Mixture Regression Model Research Articles

The status of perceived community resilience in transitional rural society: An empirical study from central China

Abstract During China's recent social transition, rural communities have experienced rapid changes in resources, organizational structure, and governance due to urbanization, rural industrialization, and rural-urban migration. How these communities react to social adversity and uncertainty can be assessed with an index of perceived community resilience. Using a Chinese version of the perceived community resilience scale, we analyze data from a multilevel survey of two rural counties in central China. Latent profile analysis and a multilevel regression mixture model are employed to classify community resilience and to explore how the social-ecological system influences this classification. Community resilience is classified into “autonomous community”, “cooperative community”, and “authoritative community”, and we find the proportion of cooperative communities to be the highest and the proportion of autonomous communities is lowest. These results suggest that cooperation among rural residents in rural communities is increasing. How rural residents perceive community resilience is based on their individual features, which reflect the impacts of recent social changes on livelihoods. Socio-ecological variables, including geographical features, financial status, social networks, and traditional culture, have significant effects on the categories of community resilience. In today's China, rural residents have decreased their dependence on rural leaders and increased cooperation at the community level. Some autonomous communities may be unsustainable as they are populated mainly by the elderly and have insufficient resources to be adaptable.

Targeted design for adaptive clinical trials via semiparametric model

Precision medicine approach that assigns treatment according to an individual's personal (including molecular) profile is revolutionizing health care. Existing statistical methods for clinical trial design typically assume a known model to estimate characteristics of treatment outcomes, which may yield biased results if the true model deviates far from the assumed one. This article aims to achieve model robustness in a phase II multi-stage adaptive clinical trial design. We propose and study a semiparametric regression mixture model in which the mixing proportions are specified according to the subjects' profiles, and each sub-group distribution is only assumed to be unimodal for robustness. The regression parameters and the error density functions are estimated by semiparametric maximum likelihood and isotonic regression estimators. The asymptotic properties of the estimates are studied. Simulation studies are conducted to evaluate the performance of the method after a real data analysis.

Identifying heterogeneity in the risk factors of dental caries status in Chinese adolescents using Poisson mixture regression

ObjectiveThe purpose of this study was to cluster individuals into groups with different dental health characteristics and make statistical inferences on the effect differences among different groups simultaneously to identify...

Hierarchical mixture-of-experts models for count variables with excessive zeros

We propose a tree-structured hierarchical architecture for estimating count variables that exhibit both excessive zeros and over-dispersion, which is commonly observed in practice. The underlying statistical model is based on the Mixture-of-experts (MoE) model, a generalization of finite mixture regression models. With two levels of experts, the proposed model can efficiently model both excessive zeros and the long right-tail, controlled by two gating networks at different levels in the hierarchy. We develop the general form of the maximum likelihood estimator for the proposed model based on the EM algorithm with two latent variables, which allows a natural interpretation and convenient optimization for the likelihood function. As a numerical application, we apply the proposed model to a well-known real dataset and found that it shows superior performance and allows better interpretations compared to other existing alternatives.

Adaptive Segmentation and Sequence Learning of human activities from skeleton data

Discovering underlying patterns for predicting future actions from spatio-temporal human activity information is a fundamental component of research related to the development of expert systems in human activity recognition and assistive robotics. Current research focuses on classification or learning representations of activities for various applications. However, not much attention is given to the pattern discovery of activities which have a major role in the prediction of unseen actions. This paper proposes a novel Adaptive Segmentation and Sequence Learning (ASSL) framework which aims at segmenting unlabelled observations of human activities from extracted 3D joint information. Learning from these obtained segments provides information about the underlying patterns of activity sequences needed in predicting subsequent actions. In the proposed method, the temporal accumulated motion energy of body parts in an activity is utilised in the segmentation process to obtain key actions from unlabelled activity sequences since body parts show changes in acceleration and deceleration during an activity. Based on the segments obtained, the temporal sequence of transitions across activity segments are learned by employing a Long Short-Term Memory Recurrent Neural Network. This ASSL technique has been evaluated using both an experimental human activity dataset and a public activity dataset, and achieved a better performance when compared with other techniques including an Auto-regressive Integrated Moving Average, Support Vector Regression and Gaussian Mixture Regression Models in learning to predict patterns of activity sequences.

