Influential Cases Research Articles

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A linear regression method is commonly used to analyze data because of its simplicity and applicability; however, it is well known that data may contain some outliers and influential cases that may have a harmful effect on a statistical analysis. Thus detection and examination of outliers or influential cases are important parts of data analysis. In detecting multiple outliers, masking effects usually occur and make it difficult to identify the true outliers. We propose to use dynamic plots as a method resistant to masking effect. The procedure using dynamic plots is useful to find appropriate basic sets with which a dependent outliers detection method start and detect a true outliers set. Examples are given to demonstrate the effectiveness of the suggested idea.

Sensitivity Analysis in Structural Equation Models: Cases and Their Influence

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability (Holzinger & Swineford, 1939) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data (Bollen, 1989; Bollen & Arminger, 1991). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced—these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.

From Steamed Bun to Grass Mud Horse: E Gao as alternative political discourse on the Chinese Internet

This article examines e gao (online spoofs) as a popular form of political expression which has recently emerged on the Chinese internet. I first introduce a cultural approach to internet-mediated political communication that emphasizes discursive integration and the mutual constitution of communicative activity and subjectivity. I then discuss how these two dimensions are configured in the specific media ecology in China with regard to the emergence of e gao. I will analyse the political implications of e gao through a close reading of the two most influential cases. Granted that these online spoofs neither qualify as rational debates aiming to achieve consensus nor have produced any visible policy consequences, but they constitute a significant component of civic culture that offers both political criticism and emotional bonding for all participants.

Detection of Outliers and Influential Observations in Binary Logistic Regression: An Empirical Study

Logistic regression is one of the most frequently used statistical methods as a standard method of data analysis in many fields over the last decade. However, analysis of residuals and identification of influential outliers are not studied so frequently to check the adequacy of the fitted logistic regression model. Detection of outliers and influential cases and corresponding treatment is very crucial task of any modeling exercise. A failure to detect influential cases can have severe distortion on the validity of the inferences drawn from such modeling. The aim of this study is to evaluate different measures of standardized residuals and diagnostic statistics by graphical methods to identify potential outliers. Evaluation of diagnostic statistics and their graphical display detected 25 cases as outliers but they did not play notable effect on parameter estimates and summary measures of fits. It is recommended to use residual analysis and note outlying cases that can frequently lead to valuable insights for strengthening the model.

QUANTIFICATION OF HARM IN DAMAGES ACTIONS FOR ANTITRUST INFRINGEMENTS: INSIGHTS FROM GERMAN CARTEL CASES

This paper argues that empirical economic analysis in court proceedings is subject to important economic and legal restrictions, cumulating in a fundamental trade-off between accuracy and practicality. We draw lessons from two influential German court cases – the paper wholesaler cartel decision of 2007 and the cement cartel decision of 2009. We characterise the trade-offs arguing that they need to be well understood, made transparent, and that decisions on how to proceed in light of these trade-offs have to be taken upfront by the court. In this respect, we believe that the three-step procedure (design, application, and robustness checks) followed by the German court in the cement case is well suited to meet the appropriate legal standard and requirements, both with respect to accuracy and practicality.

Outlier and influence diagnostics for meta-analysis.

The presence of outliers and influential cases may affect the validity and robustness of the conclusions from a meta-analysis. While researchers generally agree that it is necessary to examine outlier and influential case diagnostics when conducting a meta-analysis, limited studies have addressed how to obtain such diagnostic measures in the context of a meta-analysis. The present paper extends standard diagnostic procedures developed for linear regression analyses to the meta-analytic fixed- and random/mixed-effects models. Three examples are used to illustrate the usefulness of these procedures in various research settings. Issues related to these diagnostic procedures in meta-analysis are also discussed. Copyright © 2010 John Wiley & Sons, Ltd.

Influential Cases in Multilevel Modeling: A Methodological Comment

A large number of cross-national survey datasets have become available in recent decades. Consequently, scholars frequently apply multilevel models to test hypotheses on both the individual and the country level. However, no currently available cross-national survey project covers more than 54 countries (GESIS 2009). Multilevel modeling therefore runs the risk that higher-level slope estimates (and the substantial conclusions drawn from these estimates) are unreliable due to one or more influential cases (i.e., countries). This comment emphasizes the problem of influential cases and presents ways to detect and deal with them. To detect influential cases, one may use both graphic tools (e.g., scatter plots at the aggregate level) and numeric tools (e.g., diagnostic tests such as Cook’s D and DFBETAS). To illustrate the usefulness and necessity of these tools, we apply them to a study that was recently published in this journal (Ruiter and De Graaf 2006). Finally, we provide recommendations and tools to detect and handle influential cases, specifically in cross-sectional multilevel analyses.

