identifying the influence of each core ingredient on physical and reconstitution properties of PCB. PCB wettability was most improved by increasing the proportion of hydrolysed cereal extract, through forming powders with moderate particle surface hydrophilicities but higher glass transition temperatures and higher bulk porosities. Conversely, PCB wettability became exceptionally poor when it contained >35 % skimmed milk and <5 % palm olein. Additionally, a higher ratio of protein-rich skimmed milk against carbohydrate-rich hydrolysed cereal extract and sucrose led to solubility loss in PCB.

Risk Perception, Cooperation, and Emotional Distress During the COVID-19 Pandemic: Exploring Adaptive Risk Perception

During the COVID-19 pandemic, while risk perception may promote public cooperation with pandemic prevention, it may also increase emotional distress and thus endanger mental health. This study aimed to examine whether there is an adaptive risk perception pattern that fits both needs of pandemic control and mental health protection. Two waves of Chinese participants (N sample 1 = 1633, N sample 2 = 1899) completed the Scale of Pandemic Risk Perception, the Scale of Public Cooperation with Pandemic Prevention, the Epidemic Worry Scale, and the Positive and Negative Affective Schedule during Feb 3rd to 5th, and during Feb 18th to 20th, 2021 respectively. Four risk perception profiles were identified by using latent profile analysis based on pandemic risk perception. Regression mixture models found that individuals in the perceived-controllable-high-perceived-risk profile were the most cooperative and reported the least worries and negative affect. The perceived-uncontrollable-high-perceived-risk profile demonstrated high cooperation but serious worry and negative affect. Individuals in the ignoring-risk profile reported the least levels of cooperation and worry but the highest levels of negative affect. Finally, the perceived-moderate-perceived-risk profile reported moderate levels of both cooperation and emotional distress. These results were well repeated in two samples. Present findings point towards an adaptive risk perception pattern (the controllable-high-perceived-risk profile) which may optimize cooperation while also avoid serious emotional distress.

Prenatal air pollution and children's autism traits score: Examination of joint associations with maternal intake of vitamin D, methyl donors, and polyunsaturated fatty acids using mixture methods.

Maternal nutrient intake may moderate associations between environmental exposures and children's neurodevelopmental outcomes, but few studies have assessed joint effects. We aimed to evaluate whether prenatal nutrient intake influences the association between air pollutants and autism-related trait scores. We included 126 participants from the EARLI (Early Autism Risk Longitudinal Investigation, 2009-2012) cohort, which followed US pregnant mothers who previously had a child with autism. Bayesian kernel machine regression and traditional regression models were used to examine joint associations of prenatal nutrient intake (vitamins D, B12, and B6; folate, choline, and betaine; and total omega 3 and 6 polyunsaturated fatty acids, reported via food frequency questionnaire), air pollutant exposure (particulate matter <2.5 μm [PM2.5], nitrogen dioxide [NO2], and ozone [O3], estimated at the address level), and children's autism-related traits (measured by the Social Responsiveness Scale [SRS] at 36 months). Most participants had nutrient intakes and air pollutant exposures that met US standards. Bayesian kernel machine regression mixture models and traditional regression models provided little evidence of individual or joint associations of nutrients and air pollutants with SRS scores or of an association between the overall mixture and SRS scores. In this cohort with a high familial likelihood of autism, we did not observe evidence of joint associations between air pollution exposures and nutrient intake with autism-related traits. Future work should examine the use of these methods in larger, more diverse samples, as our results may have been influenced by familial liability and/or relatively high nutrient intakes and low air pollutant exposures.

Exposure to metal mixtures and telomere length in Bangladeshi children.

