Maximum Likelihood Estimation and Model Comparison for Mixtures of Structural Equation Models with Ignorable Missing Data

The objective of this paper is to develop the maximum likelihood approach for analyzing a finite mixture of structural equation models with missing data that are missing at random. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates. A well-known statistic in model comparison, namely the Bayesian Information Criterion (BIC), is used for model comparison. With the presence of missing data, the computation of the observed-data likelihood function value involved in the BIC is not straightforward. A procedure based on path sampling is developed to compute this function value. It is shown by means of simulation studies that ignoring the incomplete data with missing entries gives less accurate ML estimates. An illustrative real example is also presented.     

A maximum likelihood methodology for clusterwise linear regression

This paper presents a conditional mixture, maximum likelihood methodology for performing clusterwise linear regression. This new methodology simultaneously estimates separate regression functions and membership inK clusters or groups. A review of related procedures is discussed with an associated critique. The conditional mixture, maximum likelihood methodology is introduced together with the E-M algorithm utilized for parameter estimation. A Monte Carlo analysis is performed via a fractional factorial design to examine the performance of the procedure. Next, a marketing application is presented concerning the evaluations of trade show performance by senior marketing executives. Finally, other potential applications and directions for future research are identified.     

A mixture likelihood approach for generalized linear models

A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.     

Finite Mixture Modeling of Gaussian Regression Time Series with Application to Dendrochronology

Finite mixture modeling is a popular statistical technique capable of accounting for various shapes in data. One popular application of mixture models is model-based clustering. This paper considers the problem of clustering regression autoregressive moving average time series. Two novel estimation procedures for the considered framework are developed. The first one yields the conditional maximum likelihood estimates which can be used in cases when the length of times series is substantial. Simple analytical expressions make fast parameter estimation possible. The second method incorporates the Kalman filter and yields the exact maximum likelihood estimates. The procedure for assessing variability in obtained estimates is discussed. We also show that the Bayesian information criterion can be successfully used to choose the optimal number of mixture components and correctly assess time series orders. The performance of the developed methodology is evaluated on simulation studies. An application to the analysis of tree ring data is thoroughly considered. The results are very promising as the proposed approach overcomes the limitations of other methods developed so far.     

Large-sample results for optimization-based clustering methods

Many common (nonhierarchical) clustering and classification methods are optimization-based methods, in the sense described by Windham (1987) in this Journal. This paper gives some large sample properties for estimates derived by such methods. Under appropriate conditions, such estimates converge with probability one to a limit, and are asymptotically normally distributed around that limiting value. The conditions are satisfied by most of the common examples of optimization-based methods. Prepared for the 2nd International Conference, International Federation of Classification Societies, Charlottesville, VA, 1989. Supported in part by summer research funds, Graduate School of Business Administration, University of Colorado at Denver.     

Metric inference for social networks

Using a natural metric on the space of networks, we define a probability measure for network-valued random variables. This measure is indexed by two parameters, which are interpretable as a location parameter and a dispersion parameter. From this structure, one can develop maximum likelihood estimates, hypothesis tests and confidence regions, all in the context of independent and identically distributed networks. The value of this perspective is illustrated through application to portions of the friedship cognitive social structure data gathered by Krackhardt (1987).We thank Ove Frank, David Krackhardt, the editor and the referees for their constructive comments and suggestions.     

Power and Sample Size Computation for Wald Tests in Latent Class Models

Latent class (LC) analysis is used by social, behavioral, and medical science researchers among others as a tool for clustering (or unsupervised classification) with categorical response variables, for analyzing the agreement between multiple raters, for evaluating the sensitivity and specificity of diagnostic tests in the absence of a gold standard, and for modeling heterogeneity in developmental trajectories. Despite the increased popularity of LC analysis, little is known about statistical power and required sample size in LC modeling. This paper shows how to perform power and sample size computations in LC models using Wald tests for the parameters describing association between the categorical latent variable and the response variables. Moreover, the design factors affecting the statistical power of these Wald tests are studied. More specifically, we show how design factors which are specific for LC analysis, such as the number of classes, the class proportions, and the number of response variables, affect the information matrix. The proposed power computation approach is illustrated using realistic scenarios for the design factors. A simulation study conducted to assess the performance of the proposed power analysis procedure shows that it performs well in all situations one may encounter in practice.     

