Outliers in multilevel data

This paper offers the data analyst a range of practical procedures for dealing with outliers in multilevel data. It first develops several techniques for data exploration for outliers and outlier analysis and then applies these to the detailed analysis of outliers in two large scale multilevel data sets from educational contexts. The techniques include the use of deviance reduction, measures based on residuals, leverage values, hierarchical cluster analysis and a measure called DFITS. Outlier analysis is more complex in a multilevel data set than in, say, a univariate sample or a set of regression data, where the concept of an outlying value is straightforward. In the multilevel situation one has to consider, for example, at what level or levels a particular response is outlying, and in respect of which explanatory variables; furthermore, the treatment of a particular response at one level may affect its status or the status of other units at other levels in the model.     

Recursive residuals in generalised linear models

Recursive estimation and recursive residuals are introduced for generalised linear models (GLIM). Their definitions parallel those of normal theory regression models and relate to one of the outlier model definitions of GLIM residuals. An example illustrates their use.     

A. S. A. Programs

Arranged for the 25th Session of the INTERNATIONAL STATISTICAL INSTITUTE     

Modern Statistics for Spatial Point Processes*

Abstract. We summarize and discuss the current state of spatial point process theory and directions for future research, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications. In particular, we consider Poisson, Gibbs and Cox process models, diagnostic tools and model checking, Markov chain Monte Carlo algorithms, computational methods for likelihood-based inference, and quick non-likelihood approaches to inference.     

GEEs for repeated categorical responses based on generalized residuals

Clustered or correlated samples of categorical response data arise frequently in many fields of application. The method of generalized estimating equations (GEEs) introduced in Liang and Zeger [Longitudinal data analysis using generalized linear models, Biometrika 73 (1986), pp. 13–22] is often used to analyse this type of data. GEEs give consistent estimates of the regression parameters and their variance based upon the Pearson residuals. Park et al. [Alternative GEE estimation procedures for discrete longitudinal data, Comput. Stat. Data Anal. 28 (1998), pp. 243–256] considered a modification of the GEE approach using the Anscombe residual and the deviance residual. In this work, we propose to extend this idea to a family of generalized residuals. A wide simulation study is conducted for binary and Poisson correlated outcomes and also two numerical illustrations are presented.     

Simple correspondence analysis using adjusted residuals

Correspondence analysis is a versatile statistical technique that allows the user to graphically identify the association that may exist between variables of a contingency table. For two categorical variables, the classical approach involves applying singular value decomposition to the Pearson residuals of the table. These residuals allow for one to use a simple test to determine those cells that deviate from what is expected under independence. However, the assumptions concerning these residuals are not always satisfied and so such results can lead to questionable conclusions.One may consider instead, an adjustment of the Pearson residual, which is known to have properties associated with the standard normal distribution. This paper explores the application of these adjusted residuals to correspondence analysis and determines how they impact upon the configuration of points in the graphical display.     

三维内肋管内乙二醇在层流和过渡流区对流换热的实验研究

以乙二醇为工质,在Re数为250～6000,Pr数为65～90之间的工况范围内,对7根具有不同肋形结构尺寸和肋排列形式的三维内肋管管内对流换热和阻力特性进行了实验。结果表明,换热最强的三维内肋管与光管相比,在过渡流区换热强化倍数平均可达4.5倍,同时流阻增加约3倍;在层流区换热强化倍数约为2.4倍,而流阻仅增加约0.67倍。三维内肋的肋形结构尺寸和肋排列形式均对三维内肋管内的换热和阻力特性以及层流向过渡流的转换产生影响。     

Stabilizing heteroscedasticity for butterfly-distributed residuals by the weighting absolute centered external variable

In the current study, a new method by the weighting absolute centered external variable (WCEV) was proposed to stabilize heteroscedasticity for butterfly-distributed residuals (BDRs). After giving brief information about heteroscedasticity and BDRs, WCEV was introduced. The WCEV and commonly used variance stabilizing methods are compared on a simple and a multiple regression model. The WCEV was also tested for other type of heteroscedasticity patterns. In addition to heteroscedasticity, other regression assumptions were checked for the WCEV.