Health-related quality of life and opioid use disorder pharmacotherapy: A secondary analysis of a clinical trial

ObjectiveTo examine the health-related quality-of-life (HRQoL) of persons with opioid use disorder (OUD) seeking treatment in an inpatient detoxification or short-term residential setting; continuing treatment as outpatients. MethodsWe conducted a secondary analysis of data from a clinical trial (N = 508) where participants were randomized to extended-release naltrexone or buprenorphine-naloxone for the prevention of opioid relapse. We used a generalized structural equation regression mixture model to identify associations of HRQoL (EQ-5D) trajectories, including latent characteristics, over the 24-week trial and 36-week follow-up period, among participants who reported HRQoL beyond baseline. This novel framework accounted for baseline and time-varying characteristics, while simultaneously identifying latent classes. ResultsWe identified two subpopulations: HRQoL "pharmacotherapy responsive" (82.3 %) and HRQoL "characteristic sensitive" (17.7 %). The pharmacotherapy responsive subpopulation was characterized by a shortterm HRQoL improvement and then stable HRQoL over time, and by a positive association between HRQoL and receiving pharmacotherapy in the past 30 days. The characteristic sensitive subpopulation was characterized by an initial improvement in HRQoL with a gradual decline over time, and no significant HRQoL response to pharmacotherapy. HRQoL changes over time in this subpopulation were more influenced by baseline demographic, socioeconomic, and psychosocial characteristics. ConclusionOur findings suggest that while HRQoL may be improved and sustained through targeted efforts to promote use of pharmacotherapy for many persons with OUD, an identifiable subpopulation may require additional services that address socioeconomic and psychosocial issues to achieve HRQoL benefits. Our analysis provides insight for improving individualized care for persons with opioid use disorder seeking treatment.

Use of Multiensemble Track Clustering to Inform Medium-Range Tropical Cyclone Forecasts

AbstractTropical cyclone ensemble track forecasts from 153 initialization times during 2017–18 are clustered using regression mixture models. Clustering is performed on a four-ensemble dataset [ECMWF + GEFS + UKMET + CMC (EGUC)], and a three-ensemble dataset that excludes the CMC (EGU). For both datasets, five-cluster partitions are selected to analyze, and the relationship between cluster properties (size, ensemble composition) and 96–144-h cluster-mean error is evaluated. For both datasets, small clusters produce very large errors, with the least populous cluster producing the largest error in more than 50% of forecasts. The mean of the most populous EGUC cluster outperforms the most accurate (EGU) ensemble mean in only 43% of forecasts; however, when the most populous EGUC cluster from each forecast contains ≥30% of the ensemble population, its average cluster-mean error is significantly reduced compared to when the most populous cluster is smaller. Forecasts with a highly populous EGUC cluster also appear to have smaller EGUC-, EGU-, and ECMWF-mean errors. Cluster-mean errors also vary substantially by the ensembles composing the cluster. The most accurate clusters are EGUC clusters that contain threshold memberships of ECMWF, GEFS, and UKMET, but not CMC. The elevated accuracy of EGUC CMC-excluding clusters indicates the potential utility of including the CMC in clustering, despite its large ensemble-mean errors. Pruning ensembles by removing members that belong to small clusters reduces 96–144-h forecast errors for both EGUC and EGU clustering. For five-cluster partitions, a pruning threshold of 10% affects 49% and 35% of EGUC and EGU ensembles, respectively, improving 69%–74% of the forecasts affected by pruning.

On a new mixture-based regression model: simulation and application to data with high censoring

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for the continuous response variable of interest, whereas the Bernoulli distribution is used for the point mass of the censoring observations. We estimate the corresponding parameters with the maximum likelihood method. Numerical evaluation of the model is performed by means of Monte Carlo simulations and of an illustration with real data. The results show the good performance of the proposed model, making it an addition to the tool-kit of biometricians, medical doctors, applied statisticians, and data scientists.

