Mixture Regression Research Articles

The world cancer patient population (WCPP): An updated standard for international comparisons of population-based survival

PurposeThis study addresses the need for a global cancer patient-based standard population that adjusts for the expected age structure of different cancers, thus aiding the comparison of survival estimates worldwide. MethodsCounts of age-specific incidence for 36 cancer sites in 185 countries for the year 2018 were extracted from IARC’s GLOBOCAN database of national estimates. We used a multinomial mixture regression to identify clusters of cancer sites with similar age-specific profiles. ResultsAn updated standard entitled the World Cancer Patient Population (WCPP) is presented, derived from the current estimated global numbers of cancer patients that comprises three sets of age-specific weights. Around two-thirds of cancer sites were described by a unique standard, representing the majority of epithelial cancers more often diagnosed at older age groups. The two other standards represent a number of non-epithelial cancer types, and cancers common at younger and older age groups, respectively. ConclusionThe WCPP proposed here provides a contemporary and global means to estimate age-standardised survival for international benchmarking purposes.

Is Autonomy Always Beneficial for Work Engagement? A Six-year Four-Wave Follow-Up Study.

Work engagement is expected to result from job resources such as autonomy. However, previous results have yielded that the autonomy–work engagement relationship is not always particularly strong. Whereas previous longitudinal studies have examined this relationship as an average at a specific point in time, this study examined whether this relationship is different within individuals from one time to another over the years. Furthermore, experiences of work engagement are expected to affect how employees benefit from autonomy, but no studies have so far investigated whether the initial level of work engagement affects the autonomy–work engagement relationship. This study aimed to first identify the different kinds of longitudinal relationship patterns between autonomy and work engagement, and then to investigate whether the identified relationship patterns differ in terms of the initial mean level of work engagement. The four-wave study was conducted among Finnish managers (n = 329) over a period of six years. Multilevel regression mixture analysis identified five relationship patterns. Four of the patterns showed a positive predictive relationship between autonomy and work engagement. However, the relationship was statistically significant in only one of these patterns. Furthermore, when the initial mean level of work engagement was high, autonomy related more strongly to work engagement. However, an atypical pattern was identified that showed a negative association between autonomy and work engagement. In this pattern, the mean level of work engagement was low. Consequently, autonomy may not always enhance work engagement; sometimes this relationship may even be negative.

Joint model for longitudinal mixture of normal and zero-inflated power series correlated responses Abbreviated title:mixture of normal and zero-inflated power series random-effects model

ABSTRACT In this paper, a joint model is presented for analyzing longitudinal continuous and count mixed responses. The frequency distribution of continuous longitudinal response variable for each subject at any time has a skewed and or multi-modal form. Then, a suitable finite mixture of normals is used as its distribution. It seems that the continuous response comes from several distinct sub-populations. The number of zeros of the count response is inflated. Also, a zero-inflated power series (ZIPS) distribution is applied as its distribution in order to model the count response. The correlation of longitudinal responses through time and that of mixed continuous and count responses are modeled by utilizing the random-effects vectors in the finite mixtures of regression (FMR) models. Further, a full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. Then, some simulation studies are performed for assessing the performance of the model. Additionally, an application is illustrated for joint analysis of the number of days during the last month that the individual drank alcohol, as well as the respondents’ weight. Finally, the two first times of the Americans Changing Lives survey are evaluated.

Regression with Gaussian Mixture ModelsApplied to Track Fitting

This note describes the application of Gaussian mixture regression to track fitting with a Gaussian mixture model of the position errors. The mixture model is assumed to have two components with identical component means. Under the premise that the association of each measurement to a specific mixture component is known, the Gaussian mixture regression is shown to have consistently better resolution than weighted linear regression with equivalent homoskedastic errors. The improvement that can be achieved is systematically investigated over a wide range of mixture distributions. The results confirm that with constant homoskedastic variance the gain is larger for larger mixture weight of the narrow component and for smaller ratio of the width of the narrow component and the width of the wide component.

Efficient Insertion Control for Precision Assembly Based on Demonstration Learning and Reinforcement Learning

Multiple peg-in-hole insertion control is one of the challenging tasks in precision assembly for its complex contact dynamics. In this article, an insertion policy learning method is proposed for multiple peg-in-hole precision assembly. The insertion policy learning process is separated into two phases: initial policy learning and residual policy learning. In initial policy learning, a state-to-action policy mapping model based on the Gaussian mixture model (GMM) is established. And Gaussian mixture regression (GMR) is used to generalize the policy reuse. In residual policy learning, a reinforcement learning method named normalized advantage function (NAF) is employed to refine the insertion policy via agent's exploration in the insertion environment. Moreover, an adaptive action exploration (AAE) strategy is designed to improve the performance of exploration, and the prioritized experience replay strategy is introduced to make the residual policy learning from historical experience more efficient. Besides, the hierarchical reward function is designed considering the contact dynamics as well as the efficiency and safety of precision insertion. Finally, comprehensive experiments are conducted to validate the effectiveness of the proposed insertion policy learning method.

