An approach ton-mode components analysis

As an extension of Lastovicka's four-mode components analysis ann-mode components analysis is developed. Using a convenient notation, both a canonical and a least squares solution are derived. The relation between both solutions and their computational aspects are discussed.The first draft was written while Wansbeek was with the Netherlands Central Bureau of Statistics. We thank Jaap Verhees for performing the computations and for many discussions on the subject, John Lastovicka for kindly making available his data to us, and the Editor, the referees, Jeroen Weesie and Pieter Kroonenberg for their useful comments.     

Quadratic prediction of factor scores

Factor scores are naturally predicted by means of their conditional expectation given the indicatorsy. Under normality this expectation is linear iny but in general it is an unknown function ofy. It is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function ofy.The authors would like to thank Edith Nijenhuis, the anonymous referees, and the associate editor for their helpful comments and suggestions.