A spatial mixed-effects regression model for electoral data

On 4th March 2018, elections took place in Italy for the two Chambers of the Parliament. Many newspapers emphasized the victory of the 5 Star Movement (5SM) and its unprecedented dominance in most of the southern regions of Italy. Aim of this contribution is to analyze the electoral results through an ad hoc statistical model to evaluate the presence and possible impact of spatial structures. The response variable is the percentage of votes got by the 5SM in each electoral district. To handle a bounded continuous outcome with values in the open interval (0, 1), a mixture regression model is used. This model is based on a special mixture of two betas (referred to as flexible beta) sharing the same precision parameter, but displaying two distinct component means subject to an inequality constraint. Advantages of this model are its many theoretical properties which are reflected in its computational tractability. Furthermore, the special mixture structure is designed to represent a wide range of phenomena (bimodality, heavy tails, and outliers). The model is further extended through random effects to account for spatial correlation. Intensive simulation studies are performed to evaluate the fit of the proposed regression model. Inferential issues are dealt with by a (Bayesian) Hamiltonian Monte Carlo algorithm.

Least squares moment identification of binary regression mixture models

We consider finite mixtures of generalized linear models with binary output. We prove that cross moments (between the output and the regression variables) up to order three are sufficient to identify all parameters of the model. We propose a least-squares estimation method based on those moments and we prove the consistency and the Gaussian asymptotic behavior of the estimator. We provide simulation results and comparisons with likelihood methods. Numerical experiments were conducted using the R-package morpheus that we developed for our least-squares moment method and with the R-package flexmix for likelihood methods. We then give some possible extensions to finite mixtures of regressions with binary output including both continuous and categorical covariates, and possibly longitudinal data.

Optimal-robust selection of a fuel surrogate for homogeneous charge compression ignition modeling

Homogeneous Charge Compression Ignition (HCCI) combustion is a potential candidate for dealing with the stringent regulations on vehicle emissions while still providing very good energy efficiency. Despite the promising results obtained in preliminary studies, the lack of autoignition control has delayed its launch in the engine industry. In the development of the HCCI concept, the availability of reliable computer models has proved extremely valuable, due to their flexibility and lower cost compared with experiments using real engines. In order to obtain the best formulation of a fuel surrogate formulated with n-heptane, toluene and cyclohexane that efficiently estimate the autoignition behaviour, regression adjustments are made to the Root-Mean-Square Errors (RMSE) of experimental Starts of Combustion (SOC) from the modeled SOC. The canonical form of the Scheffé polynomials is widely used to fit the data from mixture experiments, however the experimenter might have only partial knowledge. In this paper we present the adaptation of the robust methodology for possibly misspecified blending model and an algorithm to obtain tailor-made optimal designs for mixture experiments, instead of using standard designs which are indiscriminately employed, to make good estimations of the parameters blending model. We maximize the determinant of the mean squared error matrix of the least square estimator over a realistic neighbourhood of the fitted regression mixture model. The maximized determinant is then minimized over the class of possible designs, yielding an optimal design. Thus, the computed desings are robust to the exact form of the true blending model. Standard mixture designs, as the simplex lattice, are around 25% efficient for estimation purposes compared with the designs obtained in this work when deviances from the considered model occur during the experiments. Once an optimal-robust design was selected (based on the level of certainty about model adequacy), we computed the optimal mixture that best reproduces the combustion property to be imitated. Optimal mixtures obtained when the considered model is inadequate agree with the results achieved in empirical studies, which validates the methodology proposed in this work.

Parenting behaviors and child psychopathy: A regression mixture analysis

The current study examined the associations between the profile of parenting behaviors and child psychopathy using a person-centered approach. Regression mixture modeling (RMM) was employed to explore the predictive ability of parenting behavior profiles on child psychopathy in a sample (N = 361, 51.9 % female) of 9 to 13-year-old Chinese children (M = 10.42, SD = 0.94). Results demonstrated that two subgroups were identified which best characterized the mother-reported parenting behaviors (positive 40%, negative 60%) and three subtypes were identified to characterize the father-reported parenting behaviors (positive 20%, negative 18%, mixture 62%). Children with a higher level of psychopathic traits were more often subjected to the negative parenting behavior profile than they were to positive or mixture parenting behavior profiles. The findings of this study advance the understanding of different parenting behaviors in predicting child psychopathy in non-Western cultural context. We also discuss the implications these findings have for clinicians working to decrease the risk of children psychopathy.

