Multivariate Finite Mixture Models Research Articles

Association of health, nutrition, and socioeconomic variables with global antimicrobial resistance: a modelling study

Although antimicrobial use is a key selector for antimicrobial resistance, recent studies have suggested that the ecological context in which antimicrobials are used might provide important factors for the prediction of the emergence and spread of antimicrobial resistance. We used 1547 variables from the World Bank dataset consisting of socioeconomic, developmental, health, and nutritional indicators; data from a global sewage-based study on antimicrobial resistance (abundance of antimicrobial resistance genes [ARGs]); and data on antimicrobial usage computed from the ECDC database and the IQVIA database. We characterised and built models predicting the global resistome at an antimicrobial class level. We used a generalised linear mixed-effects model to estimate the association between antimicrobial usage and ARG abundance in the sewage samples; a multivariate random forest model to build predictive models for each antimicrobial resistance class and to select the most important variables for ARG abundance; logistic regression models to test the association between the predicted country-level antimicrobial resistance abundance and the country-level proportion of clinical resistant bacterial isolates; finite mixture models to investigate geographical heterogeneities in the abundance of ARGs; and multivariate finite mixture models with covariates to investigate the effect of heterogeneity in the association between the most important variables and the observed ARG abundance across the different country subgroups. We compared our predictions with available clinical phenotypic data from the SENTRY Antimicrobial Surveillance Program from eight antimicrobial classes and 12 genera from 56 countries. Using antimicrobial use data from between Jan 1, 2016, and Dec 31, 2019, we found that antimicrobial usage was not significantly associated with the global ARG abundance in sewage (p=0·72; incidence rate ratio 1·02 [95% CI 0·92-1·13]), whereas country-specific World Bank's variables explained a large amount of variation. The importance of the World Bank variables differed between antimicrobial classes and countries. Generally, the estimated global ARG abundance was positively associated with the prevalence of clinical phenotypic resistance, with a strong association for bacterial groups in the human gut. The associations between bacterial groups and ARG abundance were positive and significantly different from zero for the aminoglycosides (three of the four of the taxa tested), β-lactam (all the six microbial groups), fluoroquinolones (seven of nine of the microbial groups), glycopeptide (one microbial group tested), folate pathway antagonists (four of five microbial groups), and tetracycline (two of nine microbial groups). Metagenomic analysis of sewage is a robust approach for the surveillance of antimicrobial resistance in pathogens, especially for bacterial groups associated with the human gut. Additional studies on the associations between important socioeconomic, nutritional, and health factors and antimicrobial resistance should consider the variation in these associations between countries and antimicrobial classes. EU Horizon 2020 and Novo Nordisk Foundation.

Multivariate mix-GEE models for longitudinal data with multiple outcomes

Multivariate longitudinal studies often involve two or more outcomes of interest measured repeatedly across time for each subject. A main challenge in the analysis of such data is the complex correlation structure. Appropriate modeling of the covariance matrix can provide more efficient parameter estimators. In this paper, multivariate finite mixture models are built for the working correlation matrix of the generalized estimating equations (GEE). A new procedure is proposed to estimate the parameters while ensuring the positive definiteness of the estimated working correlation matrix. Moreover, the consistency and the asymptotic normality of the parameter estimates are derived theoretically. Furthermore, if data are from a Gaussian mixture model, the estimators can be proved to be asymptotically efficient. In addition, the proposed method is illustrated through several simulation studies and a real data example of transportation safety.

Estimation of the number of components of nonparametric multivariate finite mixture models

We propose a novel estimator for the number of mixture components (denoted by M) in a nonparametric finite mixture model. The setting that we consider is one where the analyst has repeated observations of K≥2 variables that are conditionally independent given a finitely supported latent variable with M support points. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator T that is identified from the data has rank equal to M. We use this observation, in conjunction with the fact that singular values of operators are stable under perturbations, to propose an estimator of M, which essentially consists of a thresholding rule that counts the number of singular values of a consistent estimator of T that are greater than a data-driven threshold. We prove that our estimator of M is consistent, and establish nonasymptotic results, which provide finite sample performance guarantees for our estimator. We present a Monte Carlo study, which shows that our estimator performs well for samples of moderate size.

Unsupervised automated monitoring of dairy cows’ behavior based on Inertial Measurement Unit attached to their back

Automated monitoring of dairy cow behavior based on non-invasive sensors offers a great potential to improve the monitoring processes of its welfare and health in the context of the smart farm. It can detect any changes before the appearance of the clinical signs, allowing the farmer to take necessary measures as soon as possible. The objective of this study is to develop an effective un-supervised classification model of data collected by Inertial Measurement Units (IMU) attached to the back of dairy cows housed in free-stall. These data were aggregated according to different sampling frequencies and segmentation windows. The different times of lying, standing, lying down, standing up, walking and stationary behaviors were observed and recorded in real time. The designed classification model is based on univariate and multivariate Finite Mixture Models (FMM) and decision trees. The valid transitions between standing and lying behaviors are guaranteed by constraints imposed by a deterministic finite state automaton. The obtained results revealed that 99% of behaviors are well classified. Standing, lying on each side and changing between these positions are classified with 100% accuracy, followed by stationary with 99% sensitivity, 96% specificity, 99% precision and 99% accuracy. The walking behavior is classified with 96% sensitivity, 99% specificity, 91% precision and 98% accuracy. These results show that the back is an interesting location for sensors to monitor the dairy cow behavior.

Clustering via finite nonparametric ICA mixture models

We propose an extension of non-parametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. We formulate an objective function in terms of penalized smoothed Kullback Leibler distance and introduce the nonlinear smoothed majorization-minimization independent component analysis (NSMM-ICA) algorithm for optimizing this function and estimating the model parameters. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R package icamix. We illustrate this new methodology using several applications in unsupervised learning and image processing.

