Latent-variable regression models with higher-order terms: An extension of response modelling by orthogonal design and multiple linear regression

Abstract The latent-variable approach to the linear modelling of a response variable is generalized so as to encompass the possibility of interaction between predictor variables. A rapid, recursive algorithm, which is almost insensitive to roundoff, is presented for inverting the bidiagonal matrix obtained when using higher-order latent-variable regression techniques for response modelling. Expressions are derived for the interpretation and reduction of the response models. The method is demonstrated on a small data set, previously analyzed by Draper and Smith, using a number of multiple-regression techniques.