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.