Stability of principal component analysis studied by the bootstrap method

Daudin, Jean‐Jacques; Duby, Camille; Trecourt, P.

doi:10.1080/02331888808802095

Cited by 57 publications

(41 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of large samples and a normal distribution of variables, approximate variance of eigenvalues may be used [26] and a symmetrical interval can be computed. The bootstrap [27] has been proposed to construct a confidence interval in other (more numerous) cases where variables are not normally distributed [28,29]. If B bootstrap samples are used, the 1 ) 2a central percentile segment of the resulting cumulative distribution may be taken as an approximate confidence interval for the ith eigenvalue.…”

Section: New Statistical Methodsmentioning

confidence: 99%

Methodological issues in determining the dimensionality of composite health measures using principal component analysis: Case illustration and suggestions for practice

et al. 2005

View full text Add to dashboard Cite

During the early steps of the construction of composite health measures, principal component analysis (PCA) is commonly used to identify 'latent' factors that underlie observed variables and to determine the dimensionality of the instruments. The determination of the number of components to retain is critical to PCA: it markedly influences the factorial model identified and further conditions the validity of the constructed instrument. However, many researchers developing composite health measures seem to be unaware of the importance of this determination. The purposes of the paper are to illustrate (1) the variability of the factorial models obtained by using different published rules (n = 10) for determining the number of components to retain in PCA applied to two quality-of-life datasets, and (2) the value of a careful and diversified approach to the problem of the number of components to retain in PCA that we suggest, instead of the unsatisfactory 'rule-of-thumb' that many researchers use. This involves: (1) using robust rules (including parallel analysis and minimum average partial procedure) to generate a set of possible values for the number of components to retain, (2) repeating the analysis across samples, (3) comprehensively assessing the models obtained, and (4) considering complementary methods to PCA and especially confirmatory factor analysis.

show abstract

Section: New Statistical Methodsmentioning

confidence: 99%

Methodological issues in determining the dimensionality of composite health measures using principal component analysis: Case illustration and suggestions for practice

et al. 2005

View full text Add to dashboard Cite

show abstract

“…Not every dataset will give rise to an obvious separation between the outlying and nonoutlying points. Consider the data given by Daudin, Dauby and Trecourt and analyzed by Atkinson (Daudin, Duby, and Trecourt 1988;Atkinson 1994). The data are eight measurements on 85 bottles of milk.…”

Section: Affine Equivariant Estimatorsmentioning

confidence: 99%

The Distribution of Robust Distances

Hardin

Rocke

2005

Journal of Computational and Graphical Statistics

173

133

View full text Add to dashboard Cite

Mahalanobis-type distances in which the shape matrix is derived from a consistent, high-breakdown robust multivariate location and scale estimator have an asymptotic chisquared distribution as is the case with those derived from the ordinary covariance matrix. For example, Rousseeuw's minimum covariance determinant (MCD) is a robust estimator with a high breakdown. However, even in quite large samples, the chi-squared approximation to the distances of the sample data from the MCD center with respect to the MCD shape is poor. We provide an improved F approximation that gives accurate outlier rejection points for various sample sizes.

show abstract

“…Because the bootstrap sample is the same size as the original sample, it contains certain rows more than once, others not at all. Daudin et al (1988) show that the probability for the i* row to be suppressed is equal to 0.37 if n is large, and the probability that it appears twice or more is equal to 0.26. This shows that for each draw, the data are quite modified.…”

Section: Stability Of Principal Componentsmentioning

confidence: 99%

“…We have used the bootstrap method, proposed by Efron (1979), and previously used by Daudin et al (1988), in order to study the stability of PCA results.…”

Section: Stability Of Principal Componentsmentioning

confidence: 99%

Application des techniques geostatistiques et d analyse multivariable a l interpretation des releves geochimiques regionaux

Bellehumeur¹

1992

View full text Add to dashboard Cite

Stability of principal component analysis studied by the bootstrap method

Cited by 57 publications

References 2 publications

Methodological issues in determining the dimensionality of composite health measures using principal component analysis: Case illustration and suggestions for practice

Methodological issues in determining the dimensionality of composite health measures using principal component analysis: Case illustration and suggestions for practice

The Distribution of Robust Distances

Application des techniques geostatistiques et d analyse multivariable a l interpretation des releves geochimiques regionaux

Contact Info

Product

Resources

About