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The next-generation approach to behavioral research relies on intensive data collection from multiple disciplinary domains. Behavior and cognition are no longer studied from the psychological perspective only but also from other disciplinary perspectives such as environmental, social, clinical, and biomolecular. This often leads to so-called high-dimensional multiview data. In analyzing this type of data, it is of great importance to disentangle distinct mechanisms underlying each data block from common mechanisms shared by all (or multiple) data blocks. Current latent variable methods are not appropriate to address this challenge. To this end, we propose a Multiblock Regularized Least-squares Latent Variable Method. The method uses hard cardinality constraint (instead of a penalized approach such as the group lasso) to impose sparsity across and within data blocks. That is, the model is estimated under the constraint that exactly $C$ blocks of loadings are equal to zero to identify specific and shared mechanisms. In addition, within each data block, exactly $K$ loadings are imposed to be zero to encourage variable selection to ease interpretation. Both latent variable scores and loadings are estimated in an alternating optimization scheme. The performance of the proposed method is evaluated in an extensive simulation study. We also demonstrate the use of the method using a real-world dataset.

cardinality constraint, dimension reduction, multiblock data, latent variable, structural equation modeling