Causal and path modelling

A general methodology that carries out causal and path modelling by the same tools as known by linear regression is presented. Data can be one block (like in PCA), two blocks (like in regression analysis), several blocks, e.g., derived from multi-way data, or a network of data blocks. Causality questions that we typically ask in PCA can be carried out for each block of data. The data blocks can make up a path, where each node contains two adjoining blocks. The two neighbouring data blocks have either the same number of variables or the same number of samples. The methods are based on the H-principle of mathematical modelling of data. A very general path or network of data blocks can be analysed. An important aspect of this approach is that most methods of linear regression analysis can be carried out within this framework. The procedures are based on projections of one latent structure onto the following one. These methods can therefore be used to detect (differential) changes in the latent structure (e.g., in loadings or scores) from one block to another.