Bootstrap estimation and model selection for multivariate normal mixtures using parallel computing with graphics processing units

ABSTRACTIn applications of multivariate finite mixture models, estimating the number of unknown components is often difficult. We propose a bootstrap information criterion, whereby we calculate the expected log-likelihood at maximum a posteriori estimates for model selection. Accurate estimation using the bootstrap requires a large number of bootstrap replicates. We accelerate this computation by employing parallel processing with graphics processing units (GPUs) on the Compute Unified Device Architecture (CUDA) platform. We conducted a runtime comparison of CUDA algorithms between implementation on the GPU and that on a CPU. The results showed significant performance gains in the proposed CUDA algorithms over multithread CPUs.

Theoretical grounding for estimation in conditional independence multivariate finite mixture models

ABSTRACTFor the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalised smoothed Kullback–Leibler distance. The nonlinearly smoothed majorisation-minimisation (NSMM) algorithm is derived from this perspective. An elegant representation of the NSMM algorithm is obtained using a novel projection-multiplication operator, a more precise monotonicity property of the algorithm is discovered, and the existence of a solution to the main optimisation problem is proved for the first time.

Semi-parametric estimation for conditional independence multivariate finite mixture models

The conditional independence assumption for nonparametric multivariate finite mixture models, a weaker form of the well-known conditional independence assumption for random effects models for longitudinal data, is the subject of an increasing number of theoretical and algorithmic developments in the statistical literature. After presenting a survey of this literature, including an in-depth discussion of the all-important identifiability results, this article describes and extends an algorithm for estimation of the parameters in these models. The algorithm works for any number of components in three or more dimensions. It possesses a descent property and can be easily adapted to situations where the data are grouped in blocks of conditionally independent variables. We discuss how to adapt this algorithm to various location-scale models that link component densities, and we even adapt it to a particular class of univariate mixture problems in which the components are assumed symmetric. We give a bandwidth selection procedure for our algorithm. Finally, we demonstrate the effectiveness of our algorithm using a simulation study and two psychometric datasets.

A restricted mixture model for dietary pattern analysis in small samples

Multivariate finite mixture models have been applied to the identification of dietary patterns. These models are known to have many parameters, and consequently large samples are usually required. We present a special case of a multivariate mixture model that reduces the number of parameters to be estimated and seems adequate for small to moderately sized samples. We illustrate our approach with an analysis of Portuguese data from a food-frequency questionnaire and with a simulation study.

Major Habitual Dietary Patterns Are Associated with Acute Myocardial Infarction and Cardiovascular Risk Markers in a Southern European Population

Background Most dietary pattern analyses in southern Europe have relied on a priori food approaches using Mediterranean-style diet indexes. These methods may not reflect the current population's food consumption. Objective To assess the association of a posteriori dietary patterns with acute myocardial infarction (AMI) and cardiovascular risk markers in the general adult population of Porto, Portugal. Design A population-based case-control study was conducted. Information was collected by trained interviewers. Diet was assessed with a validated 82-item food frequency questionnaire. Participants/setting Cases were patients consecutively hospitalized for an incident non-fatal AMI (n=820), and controls were individuals free of previous AMI selected from the hospitals' catchment area (n=2,196). Statistical analyses Dietary patterns, representing mutually exclusive clusters of individuals, were identified by multivariate finite mixture models among controls. Odds ratios (OR) and their 95% confidence intervals (CIs) were obtained from unconditional logistic regression, with adjustment for main confounders. Results In comparison to women with a “healthy” dietary pattern, those with a “low fruit and vegetables” pattern and a “red meat and alcohol” (also characterized by lower intake of dairy products and vegetables) pattern showed a higher risk of AMI (OR 1.85, 95% CI 1.01 to 3.39 and OR 1.91, 95% CI 1.17 to 3.12, respectively). Female controls with the “red meat and alcohol” pattern also had a higher total to high-density lipoprotein cholesterol ratio. In comparison to men with a “healthy” pattern, those with the “red meat and alcohol” pattern, similar to the counterpart found in women, were more likely to experience an AMI (OR 1.98, 95% CI 1.35 to 2.92); male controls with this pattern had higher diastolic and systolic blood pressure, C-reactive protein, and uric acid levels. Conclusions A dietary pattern with lower fruit and vegetable intakes in women, and a pattern characterized by higher consumption of red meat and alcohol (and lower of dairy products and vegetables) in both sexes, were associated with an increased risk of AMI and adverse cardiovascular risk profiles. These findings highlight the importance of sustained recommendations for fruit and vegetable intake and cautious guidance on consumption of alcoholic beverages, which clusters with less healthy dietary patterns of men and women.

Multivariate Poisson Markov-dependent finite mixture models for analysis of weed counts

Multivariate Poisson Markov-dependent finite mixture models for analysis of weed counts

Mixture models for studying stellar populations. II - Multivariate finite mixture models

Multivariate finite mixture models provide a framework for analyzing and interpreting observational data that arise from the overlapping spatial, kinematical, chemical, and age distributions of stellar populations. In this paper the basic properties of multivariate finite mixture distributions are summarized. Particular emphasis is placed on the interpretation of observed overall gradients, and on the distinction between models in which a gradient exists in at least one component and those in which there are no gradients within individual stellar population components. Central to this discussion are posterior mixing proportions, which describe how the mixing proportions for an observed sample of stars vary as functions of metal abundance, age, etc., and conditional mixture distributions, which describe the relationships that exist among the variables