Telomere length is associated with chronic diseases and in younger populations, may represent a biomarker of disease susceptibility. As growing evidence suggests that environmental factors, including metals, may impact telomere length, we investigated the association between 17 metals measured in toenail samples and leukocyte relative telomere length (RTL), among 472 five- to seven-year-old children enrolled in the Bangladesh Environmental Research in Children's Health (BiRCH) cohort. In single exposure linear regression models, a doubling of arsenic (As) and mercury (Hg) (μg/g) were associated with a -0.21 (95%CI: -0.032, -0.010; p=0.0005) and -0.017 (95%CI: -0.029, -0.004; p=0.006) difference in RTL, respectively. In Bayesian Kernel Machine Regression (BKMR) mixture models, the overall metal mixture was inversely associated with RTL (P-for-trend <0.001). Negative associations with RTL were observed with both log2-As and log2-Hg, while an inverted U-shaped association was observed for log2-zinc (Zn) with RTL. We found little evidence of interaction among metals. Sex-stratification identified stronger associations of the overall mixture and log2-As with RTL among females, compared to males. Our study suggests that As and Hg may independently influence RTL in mid-childhood. Further studies are needed to investigate potential long-term impacts of metal-associated telomere shortening in childhood on health outcomes in adult life.

The Relationship Between Social Media Information Sharing Characteristics and Problem Behaviors Among Chinese College Students Under Recommendation Algorithms.

With the development of information technology and various social media, recommendation algorithms have increasingly more influence on users' social media usage. To date, there has been limited research focused on analyzing the impact of recommendation algorithms on social media use and their corresponding role in the development of problematic behaviors. The present study analyzes the impact of recommendation algorithms on college students' information sharing and internalizing, externalizing problem behaviors to address the aforementioned shortcomings. An online questionnaire survey was conducted among 34,752 college students in China. A latent profile analysis was conducted to explore the various behavioral patterns of Chinese college students' information sharing across the three social media platforms identified for this study. The Bolck-Croon-Hagenaars (BCH) method Regression Mixture Modeling was then used to analyze the differences in internalizing and externalizing problem behaviors among the different subgroups of Chinese college students. The level of information sharing by college students across different social media platforms could be divided into "WeChat Moments low-frequency information sharing", "middle-frequency comprehensive information sharing", "TikTok high-frequency information sharing", and "Sina Weibo high-frequency information sharing". Significant differences were observed regarding internalizing and externalizing problem behaviors among college students in different information-sharing subgroups. This study identified four subgroups with different information-sharing characteristics using latent profile analysis. Among them, college students who are in subgroup of social media information sharing influenced by recommendation algorithms exhibit higher frequency of information sharing and higher level of internalizing and externalizing problematic behaviors. These results expand our understanding of college students' social media usage and problem behaviors from a technological perspective. In future, the negative impacts of recommendation algorithms on college students can be reduced by improving their awareness of these algorithms and optimizing the algorithms themselves.

A Multivariate Mixture Regression Model for Constrained Responses

Compositional data are vectors typically representing proportions of a whole, that is, those whose elements are strictly positive and subject to a unit-sum constraint. The increasing number of fields where this type of data arises makes the development of proper statistical tools an important issue. From a regression perspective, whenever the multivariate response is a compositional vector, a proper model that accounts for the unit-sum constraint is the well-established Dirichlet regression model. However, there are significant drawbacks mainly due to the limited flexibility of the Dirichlet distribution. The aim of this contribution is to introduce a new multivariate regression model for constrained responses, that is based on the extended flexible Dirichlet distribution (which is a structured mixture with Dirichlet distributed components). The new model is obtained by adopting a novel reparameterization which allows for, among other things, the presence of suitably designed cluster-specific regression patterns. It is shown to provide considerably greater flexibility and better performance than the standard Dirichlet regression model. In particular, from theoretical analysis, intensive simulation studies in many challenging scenarios, as well as from a real data application, it emerges that the new regression model can handle several issues affecting the Dirichlet regression, such as the presence of outliers, latent groups, multi-modality, and positive correlations.

Model Selection for Exponential Power Mixture Regression Models.

Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.

