A note on measures of similarity based on centrality

This note presents a measure of similarity between connected nodes in terms of centrality based on Euclidean distances, and compares it to ‘assortative mixing’ [Newman, M.E.J., 2002. Assortative mixing in networks. Physical Review Letters 89, 208701], which is based on Pearson correlation coefficient. This study suggests that the measure based on Euclidean distances may be more appropriate for relatively smaller (N < 500) and denser networks.     

基于VARK学习风格的远程社会情感学习课程研究

基于VARK学习风格模型,以对应分析方法对IY、第二步、CKCC和积极行动四门远程社会情感学习课程的研究发现：课程学习风格偏好具有差异,其教学活动体现出不同的风格搭配且混合式学习是实现不同学习风格的主要方式。其中,IY偏好视觉和动觉的学习风格,教学活动主要包括观看视频,然后根据指示进行有道具的情境模拟活动,主要以视频课作为远程教学方式;第二步偏好读写的学习风格,教学活动主要包括阅读图片文字材料,然后完成书写类的作业,主要以数字课程作为实现方式;CKCC同样偏好读写的学习风格,教学活动主要包括教材阅读,同时伴随讨论和讲述,主要以直播课为远程教学方式;积极行动偏好听觉的学习风格,更加注重同伴间的讨论和互动,同样以在线直播课程为远程教学方式。这四门课程为其它远程社会情感学习课程开发提供了借鉴,包括课程特色和教学目标与学习风格需匹配,以及混合式学习促进不同学习风格活动效果。     

Feature selection based on distance correlation: a filter algorithm

Feature selection (FS) is one of the most powerful techniques to cope with the curse of dimensionality. In the study, a new filter approach to feature selection based on distance correlation is presented (DCFS, for short), which keeps the model-free advantage without any pre-specified parameters. Our method consists of two steps: hard step (forward selection) and soft step (backward selection). In the hard step, two types of associations, between univariate feature and the classes and between group feature and the classes, are involved to pick out the most relevant features with respect to the target classes. Due to the strict screening condition in the first step, some of the useful features are likely removed. Therefore, in the soft step, a feature-relationship gain (like feature score) based on the distance correlation is introduced, which is concerned with five kinds of associations. We sort the feature gain values and implement the backward selection procedure until the errors stop declining. The simulation results show that our method becomes more competitive on several datasets compared with some of the representative feature selection methods based on several classification models.     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.     

Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

On the asymptotic distribution of Cook's distance in logistic regression models

It sometimes occurs that one or more components of the data exert a disproportionate influence on the model estimation. We need a reliable tool for identifying such troublesome cases in order to decide either eliminate from the sample, when the data collect was badly realized, or otherwise take care on the use of the model because the results could be affected by such components. Since a measure for detecting influential cases in linear regression setting was proposed by Cook [Detection of influential observations in linear regression, Technometrics 19 (1977), pp. 15–18.], apart from the same measure for other models, several new measures have been suggested as single-case diagnostics. For most of them some cutoff values have been recommended (see [D.A. Belsley, E. Kuh, and R.E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, 2nd ed., John Wiley & Sons, New York, Chichester, Brisban, (2004).], for instance), however the lack of a quantile type cutoff for Cook's statistics has induced the analyst to deal only with index plots as worthy diagnostic tools. Focussed on logistic regression, the aim of this paper is to provide the asymptotic distribution of Cook's distance in order to look for a meaningful cutoff point for detecting influential and leverage observations.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.     

Diagnostic tools in generalized Weibull linear regression models

We propose some statistical tools for diagnosing the class of generalized Weibull linear regression models [A.A. Prudente and G.M. Cordeiro, Generalized Weibull linear models, Comm. Statist. Theory Methods 39 (2010), pp. 3739–3755]. This class of models is an alternative means of analysing positive, continuous and skewed data and, due to its statistical properties, is very competitive with gamma regression models. First, we show that the Weibull model induces ma-ximum likelihood estimators asymptotically more efficient than the gamma model. Standardized residuals are defined, and their statistical properties are examined empirically. Some measures are derived based on the case-deletion model, including the generalized Cook's distance and measures for identifying influential observations on partial F-tests. The results of a simulation study conducted to assess behaviour of the global influence approach are also presented. Further, we perform a local influence analysis under the case-weights, response and explanatory variables perturbation schemes. The Weibull, gamma and other Weibull-type regression models are fitted into three data sets to illustrate the proposed diagnostic tools. Statistical analyses indicate that the Weibull model fitted into these data yields better fits than other common alternative models.     

Uniform Design for Experiments with Mixtures

The goal of uniform mixture design is to scatter the design points in the experimental region uniformly. The commonly used criteria, such as mean square distance, are based on the Euclidean distance. Based on the Lee distance, a new criterion is proposed in this article. And an algorithm, called NTLBG, is also proposed to refine the randomly generated design for the experimental design with mixtures. Some examples show that the design generated by the NTLBG algorithm has a lower criteria value.