In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite difference approximations to the derivatives

Burg, Eeke van der

Leeuw, Jan de

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van der Burg, Eeke

de Leeuw, Jan

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Use of the multinomial jack-knife and bootstrap in generalized non-linear canonical correlation analysis

University of Twente Research Information

The estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS) is discussed. Starting points are the delta method equations. The jackknife and bootstrap methods are compared for providing finite difference approximations to the derivatives. Examining the basic properties of the jackknife method indicates that the vector of profile proportions is perturbed by leaving out single observations. The grid of perturbed values is used to estimate relevant derivatives. Bootstrapping means resampling with replacement from the original sample. Both procedures, bootstrapping and jackknifing, are used to compute pseudo-value means and standard errors for four different data sets: (1) the characteristics of 36 kinds of marine mammals; (2) data describing the attributes of 47 countries; (3) data from a study of school choice for 520 children leaving elementary school; and (4) a sample of 4,863 secondary students from the Second International Mathematics Study. For the small data sets the jackknife and bootstrap were used; for the larger sets, Monte Carlo versions of both were used. The jackknife method appeared less imprecise than the bootstrap method, and jackknife approximations were less stable for smaller samples. It is concluded that the bootstrap method performed better than did the jackknife method. For large samples, the bootstrap procedure works quite well for computing confidence intervals, and eigenvalues computed from OVERALS seem quite stable

Use of the multinomial jackknife and bootstrap in generalized nonlinear canonical correlation analysis

A new approach to non-linear canonical correlation analysis’,

Asymptotic distributions of the canonical correlations From contingency tables’,

Automatic classification of cetaceans by similarity aggregation’, in

Canonical analysis of several sets of variables’,

Eigenvalue Techniques for Quali/a/ive Dala,

Evaluation of mathematics education on the national level’,

Generalization of canonical correlation analysis to three or more set5 of variables’,

Generalized nonlinear canonical correlation with M sets of variables’,

HOMALS classification of whales, porpoises and dolphins’,

Interpreting analysis of qualitative multivariate data using boot5trap methods’, Contribution to the ZUMA conference,

Lineur S/o/is/icirl Inference and /IS

Mairix Eigensys/eiu Routines - EISPACK Guide,

Meer sets analyse voor kwaliratieve gegevens (More sets analysis for qualitative data)’,

Non-linear canonical correlation’.

Nonlinear canonical correlation with k sets of variables’,

Notilineur Mullivuriare Anulysis,

On the use of bootstrap and jackknife in covariance structure analysis’, in

Order Dependence, Series: CWI tracts no. 20, CWI,

Relations among in sets of measures’,

Sekundaire analyre “van jaar tot jaar” met behulp van niet lineaire multivariatc technieken (Second analysis ”From year to year” with the help of nonlinear multitariate techniques)’,

Statistical properties of multiple correspondence analysis’,

Submitted for publication. 76’rh APA Convention,

The Gifi-system of nonlinear mulrivariate analysis’, in

The Jackknife, /he Boolslrap, rind o/her Resanipling Plans,

The permutational limit distribution of generalized canonical correlations’, in

Tweede Wiskunde Projeckr: Opzer en Uirvoering (Second Marheniu/ic:r Projecr: Plans and Perfortnutice), Technische Hogeschool Twente, Toegepaste Onderwijskunde,

http://purl.utwente.nl/publications/70849

Use of the multinomial jack-knife and bootstrap in generalized non-linear canonical correlation analysis

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University of Twente Research Information

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