Generalized finite mixture of multivariate regressions with applications to therapeutic biomarker identification.

Finite mixtures of regressions have been used to analyze data that come from a heterogeneous population. When more than one response is observed, accommodating a multivariate response can be useful. In this article, we go a step further and introduce a multivariate extension that includes a latent overlapping cluster indicator variable that allows for potential overdispersion. A generalized mixture of multivariate regressions in connection with the proposed model and a new EM algorithm for fitting are provided. In addition, we allow for high-dimensional predictors via shrinkage estimation. This model proves particularly useful in the analysis of complex data like the search for cancer therapeutic biomarkers. We demonstrate this using the genomics of drug sensitivity in cancer resource.

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.

A Bayesian mixture of experts approach to covariate misclassification

AbstractThis article considers misclassification of categorical covariates in the context of regression analysis; if unaccounted for, such errors usually result in mis‐estimation of model parameters. With the presence of additional covariates, we exploit the fact that explicitly modelling non‐differential misclassification with respect to the response leads to a mixture regression representation. Under the framework of mixture of experts, we enable the reclassification probabilities to vary with other covariates, a situation commonly caused by misclassification that is differential on certain covariates and/or by dependence between the misclassified and additional covariates. Using Bayesian inference, the mixture approach combines learning from data with external information on the magnitude of errors when it is available. In addition to proving the theoretical identifiability of the mixture of experts approach, we study the amount of efficiency loss resulting from covariate misclassification and the usefulness of external information in mitigating such loss. The method is applied to adjust for misclassification on self‐reported cocaine use in the Longitudinal Studies of HIV‐Associated Lung Infections and Complications.

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.

Semiparametric mixture regression with unspecified error distributions

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal assumption is violated. To relax the normal assumption on the error distribution hence reduce the modeling bias, we propose semiparametric mixture of linear regression models with unspecified error distributions. We establish a more general identifiability result under weaker conditions than existing results, construct a class of new estimators, and establish their asymptotic properties. These asymptotic results also apply to many existing semiparametric mixture regression estimators whose asymptotic properties have remained unknown due to the inherent difficulties in obtaining them. Using simulation studies, we demonstrate the superiority of the proposed estimators over the MLE when the normal error assumption is violated and the comparability when the error is normal. Analysis of a newly collected Equine Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness of the new estimator.

An Enhanced Robot Massage System in Smart Homes Using Force Sensing and a Dynamic Movement Primitive.

With requirements to improve life quality, smart homes, and healthcare have gradually become a future lifestyle. In particular, service robots with human behavioral sensing for private or personal use in the home have attracted a lot of research attention thanks to their advantages in relieving high labor costs and the fatigue of human assistance. In this paper, a novel force-sensing- and robotic learning algorithm-based teaching interface for robot massaging has been proposed. For the teaching purposes, a human operator physically holds the end-effector of the robot to perform the demonstration. At this stage, the end position data are outputted and sent to be segmented via the Finite Difference (FD) method. A Dynamic Movement Primitive (DMP) is utilized to model and generalize the human-like movements. In order to learn from multiple demonstrations, Dynamic Time Warping (DTW) is used for the preprocessing of the data recorded on the robot platform, and a Gaussian Mixture Model (GMM) is employed for the evaluation of DMP to generate multiple patterns after the completion of the teaching process. After that, a Gaussian Mixture Regression (GMR) algorithm is applied to generate a synthesized trajectory to minimize position errors. Then a hybrid position/force controller is integrated to track the desired trajectory in the task space while considering the safety of human-robot interaction. The validation of our proposed method has been performed and proved by conducting massage tasks on a KUKA LBR iiwa robot platform.

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.

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.

The Pitman–Yor multinomial process for mixture modelling

SummaryDiscrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features, such as in clustering, mixtures and curve fitting. They are effective and well-developed tools, though their infinite dimensionality is unsuited to some applications. If one restricts to a finite-dimensional simplex, very little is known beyond the traditional Dirichlet multinomial process, which is mainly motivated by conjugacy. This paper introduces an alternative based on the Pitman–Yor process, which provides greater flexibility while preserving analytical tractability. Urn schemes and posterior characterizations are obtained in closed form, leading to exact sampling methods. In addition, the proposed approach can be used to accurately approximate the infinite-dimensional Pitman–Yor process, yielding improvements over existing truncation-based approaches. An application to convex mixture regression for quantitative risk assessment illustrates the theoretical results and compares our approach with existing methods.