Iteratively reweighted generalized rank annihilation method: 2. Least squares property and variance expressions

The generalized rank annihilation method (GRAM) has been criticised for not having a global least squares fitting property such as the alternating least squares (ALS) method. In Part 1 of this series, we have modified GRAM by introducing a weight for the data matrices. The proposed modification is called iteratively reweighted GRAM (IRGRAM). Here, it is shown that these weights enable one to shed new light on the least squares fitting properties of GRAM and ALS. Inequalities are derived which suggest that IRGRAM compares favourably with ALS in terms of model fit to the data matrices. Although applying different weights directly affects the sums of squares explained by IRGRAM and ALS, error propagation shows that the first-order approximation to prediction variance remains unaltered when using IRGRAM. In contrast, the effect on the variance in the estimated profiles depends on the analyte under consideration. This result suggests that the amount of fitted data does not give a clear indication of the performance of bilinear calibration models.