A latent class procedure for the structural analysis of two-way compositional data

This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.     

Complexity and Context-Dependency

It is argued that given the “anti-anthropomorphic” principle—that the universe is not structured for our benefit—modelling trade-offs will necessarily mean that many of our models will be context-specific. It is argued that context-specificity is not the same as relativism. The “context heuristic”—that of dividing processing into rich, fuzzy context-recognition and crisp, conscious reasoning and learning—is outlined. The consequences of accepting the impact of this human heuristic in the light of the necessity of accepting context-specificity in our modelling of complex systems is examined. In particular the development of “islands” or related model clusters rather than over-arching laws and theories. It is suggested that by accepting and dealing with context (rather than ignoring it) we can push the boundaries of science a little further.     

对工程进步中合规律性的探讨

工程合理性是对工程进步的本质和规律的评价。其中,将工程合理性表征为不充足理由律的认识在工程研究领域中具有重要影响。尽管这一认识揭示了工程合目的性的内涵,但它所具有的相对主义特征的建构论,造成了人们对工程合理性的片面认识,即忽视了工程合理性是合目的性和合规律性的统一。武钢和鞍钢连铸工艺的实践过程表明,工程合规律性是构成工程合理性中不容忽视的重要内容,它具体包括历史传承有序的依赖性,工序整体关联的依赖性,生产效率优先的依赖性和工序主客同一的依赖性等。对工程合理性的跨学科研究包括工程哲学、工程管理、工程科学与工程实践等,应当成为工程研究的重要途径。     

Dimensionally Reduced Model-Based Clustering Through Mixtures of Factor Mixture Analyzers

Dimensionally reduced model-based clustering methods are recently receiving a wide interest in statistics as a tool for performing simultaneously clustering and dimension reduction through one or more latent variables. Among these, Mixtures of Factor Analyzers assume that, within each component, the data are generated according to a factor model, thus reducing the number of parameters on which the covariance matrices depend. In Factor Mixture Analysis clustering is performed through the factors of an ordinary factor analysis which are jointly modelled by a Gaussian mixture. The two approaches differ in genesis, parameterization and consequently clustering performance. In this work we propose a model which extends and combines them. The proposed Mixtures of Factor Mixture Analyzers provide a unified class of dimensionally reduced mixture models which includes the previous ones as special cases and could offer a powerful tool for modelling non-Gaussian latent variables.     

Estimating the Cluster Tree of a Density by Analyzing the Minimal Spanning Tree of a Sample

runt pruning , a new clustering method that attempts to find modes of a density by analyzing the minimal spanning tree of a sample. The method exploits the connection between the minimal spanning tree and nearest neighbor density (e.g. normal mixture) or about the geometric shapes of the clusters, and is computationally feasible for large data sets.     

Functional PCA and Base-Line Logit Models

In many statistical applications data are curves measured as functions of a continuous parameter as time. Despite of their functional nature and due to discrete-time observation, these type of data are usually analyzed with multivariate statistical methods that do not take into account the high correlation between observations of a single curve at nearby time points. Functional data analysis methodologies have been developed to solve these type of problems. In order to predict the class membership (multi-category response variable) associated to an observed curve (functional data), a functional generalized logit model is proposed. Base-line category logit formulations will be considered and their estimation based on basis expansions of the sample curves of the functional predictor and parameters. Functional principal component analysis will be used to get an accurate estimation of the functional parameters and to classify sample curves in the categories of the response variable. The good performance of the proposed methodology will be studied by developing an experimental study with simulated and real data.     

