Influence in covariance structure analysis: with an application to confirmatory factor analysis

Tanaka, Yutaka; Watadani, Shingo; Moon, Sung Ho

doi:10.1080/03610929108830742

Cited by 50 publications

(55 citation statements)

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“…Therefore, it is of interest to locate these observations. In effect, the identification and accommodation of influential observations has long been an important topic in various statistical analyses (see, e.g., Andersen, 1992;Cook, 1977;Poon &Poon, 2002;Poon, Wang & Lee, 1999;Tanaka, Watadani & Moon, 1991;Thomas & Cook, 1990;Yuan & Bentler, 2001;Yuan, Chan& Bentler, 2000). However, it has received very little attention in the analysis of ranking data.…”

Section: Introductionmentioning

confidence: 98%

Influence analysis of ranking data

Poon

Chan

2002

Psychometrika

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Section: Introductionmentioning

confidence: 98%

Influence analysis of ranking data

Poon

Chan

2002

Psychometrika

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“…As in the case of exploratory factor analysis we can define the three influence measures D, CV R and 0X2, as scalar measures of influence. Confirmatory factor analysis is a special case of CSA and its sensitivity analysis has been studied with a numerical example by Tanaka, Watadani and Moon(1991). Example.…”

Section: Influence Measuresmentioning

confidence: 99%

“…The parameter vector 9 is estimated by minimizing a function called discrepancy function or fitting function G(S, E(0)), which measures the discrepancy between the assumed covariance matrix E(0) and the sample covariance matrix S (see, e.g., Browne, 1982;Bollen, 1989). Tanaka, Watadani and Moon (1991) and have proposed sensitivity analysis procedures for CSA without constraints and CSA with equality constraints, respectively. They have derived the influence functions for the parameters in CSA and have proposed some measures of influence which indicate the influence on the estimate, on its precision and on the goodness-of-fit.…”

Section: Influence Measuresmentioning

confidence: 99%

“…The same expansions are used to evaluate the changes of the configurations of principal components or factors with RV coefficients (Benasseni, 1990;Tanaka, 1990,1991). Tanaka, Watadani and Moon (1991), and Tanaka, Watadani and Inoue (1992) have considered sensitivity analysis in covariance structure analysis including LISREL models. Major concerns of those papers are to derive influence functions or the equivalent quantities and to evaluate the influence of data perturbation (case deletion or downweighting) on the results of analysis.…”

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confidence: 99%

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Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods

Tanaka

1994

Journal of the Japanese Society of Computational Statistics

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Methodologies have been developed in the last two decades for detecting influential observations and evaluating the stability of the results of analysis not only in regression and related methods but also in other multivariate methods. In developing these methodologies influence functions play important roles. The present paper shows that influence functions can be derived in various multivariate statistical methods and that a general strategy based on influence functions and its robust version are useful for detecting singly and/or jointly influential observations. Cases of principal component analysis, exploratory factor analysis and confirmatory factor analysis are studied with numerical examples.

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“…This algorithm can be applied to various multivariate methods such as PCA, CVA, quantification methods, exploratory factor analysis and covariance structure analysis where influence functions have been derived(see e.g., Critchley,1985;Tanaka, 1984Tanaka, , 1988Tanaka and Tarumi, 1986;Tanaka and Odaka, 1989a,b,c;Tanaka, Watadani and Moon, 1991;. In section 2, influence functions for single-case and multiple-case diagnostics are presented, and then related influence measures, such as influence on the estimate, on its precision and on the goodness of fit, are defined in section 3.…”

Section: Yanagimentioning

confidence: 99%

A Clustering Algorithm for Detecting Influential Subsets in Multivariate Methods

Moon

Yanagi

Tanaka

1992

Journal of the Japanese Society of Computational Statistics

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IntroductionThe problem of detecting influential observations has been considered by a number of researchers in the field of regression diagnostics. However, most of them are concerned with the influence of a single observation and related diagnostic measures are numerous. Although those single-case diagnostic measures can be easily generalized to multiple-case diagnostic measures, the practical application of detecting jointly influential subsets is still problematic because of the presence of the so-called "masking and swamping effects" as well as the prohibitive computation in view of large subsets involved. There have been proposed two major types of practical methods for this problem. One is the method based on the cluster analysis with similarities defined by the modified hat matrix. This type was originally proposed by Gray and Ling(1984) and was modified by Hadi(1985). The other is the method based on robust regression such as Rousseeuw(1984Rousseeuw( , 1990's method based on his least median of squares regression. Both are useful for detecting influential subsets in regression analysis, but the ideas behind them can not be applied directly to other multivariate methods.The objective of the present paper is to propose a method for detecting influential subsets in multivariate methods where the empirical influence functions(EIF) are available. Regarding this topic Tanaka, Castano-Tostado and Odaka(1990) among others have recommended and illustrated to use principal component analysis(PCA) or canonical variate analysis(CVA) for detecting individuals with relatively large EIF vectors and similar influence patterns, on the basis of the additivity property of the EIF. Though their method is useful, it has some problems such that it depends on subjective judgement to make clusters from scatter diagrams of principal components or canonical variates and that it is difficult to consider different aspects of influence. Our clustering algorithm, which is free from the * Graduate

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Influence in covariance structure analysis: with an application to confirmatory factor analysis

Cited by 50 publications

References 14 publications

Influence analysis of ranking data

Influence analysis of ranking data

Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods

A Clustering Algorithm for Detecting Influential Subsets in Multivariate Methods

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