Estimation and inference for mixture of partially linear additive models

In this paper, a semiparametric mixture of regression models is proposed, where the regression functions are partially linear additive while the mixing proportions and variances are unknown constant. The asymptotic normality of the SBK estimators and the model selection consistency of the proposed BIC based on B-spline estimators are established. Simulations and applications are presented to illustrate the performance of the proposed.

Self-assessed life expectancy among older adults in C\xf4te d\u2019Ivoire

BackgroundThe purpose of this study was to estimate individuals’ expected longevity based on self-assessed survival probabilities and determine the predictors of such subjective life expectancy in a sample of elderly people (50 years and older) in Côte d’Ivoire.MethodsPaper-based questionnaires were administered to a sample (n = 267) of older adults residing in the city of Dabou, Côte d’Ivoire in May 2017. Information on subjective expectations regarding health, comorbidities, and self-assessed survival probabilities was collected. We estimated self-assessed life expectancy and its determinants using a two-pronged approach by: (i) estimating individuals’ life expectancy using the self-assessed survival probabilities (SSPs), and (ii) applying a finite mixture of regression models to form homogenous groups of individuals (clusters/components) and investigate the determinants.A spline-based approach was used to estimate the overall distribution of life expectancy for each individual using two to four points of self-assessed survival probabilities. A finite mixture of regression models was used to identify homogeneous groups of individuals (i.e. clusters/components) of the overall subjective life expectancy distribution of the study participants.ResultsThe mean subjective life expectancy in older people varied according to four components/clusters. The average subjective life expectancy among the elderly was 79.51, 78.89, 80.02, and 77.79 years in the first, second, third, and fourth component of the subjects’ overall subjective life expectancy, respectively. The effect of sociodemographic characteristics, comorbidities, and lifestyle on subjective life expectancy varied across components. For instance, a U-shape relationship between household per capita income and subjective life expectancy was found for individuals classified into the third component, and an inverse U-shape relationship was found for individuals classified into the fourth component.ConclusionsWe extended the estimation of subjective life expectancy by accounting for heterogeneity in the distribution of the estimated subjective life expectancy. This approach improved the usual methods for estimating individual subjective life expectancies and may provide insight into the elderly’s perception of aging, which could be used to forecast the demand for health services and long-term care needs.

Semiparametric Mixture of Regression Models Under Unimodal Error Distribution

A semiparametric model has the advantage of being more robust than a parametric model and more efficient than a nonparametric model. In this paper, a semiparametric regression mixture model, in which the regression coefficients are specified to be parametric and the common sub-distribution is nonparametric, is proposed and studied. For parameter identifiability, the sub-distribution is assumed to be unimodal. The symmetry condition is also considered, and it is shown that it can be used to reduce estimation variability. The semiparametric maximum likelihood method is used to estimate the model parameters. The estimators are shown to be strongly consistent, the convergence rate is derived, and a weak convergence of the estimated density is established with a rate of $$n^{1/3}$$ and a Chernoff-type weak limit. Simulation studies are conducted to evaluate the performance of the proposed method, and then, the method is applied to analyze a real data.

Semiparametric mixtures of regressions with single-index for model based clustering

In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified EM algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

Dealing with highly skewed hospital length of stay distributions: The use of Gamma mixture models to study delivery hospitalizations.

The increased focus on addressing severe maternal morbidity and maternal mortality has led to studies investigating patient and hospital characteristics associated with longer hospital stays. Length of stay (LOS) for delivery hospitalizations has a strongly skewed distribution with the vast majority of LOS lasting two to three days in the United States. Prior studies typically focused on common LOSs and dealt with the long LOS distribution tail in ways to fit conventional statistical analyses (e.g., log transformation, trimming). This study demonstrates the use of Gamma mixture models to analyze the skewed LOS distribution. Gamma mixture models are flexible and, do not require data transformation or removal of outliers to accommodate many outcome distribution shapes, these models allow for the analysis of patients staying in the hospital for a longer time, which often includes those women experiencing worse outcomes. Random effects are included in the model to account for patients being treated within the same hospitals. Further, the role and influence of differing placements of covariates on the results is discussed in the context of distinct model specifications of the Gamma mixture regression model. The application of these models shows that they are robust to the placement of covariates and random effects. Using New York State data, the models showed that longer LOS for childbirth hospitalizations were more common in hospitals designated to accept more complicated deliveries, across hospital types, and among Black women. Primary insurance also was associated with LOS. Substantial variation between hospitals suggests the need to investigate protocols to standardize evidence-based medical care.

