Algorithms for compositional tensors of third-order

The PARAFAC-ALS procedure for estimating CP parameters on tridimen-sional tensors is sensitive to data collinearity. This inefficiency is especially problematic if collinearity is paired with other issues such as data of large dimensions and difficulties in establishing correct model rank. When dealing with compositional data, i.e. positive values with a covariance bias, multicollinearity is inherent by definition, and it is preserved also if the data is transformed in log-ratios by means of the clr function. For this reason, alternative estimating procedures may be considered, such as INT and INT-2. These dual-step methods use the properties of the SWATLD and ATLD algorithms during initialization to overcome ALS inefficiency while still providing least squares results. Their comparative performance is tested in an extensive simulation study on collinear data.