GME Estimation of Spatial Structural Equations Models

The objective of this paper is to develop a GME formulation for the class of spatial structural equations models (S-SEM). In this respect, two innovatory aspects are introduced: (i) the formalization of the GME estimation approach for structural equations models that account for spatial heterogeneity and spatial dependence; (ii) the extension of the methodology to a panel data framework. We also present an application of the method to real data finalized to investigate disparities of unemployment rates in OECD countries over the period 1998-2006.     

Mixtures of Autoregressions with an Improper Component for Panel Data

An EM algorithm for fitting mixtures of autoregressions of low order is constructed and the properties of the estimators are explored on simulated and real datasets. The mixture model incorporates a component with an improper density, which is intended for outliers. The model is proposed as an alternative to the search for the order of a single-component autoregression. The methods can be adapted to other patterns of dependence in panel data. An application to the monthly records of income of the outlets of a retail company is presented.     

Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects

Unique parametrizations of models are very important for parameter interpretation and consistency of estimators. In this paper we analyze the identifiability of a general class of finite mixtures of multinomial logits with varying and fixed effects, which includes the popular multinomial logit and conditional logit models. The application of the general identifiability conditions is demonstrated on several important special cases and relations to previously established results are discussed. The main results are illustrated with a simulation study using artificial data and a marketing dataset of brand choices.     

On the Imputation of Missing Data in Surveys with Likert-Type Scales

Starting from the problem of missing data in surveys with Likert-type scales, the aim of this paper is to evaluate a possible improvement for the imputation procedure proposed by Lavori, Dawson, and Shera (1995) here called Approximate Bayesian bootstrap with Propensity score (ABP). We propose an imputation procedure named Approximate Bayesian bootstrap with Propensity score and Nearest neighbour (ABPN), which, after the ??propensity score step?? of ABP, randomly selects a donor in the nonrespondent??s neighbourhood, which includes cases with response patterns similar to the one of the nonrespondent to be imputed. A preliminary simulation study with single imputation on missing data in two Likerttype scales from a real data set shows that ABPN: (a) performed better than the ABP imputation, and (b) can be considered as a serious competitor of other procedures used in this context.     

Estimation of Generalized DINA Model with Order Restrictions

Cognitive diagnostic models provide valuable information on whether a student has mastered each of the attributes a test intends to evaluate. Despite its generality, the generalized DINA model allows for the possibility of lower correct rates for students who master more attributes than those who know less. This paper considers the use of order-constrained parameter space of the G-DINA model to avoid such a counter-intuitive phenomenon and proposes two algorithms, the upward and downward methods, for parameter estimation. Through simulation studies, we compare the accuracy in parameter estimation and in classification of attribute patterns obtained from the proposed two algorithms and the current approach when the restricted parameter space is true. Our results show that the upward method performs the best among the three, and therefore it is recommended for estimation, regardless of the distribution of respondents’ attribute patterns, types of test items, and the sample size of the data.     

Market Segmentation Using Brand Strategy Research: Bayesian Inference with Respect to Mixtures of Log-Linear Models

This paper presents a Bayesian model based clustering approach for dichotomous item responses that deals with issues often encountered in model based clustering like missing data, large data sets and within cluster dependencies. The approach proposed will be illustrated using an example concerning Brand Strategy Research.     

Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches

In this paper two techniques for units clustering and factorial dimensionality reduction of variables and occasions of a three-mode data set are discussed. These techniques can be seen as the simultaneous version of two procedures based on the sequential application of k-means and Tucker2 algorithms and vice versa. The two techniques, T3Clus and 3Fk-means, have been compared theoretically and empirically by a simulation study. In the latter, it has been noted that neither T3Clus nor 3Fk-means outperforms the other in every case. From these results rises the idea to combine the two techniques in a unique general model, named CT3Clus, having T3Clus and 3Fk-means as special cases. A simulation study follows to show the effectiveness of the proposal.     

