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A bootstrap procedure for mixture models: applied to multidimensional scaling latent class models. (English) Zbl 1039.62026

The paper presents two distinct applications of the bootstrap to analysis of mixture models, particularly multidimensional scaling models (MDS). The first, most innovative, the so-called LC bootstrap, is proposed to determine the appropriate number of latent class models. The second, more conventional application, uses the bootstrap technique (SE bootstrap) to asses the standard errors of the parameters in an MDS model. Although the authors’ approach is applicable in any latent class context, its usage is illustrated in the context of CLASCAL, i.e., latent class weighted Euclidian MDS models. Five sets of data, three simulated and two real, are analysed. It turns out that the SL bootstrap selects the number of latent classes correctly at both low and high error levels. The SE bootstrap seems to reproduce Monte-Carlo results correctly, too.

MSC:

62F40 Bootstrap, jackknife and other resampling methods
91C15 One- and multidimensional scaling in the social and behavioral sciences
62H99 Multivariate analysis
62G09 Nonparametric statistical resampling methods
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