![]() ![]() Dimension folding PFC gains further efficiency by effective use of the response information. ![]() ![]() The proposed methods can simultaneously reduce a predictor’s multiple dimensions and inherit asymptotic properties from maximum likelihood estimation. We refer to them as dimension folding PCA and dimension folding PFC. We propose model-based dimension folding methods that can be treated as extensions of conventional principal components analysis (PCA) and principal fitted components (PFC). This can be inadequate when the number of slices is not chosen properly. Their methods, however, are moment-based and rely on slicing the responses to gain information about the conditional distribution of X|Y. Li, Kim, and Altman (2010) proposed dimension folding methods that effectively improve major moment-based dimension reduction techniques for the more complex data structure. Conventional dimension reduction methods deal mainly with simple data structure and are inappropriate for data with matrix-valued predictors. ![]()
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