, Jan Use of the Multinomial Jackknife and Bootstrap in Generalized Nonlinear Canonical Correlation Analysis

DOCUMENT RESUME TM 013 689 van der Burg, Eeke; de Leeuw, Jan Use of the Multinomial Jackknife and Bootstrap in Generalized Nonlinear Canonical Correlation Analysis. Research Report 87-4. Twente Univ., Enschede (Netherlands). Dept. of Education. 87 50p. Mediatheek, Faculteit Toegepaste Onderwijskunde, Universiteit Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Reports Evaluative/Feasibility (142) mFo1 /Pc02 Plus Postage. *Correlation; Elementary Secondary Education; *Error of Measurement; *Estimation (Mathematics); Mathematical Models; Monte Carlo Methods; Statistical Analysis *Bootstrap Methods; Eigenvalues; *Jackknifing Technique; Multinomial Models; Nonlinear Transformations; OVERALS Technique The estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS) is discussed. Start.ng 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 Lo 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 if 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. Eight tables present the values from the fcar data sets, and four figures illustrate category quantifications for all data sets. (Author/SLD) *********************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * ************************************ ***** ****************************** cps Use of the Multinomial Jackknife and r-4 Bootstrap in Generalized Nonlinear Research r-4 Canonical Correlation Analysis Report O 87-4 1'4 "PERMISSION '4 PA °' US DENT/AENT OF EDUCATION I I TO REPRODUCE THIS CeZ Mow of Edizcational Research and Improvement EDUCATIONAL RESOURCES INFORMATION MATERIAL HAS BEEN GRANTED BY CENTER (ERIC) 1. AkA isst-Ai = es document has been reproduced as moved from Me person or organization ;161 originating D tsnor changes a naave been made to improve Pants of view a oppinoWS stated in this document do not necessarily represent official OE RI position or policy Eeke van der Burg Jan de Leeuw TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC)" Division of Educaational Measurement and Data Analysis University of Twente BEST COPY AVAILIkat 2 Use of the Multinomial Jackknife and Bootstrap in Generalized Nonlinear Canonical Correlation Analysis Eeke van der Burg Jan de Leeuw