Financial Inclusion, Globalization and Structural Transformation in Developing Countries: A Finite Mixture-of-Regressions Approach

Industrialization plays a key role in job creation and economic development. We extend the abundant literature on the determinants of industrialization by exploring the potential effects of financial inclusion in 64 developing countries over the period 2000-2020. Using a finite mixture regression model, we find that our sample is best described by a model with three classes of countries. We then incorporate the potential presence of hidden heterogeneity and, we explain the class membership of countries based on globalization. We find that the impact of financial inclusion on industrialization differs across these three classes of countries. Specifically, financial inclusion is negatively associated with industrialization in the first class of countries where the level of industrialization is low, while it positively affects industrialization in relatively more industrialized countries (class 2 and class 3). We also show that better-integrated countries into the global economy are more likely to be in the class where financial inclusion promotes industrialization. Our results are robust to several robustness checks. Our findings suggest that developing countries could reap more benefits from financial inclusion by strengthening their integration into the global economy.

Expectation Parameters in the Poisson Mixture Regression Model for Latent Class by Applying Genetic Algorithm and Maximization Algorithm

In a Poisson mixture regression model for latent class, observations come from different sub-sources or classes, and the observed data are assumed to be generated by a specific (finite) mixture of unobserved or latent classes. The problem lies in the optimal assignment of observations to their respective classes. This requires sophisticated methods for estimating the parameters in the model. Usually, the model parameters are estimated by the conventional EM algorithm. The research aims to compare the EM algorithm and the genetic algorithm GA. Using simulation, the two algorithms were compared based on the MSE criterion, with different sample sizes (n = 50, 90, 120) and three scenarios (S1, S2, S3) for default values of the parameters. The results showed the superiority of the GA genetic algorithm over the EM algorithm, as the GA genetic algorithm gave the lowest MSE values. Paper type: Research paper

Modeling agricultural and methane emission data: a finite mixture regression approach

In this paper, the method for unsupervised learning of finite mixture regression (FMR) models is presented for evaluation using agricultural and emissions data sets. The FMR models can be written as problems with incomplete data, and the expectation–maximization (EM) algorithm can be used to estimate unknown variables. The goals of this research are to find the best clustering model with different sets of training and test data and examine the relationship between crop production index and methane emissions in 22 countries from 1990 to 2019 using FMR. In this study also use machine learning process for a FMR model from real world data. According to the findings, the performance of the random training data (RDM) in time series is preferable to that of the fixed training data (FXM). In addition, both RDM and FXM are capable of classifying the 22 countries into two distinct groups and constructing the parameters for the regression model. However, selecting training and test data will result in a good prediction; it is dependent on the data collected. Picking the right training and test data is crucial for accurate predictions-it all comes down to having good data in the first place.

Characteristics and influencing factors of anticipated HIV stigma among HIV-negative/unknown MSM in China: A regression mixture model.

Anticipated HIV stigma among men who have sex with men's (MSM) has a severe negative effect on their physical and mental health wellbeing and hence requires specific attention. The current study aims to identify the characteristics and the psychosocial influencing factors of anticipated HIV stigma in MSM using regression mixture model (RMM) and to determine the cut-off point of the seven-item Anticipated HIV Stigma Questionnaire (AHSQ) using the receiver operating characteristic (ROC) analysis. A cross-sectional study was conducted among HIV-negative/unknown MSM from Blued online platform in China from December 16th, 2020 to March 1st, 2021, enrolling 1394 participants. Data were collected on demographic characteristics, perceived social support, anticipated HIV stigma, depressive symptoms, and HIV knowledge. Latent profile analysis was performed to identify different profiles of anticipated HIV stigma level. Chi-square test, analysis of variance, and RMM analysis were conducted to explore the influencing factors in different profiles. ROC analyses were carried out to identify the cut-off value of anticipated stigma. Among the participants, three profiles of anticipated stigma were identified: "low anticipated HIV stigma" (12.0%), "moderate anticipated HIV stigma" (52.1%), and "severe anticipated HIV stigma" (35.9%). RMM analysis showed that higher income and higher levels of knowledge were positively associated with moderate anticipated HIV stigma, whereas full-time job and social support were negatively associated with moderate anticipated HIV stigma; higher income, depressive symptoms, and knowledge were positively associated with severe anticipated HIV stigma, whereas minor ethnicity and social support were negatively associated with severe anticipated HIV stigma. ROC curve of the AHSQ showed that the optimal cut-off value of ≥16 could indicate positive anticipated HIV stigma. The study focuses on the level of anticipated HIV stigma and its psycho-socio influencing factors among HIV-negative/unknown MSM. It provides evidence for implementing relevant psychological interventions to HIV-negative/unknown MSM.