Constrained Multilevel Latent Class Models for the Analysis of Three-Way Three-Mode Binary Data

Probabilistic feature models (PFMs) can be used to explain binary rater judgements about the associations between two types of elements (e.g., objects and attributes) on the basis of binary latent features. In particular, to explain observed object-attribute associations PFMs assume that respondents classify both objects and attributes with respect to a, usually small, number of binary latent features, and that the observed object-attribute association is derived as a specific mapping of these classifications. Standard PFMs assume that the object-attribute association probability is the same according to all respondents, and that all observations are statistically independent. As both assumptions may be unrealistic, a multilevel latent class extension of PFMs is proposed which allows objects and/or attribute parameters to be different across latent rater classes, and which allows to model dependencies between associations with a common object (attribute) by assuming that the link between features and objects (attributes) is fixed across judgements. Formal relationships with existing multilevel latent class models for binary three-way data are described. As an illustration, the models are used to study rater differences in product perception and to investigate individual differences in the situational determinants of anger-related behavior.     

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.     

Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure

a posteriori blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on the Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1.     

Using Neural Network Analysis to Define Methods of DINA Model Estimation for Small Sample Sizes

The DINA model is a commonly used model for obtaining diagnostic information. Like many other Diagnostic Classification Models (DCMs), it can require a large sample size to obtain reliable item and examinee parameter estimation. Neural Network (NN) analysis is a classification method that uses a training dataset for calibration. As a result, if this training dataset is determined theoretically, as was the case in Gierl’s attribute hierarchical method (AHM), the NN analysis does not have any sample size requirements. However, a NN approach does not provide traditional item parameters of a DCM or allow for item responses to influence test calibration. In this paper, the NN approach will be implemented for the DINA model estimation to explore its effectiveness as a classification method beyond its use in AHM. The accuracy of the NN approach across different sample sizes, item quality and Q-matrix complexity is described in the DINA model context. Then, a Markov Chain Monte Carlo (MCMC) estimation algorithm and Joint Maximum Likelihood Estimation is used to extend the NN approach so that item parameters associated with the DINA model are obtained while allowing examinee responses to influence the test calibration. The results derived by the NN, the combination of MCMC and NN (NN MCMC) and the combination of JMLE and NN are compared with that of the well-established Hierarchical MCMC procedure and JMLE with a uniform prior on the attribute profile to illustrate their strength and weakness.     

中国古代历法与印度及阿拉伯的关系——以日月食起讫算法为例

本概述了中国古代历法中计算日食三限与月食五限的算法沿革,详细论述了宋元时期日月食起讫算法之精度的演变发展。在元代郭守敬的《授时历》（１２８０年）之前的中国传统历法,采用的都是纯粹的数值方法去构造一系列相应的函数。自《授时历》起,开始利用日月食的几何模型构造一类十分不同的函数。研究表明,《授时历》运用的几何模型与唐代印度风格的《九执历》运用的几何模型与唐代印度风格的《九执历》（７１８年）,及元代阿     

Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data

Clustering techniques are based upon a dissimilarity or distance measure between objects and clusters. This paper focuses on the simplex space, whose elements??compositions??are subject to non-negativity and constant-sum constraints. Any data analysis involving compositions should fulfill two main principles: scale invariance and subcompositional coherence. Among fuzzy clustering methods, the FCM algorithm is broadly applied in a variety of fields, but it is not well-behaved when dealing with compositions. Here, the adequacy of different dissimilarities in the simplex, together with the behavior of the common log-ratio transformations, is discussed in the basis of compositional principles. As a result, a well-founded strategy for FCM clustering of compositions is suggested. Theoretical findings are accompanied by numerical evidence, and a detailed account of our proposal is provided. Finally, a case study is illustrated using a nutritional data set known in the clustering literature.     

《同文算指》中高次方程数值解法的来源及其影响

一般认为《同文算指》主要是一部翻译作品,大部分内容来自丁先生的《实用算术概论》,同时也参考了一些传统的数学著作。事实上,《同文算指》有更广泛的资料来源,是李之藻试图会通中西数学的一部著作。在进一步发掘史料的基础上,指出《同文算指》中高次方程数值解法来自德国数学大师斯蒂弗尔的《整数算术》。这种方法与传统算学中的立成释锁法类似,李之藻认为比传统的方法更先进而收录。明清时期的算学家根据《同文算指》的记录对这种方法进行了研究和推广,从而在某种意义上达到了李之藻会通中西数学的目的。