Perturbation Selection and Local Influence Analysis for Generalized Linear Mixed Models

Identification of influential cases is an important step in data analysis. However, arbitrarily perturbing a model may result in misleading inference about the influential cases. Hence, an important issue of local influence analysis is to select an appropriate perturbation vector. In this article, we develop a perturbation selection method and a second-order local influence measure to address this issue and conduct local influence analysis in generalized linear mixed models. Four perturbation schemes are considered. The proposed approach is illustrated by a simulation study and two real examples. Some technical details are given in three appendices contained in a supplemental material which is available online.

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.

Diagnostic procedures

AbstractDiagnostic procedures are used to check the quality of a fit of a model, to verify the validity of the assumptions behind the model, and to find outlying and/or highly influential observations. Our discussion focuses on the linear model (the most widely used model). Much of our discussion, however, pertains to other models, as we show when we extend our discussion to mixed models at the end of the paper. The traditional fit, least squares (LS), can be severely impaired by just one outlier. So along with LS we present two robust fits and diagnostic procedures which explore the differences among the three fits. These comparisons generally find the outlying and influential cases. Armed with this methodology, we then proceed to discuss diagnostics that explore the quality of fit and verify the validity of the assumptions, including independent and identically distributed errors and normality. Copyright © 2009 John Wiley & Sons, Inc.This article is categorized under: Statistical Models > Linear Models Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical Models > Fitting Models Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Abstract: Local Influence and Robust Methods for Mediation Models

Mediation analysis investigates how certain variables mediate the effect of predictors on outcome variables. Existing studies of mediation models have been limited to normal theory maximum likelihood (ML) or least squares with normally distributed data. Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods can result in biased and inefficient estimates, which lead to inaccurate or unreliable test of the meditated effect. The authors propose two approaches for better mediation analysis. One is to identify cases that strongly affect test results of mediation using local influence methods and robust methods. The other is to use robust methods for parameter estimation, and then test the mediated effect based on the robust estimates. Analytic details of both local influence and robust methods particular for mediation models were provided and one real data example was given. We first used local influence and robust methods to identify influential cases. Then, for the original data and the data with the identified influential cases removed, the mediated effect was tested using two estimation methods: normal theory ML and the robust method, crossing two tests of mediation: the Sobel (1982) test using information-based standard error (z I ) and sandwich-type standard error (z SW ). Results show that local influence and robust methods rank the influence of cases similarly, while the robust method is more objective. The widely used z I statistic is inflated when the distribution is heavy-tailed. Compared to normal theory ML, the robust method provides estimates with smaller standard errors and more reliable test.

A visual procedure for optimal response transformations and curvature specifications

Consider a general regression model in which a covariate enters nonlinearly with a power transformed response variable. Under this formulation a dynamic graphical procedure using inverse response plot and forward response plot is suggested for finding an optimal response transformation parameter value and capturing a curvature. Examples demonstrate that the method works well and also can be used to detect the influential cases.

Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

In this article we extend and implement the forward search algorithm for identifying atypical subjects/observations in factor analysis models. The forward search has been mainly developed for detecting aberrant observations in regression models (Atkinson, 1994) and in multivariate methods such as cluster and discriminant analysis (Atkinson, Riani, & Cerioli, 2004). Three data sets and a simulation study are used to illustrate the performance of the forward search algorithm in detecting atypical and influential cases in factor analysis models. The first data set has been discussed in the literature for the detection of outliers and influential cases and refers to the grades of students on 5 exams. The second data set is artificially constructed to include a cluster of contaminated observations. The third data set measures car's characteristics and is used to illustrate the performance of the forward search when the wrong model is specified. Finally, a simulation study is conducted to assess various aspects of the forward search algorithm.