科学传播中新媒体艺术的文化诉求

现代科学传播并不是一种单纯知识性的传播活动,而是一个通过传播主体对科学内容传播的解读与延伸,复合思想理念、艺术价值、娱乐效果等文化属性的传播过程。随着新媒体技术的不断进步与展示方式的不断变革,能够带来"沉浸式"体验的新媒体艺术越来越广泛的运用于科学传播之中。作为科学传播展示手段之一的新媒体艺术,只是科学传播的一种媒介,其创作与设计需以科学启蒙和科学内容传播为最终目的,以尊重科学传播主体、受众两个群体和他们的创造精神为基本要求,注重文化内涵的传递以及"人"的思考与价值。     

Selection of a Representative Sample

Sometimes a larger dataset needs to be reduced to just a few points, and it is desirable that these points be representative of the whole dataset. If the future uses of these points are not fully specified in advance, standard decision-theoretic approaches will not work. We present here methodology for choosing a small representative sample based on a mixture modeling approach.     

Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation

This paper introduces a novel mixture model-based approach to the simultaneous clustering and optimal segmentation of functional data, which are curves presenting regime changes. The proposed model consists of a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm, then yielding a fuzzy partition of the curves into K clusters obtained at convergence by maximizing the posterior cluster probabilities. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is a probabilistic version generalizing the deterministic K-means-like algorithm proposed in Hébrail, Hugueney, Lechevallier, and Rossi (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means-like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.     

Design of Blurring Mean-Shift Algorithms for Data Classification

The mean-shift algorithm is an iterative method of mode seeking and data clustering based on the kernel density estimator. The blurring mean-shift is an accelerated version which uses the original data only in the first step, then re-smoothes previous estimates. It converges to local centroids, but may suffer from problems of asymptotic bias, which fundamentally depend on the design of its smoothing components. This paper develops nearest-neighbor implementations and data-driven techniques of bandwidth selection, which enhance the clustering performance of the blurring method. These solutions can be applied to the whole class of mean-shift algorithms, including the iterative local mean method. Extended simulation experiments and applications to well known data-sets show the goodness of the blurring estimator with respect to other algorithms.     

Beyond Politization of Technology and Sustainability: A Plea for Visioning

Most protagonists of sustainable development ignore modern insights in the nature of technology, which has led to an emphasis on technological solutions. The notable exception is transition management. However, both social construction of technology and transition management have been criticized as ignoring distributions of power in society, and for not offering guidance in the choice of the most sustainable technologies. The reviewer criticizes this approach: the issue is not to choose the right technologies, but to address the root causes of unsustainability in society. In addition to politization of transition management the reviewer argues that strong visions are necessary to lead the way. Technologies could help to develop those visions.     

时间正义与空间正义:一种新型的可持续发展伦理观--从约翰内斯堡可持续发展世界首脑会议看可持续发展伦理层面的重建

自1992年联合国环境与发展大会到现在，可持续发展作为全人类的共识和共同行动，既取得了长足的进展，也面临了诸多因素的困扰。这其中，始终未能从伦理层面上为可持续发展确立起一种能够为不同发展水平的国家都接受和认同的基本伦理观念，无疑是困扰目前全球可持续发展事业的一个重要因素。导致这种状况的一个重要原因，就在于以往的可持续发展伦理观忽视了时间和空间作为可持续发展的内在构成因素以及没有能够明确区分时间和空间在自然维度和社会维度上的不同涵义。为此，笔者通过提出“时间正义”和“空间正义”这样两个概念，阐述了一种重建可持续发展的伦理层面的新理念。     

Adaptive Mixture Discriminant Analysis for Supervised Learning with Unobserved Classes

In supervised learning, an important issue usually not taken into account by classical methods is that a class represented in the test set may have not been encountered earlier in the learning phase. Classical supervised algorithms will automatically label such observations as belonging to one of the known classes in the training set and will not be able to detect new classes. This work introduces a model-based discriminant analysis method, called adaptive mixture discriminant analysis (AMDA), which can detect several unobserved groups of points and can adapt the learned classifier to the new situation. Two EM-based procedures are proposed for parameter estimation and model selection criteria are used for selecting the actual number of classes. Experiments on artificial and real data demonstrate the ability of the proposed method to deal with complex and real-world problems. The proposed approach is also applied to the detection of unobserved communities in social network analysis.