Latent class DEDICOM

A probabilistic DEDICOM model was proposed for mobility tables. The model attempts to explain observed transition probabilities by a latent mobility table and a set of transition probabilities from latent classes to observed classes. The model captures asymmetry in observed mobility tables by asymmetric latent mobility tables. It may be viewed as a special case of both the latent class model and DEDICOM with special constraints. A maximum penalized likelihood (MPL) method was developed for parameter estimation. The EM algorithm was adapted for the MPL estimation. Two examples were given to illustrate the proposed method. The work reported in this paper has been supported by grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada and by a fellowship of the Royal Netherlands Academy of Arts and Sciences to the second author. We would like to thank anonymous reviewers for their insightful comments.     

FINDCLUS: Fuzzy INdividual Differences CLUStering

ADditive CLUStering (ADCLUS) is a tool for overlapping clustering of two-way proximity matrices (objects?×?objects). In Simple Additive Fuzzy Clustering (SAFC), a variant of ADCLUS is introduced providing a fuzzy partition of the objects, that is the objects belong to the clusters with the so-called membership degrees ranging from zero (complete non-membership) to one (complete membership). INDCLUS (INdividual Differences CLUStering) is a generalization of ADCLUS for handling three-way proximity arrays (objects?×?objects?×?subjects). Here, we propose a fuzzified alternative to INDCLUS capable to offer a fuzzy partition of the objects by generalizing in a three-way context the idea behind SAFC. This new model is called Fuzzy INdividual Differences CLUStering (FINDCLUS). An algorithm is provided for fitting the FINDCLUS model to the data. Finally, the results of a simulation experiment and some applications to synthetic and real data are discussed.     

A modification of the SINDCLUS algorithm for fitting the ADCLUS and INDCLUS models

The SINDCLUS algorithm for fitting the ADCLUS and INDCLUS models deals with a parameter matrix that occurs twice in the model by considering the two occurrences as independent parameter matrices. This procedure has been justified empirically by the observation that upon convergence of the algorithm to the global optimum, the two independently treated parameter matrices turn out to be equal. In the present paper, results are presented that contradict this finding, and a modification of SINDCLUS is presented which obviates the need for independently treating two occurrences of the same parameter matrix.     

Rotation in Correspondence Analysis

In correspondence analysis rows and columns of a nonnegative data matrix are depicted as points in a, usually, two-dimensional plot. Although such a two-dimensional plot often provides a reasonable approximation, the situation can occur that an approximation of higher dimensionality is required. This is especially the case when the data matrix is large. In such instances it may become difficult to interpret the solution. Similar to what is done in principal component analysis and factor analysis the correspondence analysis solution can be rotated to increase the interpretability. However, due to the various scaling options encountered in correspondence analysis, there are several alternative options for rotating the solutions. In this paper we consider two options for rotation in correspondence analysis. An example is provided so that the benefits of rotation become apparent.     

上海市百岁老人的谱系及其分析

本文调查了上海市百岁老人的性别、职业和谱系,并绘制了57个完整的寿命谱系图,其中男性10名(占总数的17.5%),女性47名(占82.5%).男性中脑力劳动者4名(占男性总数的40%),体力劳动者6名(占60%);女性中脑力劳动者1人(占女性总数的2.1%),体力劳动者3人(占6.4%),操持家务者43人(占91.5%).有长寿家族史者40人(占寿命家族史清楚者的70.2%),无长寿家族史者17人(占29.8%).百岁老人配偶寿长≥70岁者,其已故子女的平均寿命高于配偶<70岁的.作者认为长寿是遗传的,并着重从遗传和环境两方面分析了女寿星数明显多于男寿星数的原因.     

Host sanctions and the legume-rhizobium mutualism

Explaining mutualistic cooperation between species remains one of the greatest problems for evolutionary biology. Why do symbionts provide costly services to a host, indirectly benefiting competitors sharing the same individual host? Host monitoring of symbiont performance and the imposition of sanctions on 'cheats' could stabilize mutualism. Here we show that soybeans penalize rhizobia that fail to fix N(2) inside their root nodules. We prevented a normally mutualistic rhizobium strain from cooperating (fixing N(2)) by replacing air with an N(2)-free atmosphere (Ar:O(2)). A series of experiments at three spatial scales (whole plants, half root systems and individual nodules) demonstrated that forcing non-cooperation (analogous to cheating) decreased the reproductive success of rhizobia by about 50%. Non-invasive monitoring implicated decreased O(2) supply as a possible mechanism for sanctions against cheating rhizobia. More generally, such sanctions by one or both partners may be important in stabilizing a wide range of mutualistic symbioses.     

A generalization of GIPSCAL for the analysis of nonsymmetric data

Graphical representation of nonsymmetric relationships data has usually proceeded via separate displays for the symmetric and the skew-symmetric parts of a data matrix. DEDICOM avoids splitting the data into symmetric and skewsymmetric parts, but lacks a graphical representation of the results. Chino's GIPSCAL combines features of both models, but may have a poor goodness-of-fit compared to DEDICOM. We simplify and generalize Chino's method in such a way that it fits the data better. We develop an alternating least squares algorithm for the resulting method, called Generalized GIPSCAL, and adjust it to handle GIPSCAL as well. In addition, we show that Generalized GIPSCAL is a constrained variant of DEDICOM and derive necessary and sufficient conditions for equivalence of the two models. Because these conditions are rather mild, we expect that in many practical cases DEDICOM and Generalized GIPSCAL are (nearly) equivalent, and hence that the graphical representation from Generalized GIPSCAL can be used to display the DEDICOM results graphically. Such a representation is given for an illustration. Finally, we show Generalized GIPSCAL to be a generalization of another method for joint representation of the symmetric and skew-symmetric parts of a data matrix.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author, and by research grant number A6394 to the second author, from the Natural Sciences and Engineering Research Council of Canada. The authors are obliged to Jos ten Berge and Naohito Chino for stimulating comments.     

A Comparison of Two Methods for Fitting the INDCLUS Model

Chaturvedi and Carroll have proposed the SINDCLUS method for fitting the INDCLUS model. It is based on splitting the two appearances of the cluster matrix in the least squares fit function and relying on convergence to a solution where both cluster matrices coincide. Kiers has proposed an alternative method which preserves equality of the cluster matrices throughout. This paper shows that the latter method is generally to be preferred. However, because the method has a serious local minimum problem, alternative approaches should be contemplated.