8. Outliers, Leverage Observations, and Influential Cases in Factor Analysis: Using Robust Procedures to Minimize Their Effect

Parallel to the development in regression diagnosis, this paper defines good and bad leverage observations in factor analysis. Outliers are observations that deviate from the factor model, not from the center of the data cloud. The effects of each kind of outlying observations on the normal distribution-based maximum likelihood estimator and the associated likelihood ratio statistic are studied through analysis. The distinction between outliers and leverage observations also clarifies the roles of three robust procedures based on different Mahalanobis distances. All the robust procedures are designed to minimize the effect of certain outlying observations. Only the robust procedure with a residual-based distance properly controls the effect of outliers. Empirical results illustrate the strength or weakness of each procedure and support those obtained in analysis. The relevance of the results to general structural equation models is discussed and formulas are provided.

Case Selection Techniques in Case Study Research

How can scholars select cases from a large universe for in-depth case study analysis? Random sampling is not typically a viable approach when the total number of cases to be selected is small. Hence attention to purposive modes of sampling is needed. Yet, while the existing qualitative literature on case selection offers a wide range of suggestions for case selection, most techniques discussed require in-depth familiarity of each case. Seven case selection procedures are considered, each of which facilitates a different strategy for within-case analysis. The case selection procedures considered focus on typical, diverse, extreme, deviant, influential, most similar, and most different cases. For each case selection procedure, quantitative approaches are discussed that meet the goals of the approach, while still requiring information that can reasonably be gathered for a large number of cases.

Atoms for Peace, Atoms for War: Probing the Paradoxes of Modernity*

Macrostructural analyses have long dominated the field of social theories of modernity, with the work of Habermas, Giddens, and Beck providing influential cases in point. Empirical studies, however, have raised questions about the applicability and empirical soundness of macrostructural approaches to risks, technology, and nature, and U.S.‐based sociologists have offered alternative theories that have been identified in some studies as providing better predictions and explanations than the macrostructural analyses. Informed by all of the above theories, this article examines the “Atoms for Peace” program, which established the civilian uses of nuclear energy, providing one of the central scientific and technological achievements of modernity. Given the mixed results of nuclear technology development, the mid‐range, structurally informed perspectives of Short and other U.S.‐based sociologists do appear to provide the best interpretations, both for the “Atoms for Peace” program and for the broader legacy of the technological and environmental risks of modernity.

Diagnostics for Linear Models With Functional Responses

Linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations. Residual analysis and diagnostics are considered for such models. Studentized residuals are defined, and their properties are studied. Chi-squared quantile–quantile plots are proposed to check the assumption of Gaussian error process and outliers. Jackknife residuals and an associated test are proposed to detect outliers. Cook's distance is defined to detect influential cases. The methodology is illustrated by an example from a robust design study.

The Americans with Disabilities Act

PurposeImportant Americans with Disabilities Act (ADA)‐related issues that derive from the case law are described and analyzed with the aim of providing guidance both for those responsible for establishing organizational policies, procedures, and practices.Design/methodology/approachA total of 50 influential court cases spanning the past ten years are reviewed and synthesized to better understand the current and future impact of the ADA.FindingsBetter understanding of ADA can help employers both avoid costly litigation and take advantage of a segment of the US labor market that has not yet been fully utilized.Originality/valueThis paper helps practitioner and researchers better understand the organizational implications of the ADA. Better understanding the current case law should lead to employer policies, procedures, and practices that facilitate the better utilization of the qualified disabled work force without compromising employer concerns related to productivity and other job‐related outcomes.

Identifying multiple influential observations in linear regression

The identification of influential observations has drawn a great deal of attention in regression diagnostics. Most of these identification techniques are based on single case deletion and among them DFFITS has become very popular with the statisticians. But this technique along with all other single case diagnostics may be ineffective in the presence of multiple influential observations. In this paper we develop a generalized version of DFFITS based on group deletion and then propose a new technique to identify multiple influential observations using this. The advantage of using the proposed method in the identification of multiple influential cases is then investigated through several well-referred data sets.

Influential data cases when the [formula omitted] criterion is used for variable selection in multiple linear regression

The influence of data cases when the C p criterion is used for variable selection in multiple linear regression analysis is studied in terms of the predictive power and the predictor variables included in the resulting model when variable selection is applied. In particular, the focus is on the importance of identifying and dealing with these so-called selection influential data cases before model selection and fitting are performed. A new selection influence measure based on the C p criterion to identify selection influential data cases is developed. The success with which this influence measure identifies selection influential data cases is evaluated in two example data sets.