In the social and behavioral sciences, data sets often do not meet the assumptions of traditional analysis methods. Therefore, nonlinear alternatives to traditional methods have been developed.... Show moreIn the social and behavioral sciences, data sets often do not meet the assumptions of traditional analysis methods. Therefore, nonlinear alternatives to traditional methods have been developed. This thesis starts with a didactic discussion of nonlinear principal components analysis (NLPCA), illustrated by an application considering caregiver-child interactions in day-care. Traditional PCA explores data structures, summarizing the observed information in underlying variables, called principal components. The method only gives a sensible solution if the variables are numeric, and linearly related to each other. NLPCA is developed for situations in which these assumptions do not apply. It incorporates different types of variables (nominal, ordinal, and numeric) and discovers and handles nonlinear relationships. As PCA does not make assumptions about variable distributions, it does not seem theoretically sensible to apply standard (asymptotic) formulas for statistical inference. Therefore, this thesis shows easily applicable ways of assessing stability and statistical significance of the elements of the NLPCA solution (eigenvalues, component loadings, component scores, category quantifications) without making prior assumptions about the data (i.e., nonparametrically), using the bootstrap and permutation tests, respectively. By providing relatively simple inferential measures for NLPCA, a wider use of this method in the psychological and educational context may be promoted. Show less