Estimation Parameters in the fuzzy class Poisson mixture regression model

In the Poisson mixture regression for the fuzzy class model, observations originate from distinct sub-sources or classes due to the problem of heteroscedasticity. The underlying assumption posits that the observed data stem from a finite mixture of fuzzy classes. The primary challenge lies in achieving the optimal assignment of observations to their respective categories, necessitating the utilization of sophisticated methods for parameter estimation within the model. This research paper explores the estimation of parameters in a Poisson mixture regression model designed for the fuzzy class. Leveraging the FCML (Fuzzy Classification Maximum Likelihood algorithm) and genetic algorithm methodologies, we conducted simulations to assess the accuracy and efficacy of parameter estimation. Our findings reveal a clear superiority of the genetic algorithm over the FCML algorithm, as evidenced by the Mean Square Error (MSE) criterion. The genetic algorithm consistently produced lower MSE values, indicating more precise and reliable parameter estimates compared to the FCML algorithm. This research underscores the potential of the genetic algorithm as a robust and effective tool for parameter estimation in complex statistical models, offering researchers an alternative approach for tackling challenges in the estimation of parameters within the context of the fuzzy class

Do natural resources rents reduce income inequality? A finite mixture of regressions approach

The World Bank report (2023) highlights that almost all types of natural capital, the global stock of resources and services provided by nature, are in decline while inequalities persist. Based on this context, the objective of this article is to analyze the effect of natural resources on income inequality in 73 developing countries over the period 2005–2020. Unlike previous works, this article examines the possibility that countries follow different inequality regimes and test the hypothesis that whether natural resources, reduce or increase income inequality depending on the inequality regime to which countries belong. We used a finite mixture regression model, and we found that our sample is best described by a model with five regimes of countries. The results show that the effect of natural resource rents on income inequality varies across five distinct regimes of countries. In regimes 1 and 2, natural resources have a positive effect on inequality, while in regimes 3 and 4, they have a negative effect on inequality. In regime 5, the effect is not significant. Furthermore, our analysis shows that countries that have low levels of political risk are likely to be in the regime where the dependence of natural resources decreases income inequality. These results clearly emphasize that for countries with abundant natural resources to fully benefit from reduced inequality, they must undertake strong reforms to reduce political risk. These reforms include improving the quality of the judicial system, intensifying the fight against corruption, and reducing investment risks.

A Dirichlet process mixture regression model for the analysis of competing risk events

We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud and Dutang (2018). The approach yields an improved predictive performance of the surrending rates.

Gaussian–Poisson Mixture Regression model for defects prediction in steelmaking

In the steelmaking process, real-time prediction of the occurrence of defects is crucial. To this end, a novel Gaussian–Poisson Mixture Regression (GPMR) model is proposed in this work. GPMR utilizes Poisson and Gaussian distributions to describe input process measurements and the count-type output quality variable, respectively. At the same time, inspired by the idea of finite mixture models, the two distributions are further extended into a mixture form to improve the predictive performance of the model, which also fully considers the characteristics of multi-mode and process variation in the steelmaking process. In addition, a parameter learning strategy based on variational inference is designed for the training of GPMR. The application results of a numerical example and an actual steelmaking process demonstrate the effectiveness and superiority of the proposed GPMR method compared to other traditional methods.

