G alternatives to centering

Instead of modeling the data in two steps - removing offsets by centering and fitting a model to the residuals - it is possible to fit the model in one step, alleviating the need for projecting the offsets away. Two examples are given. 

The example of missing data (Appendix 9.E) can be fitted directly in the following way. Assume that the offsets are, for instance, constant across the first mode and that a principal component analysis model is sought including offsets across the first mode. Such a PCA model of the data held in the matrix X including offsets reads 

Initialize missing values with reasonable values. Then the data-set is complete and can be modeled by ordinary techniques. 

Fit the model including offsets to the (now complete) data set. For PCA, this amounts to centering the data and fitting the PCA model. 

Exchange missing values in the data matrix with the current model estimates. These estimates will improve the current estimates and thus provide a data set where the estimated missing elements are closer to the correct ones according to the (yet unknown) tme least squares model. 

---