Optimization of a fruit juice cocktail containing soursop, pineapple, orange and mango using mixture design

A simplex lattice mixture design was used to optimize the formulation of a juice cocktail containing soursop, pineapple, mango and orange, based on physicochemical and sensory attributes of the cocktail. In this study, juice from soursop, pineapple, mango and orange were the components. Physicochemical and sensory parameters were determined using standard methods. Mixture regression models explained up to 99% of the variability in the experimental data. Cox response trace plots generated from the fitted models indicated that pH of the cocktail (ranging from 4.0 to 4.2) was greatly influenced by orange, pineapple and soursop. Increasing amounts of soursop juice resulted in a reduction in °Brix and b* value, which indicates yellowness. Whereas taste of the cocktail was positively influenced by all the components, only extreme amounts of soursop or high amounts of either pineapple or mango enhanced product likeness. Results of the optimization indicated that high amounts of pineapple juice is required to achieve the best cocktail containing these four fruit components. The study demonstrates the potential of utilizing soursop in a juice cocktail together with popular tropical fruits.

Mapping Dermatology Life Quality Index (DLQI) scores to EQ-5D utility scores using data of patients with atopic dermatitis from the National Health and Wellness Study

PurposeTo develop a mapping algorithm for generating EQ-5D-5-level (EQ-5D-5L) utility scores from the Dermatology Life Quality Index (DLQI) in patients with atopic dermatitis (AD).MethodsThe algorithm was developed using data from 1232 patients from four countries participating in the National Health and Wellness Study. Spearman’s rank correlation coefficient was used to evaluate the conceptual overlap between DLQI and EQ-5D-5L. Six mapping models (ordinary least squares [OLS], Tobit, three different two-part models, and a regression mixture model) were tested with different specifications to determine model performance and were ranked based on the sum of mean absolute error (MAE), and root mean squared error (RMSE).ResultsThe mean DLQI score was 7.23; mean EQ-5D-5L score was 0.78; and there were moderate negative correlations between DLQI and EQ-5D-5L scores (p = − 0.514). A regression mixture model with total DLQI, and age and sex as independent variables performed best for mapping DLQI to EQ-5D-5L (RMSE = 0.113; MAE = 0.079).ConclusionThis was the first study to map DLQI to EQ-5D-5L exclusively in patients with AD. The regression mixture model with total DLQI, and age and sex as independent variables was the best performing model and accurately predicted EQ-5D-5L. The results of this mapping can be used to translate DLQI data from clinical studies to health state utility values in economic evaluations.

DETERMINATION OF THE FACTORS AFFECTING STUDENTS’ SCIENCE ACHIEVEMENT LEVEL IN TURKEY AND SINGAPORE: AN APPLICATION OF QUANTILE REGRESSION MIXTURE MODEL

In the last decade, the usage of advanced statistical models is growing rapidly in many different disciplines. However, the Quantile Regression Mixture Model (QRMIX), which is a developed approach of the Finite Mixture Model (FMM), is an applicable new method in the educational literature. The aim of the proposed study was to determine factors affecting students' science achievement using the QRMIX approach. To reach this aim, data of the Programme for International Student Assessment (PISA) survey, which has been conducted by the Organization Economic for Co-Operation and Development (OECD) every 3 years, was used. Dataset used in the research is composed of 6,115 students from Singapore, which is the top-performer country among the participant countries, and 5,895 students from Turkey. The results showed that the factors affecting students' science achievement and its importance on the achievement differentiated according to the achievement levels of the students. In conclusion, it was revealed that Turkish students with the lowest science achievement level should be supported with home possessions, perceived feedback, and environmental awareness and Singaporean students with the lowest achievement level should be supported with perceived feedback, enjoyment of science, and epistemological beliefs. Keywords: finite mixture models, Programme for International Student Assessment, quantile regression mixture models, science performance.