Soft Sensor Development for Real-Time Interface Tracking in Multiple Product Pipelines Based on Knowledge and Data

Summary Petroleum products are usually consecutively transported in the same multiple-product pipeline, and the occurrence of mixed oil happens during the process. Accurately tracking the mixed oil interface is essential for the optimal scheduling of oil transportation. However, complicated operating conditions and unavoidable measurement noise pose challenges to methods for locating the interface. The data-driven modeling method is a potential solution, but it may face limitations due to issues of overfitting, especially when the data set is contaminated with noise. To tackle such problems, in this paper, we propose a knowledge-informed Bayesian-Gaussian mixture regression (KIBGMR) model to enable the real-time tracking of the interface. The KIBGMR employs finite Gaussian distribution to learn the multimode characteristics of input data, including the hydrothermal data, measured density of tail oil, and the velocity of interface transportation and output data including the measured density of tail oil and interface transportation velocity. Subsequently, it utilizes the prior knowledge related to the regression coefficient through the Bayesian treatment. Evaluations demonstrate that the R2 index achieved by the proposed model in predicting the interface arrival time is greater than 0.98, even with the contaminated data set. This research can help operators accurately grasp the location of the mixed oil interface, formulate reasonable valve switch operations for better management of the mixed oil section, and provide a reference for the method of knowledge-data hybrid modeling.

Multivariate contaminated normal mixture regression modeling of longitudinal data based on jointmean‐covariancemodel

AbstractOutliers are common in longitudinal data analysis, and the multivariate contaminated normal (MCN) distribution in model‐based clustering is often used to detect outliers and provide robust parameter estimates in each subgroup. In this paper, we propose a method, the mixture of MCN (MCNM), based on the joint mean‐covariance model, specifically designed to analyze longitudinal data characterized by mild outliers. Our model can automatically detect outliers in longitudinal data and provide robust parameter estimates in each subgroup. We use iteratively expectation‐conditional maximization (ECM) algorithm and Aitken acceleration to estimate the model parameters, achieving both algorithm acceleration and stable convergence. Our proposed method simultaneously clusters the population, identifies progression patterns of the mean and covariance structures for different subgroups over time, and detects outliers. To demonstrate the effectiveness of our method, we conduct simulation studies under various cases involving different proportions and degrees of contamination. Additionally, we apply our method to real data on the number of people infected with AIDS in 49 countries or regions from 2001 to 2021. Results show that our proposed method effectively clusters the data based on various mean progression trajectories. In summary, our proposed MCNM based on the joint mean‐covariance model and MCD of covariance matrices provides a robust method for clustering longitudinal data with mild outliers. It effectively detects outliers and identifies progression patterns in different groups over time, making it valuable for various applications in longitudinal data analysis.

Biosensor-Based Multimodal Deep Human Locomotion Decoding via Internet of Healthcare Things.

Multiple Internet of Healthcare Things (IoHT)-based devices have been utilized as sensing methodologies for human locomotion decoding to aid in applications related to e-healthcare. Different measurement conditions affect the daily routine monitoring, including the sensor type, wearing style, data retrieval method, and processing model. Currently, several models are present in this domain that include a variety of techniques for pre-processing, descriptor extraction, and reduction, along with the classification of data captured from multiple sensors. However, such models consisting of multiple subject-based data using different techniques may degrade the accuracy rate of locomotion decoding. Therefore, this study proposes a deep neural network model that not only applies the state-of-the-art Quaternion-based filtration technique for motion and ambient data along with background subtraction and skeleton modeling for video-based data, but also learns important descriptors from novel graph-based representations and Gaussian Markov random-field mechanisms. Due to the non-linear nature of data, these descriptors are further utilized to extract the codebook via the Gaussian mixture regression model. Furthermore, the codebook is provided to the recurrent neural network to classify the activities for the locomotion-decoding system. We show the validity of the proposed model across two publicly available data sampling strategies, namely, the HWU-USP and LARa datasets. The proposed model is significantly improved over previous systems, as it achieved 82.22% and 82.50% for the HWU-USP and LARa datasets, respectively. The proposed IoHT-based locomotion-decoding model is useful for unobtrusive human activity recognition over extended periods in e-healthcare facilities.