A generalization of partial least squares regression and correspondence analysis for categorical and mixed data: An application with the ADNI data

Abstract

The present and future of large scale studies of human brain and behaviorin typical and disease populationsis mutli-omics, deep-phenotyping, or other types of multi-source and multi-domain data collection initiatives. These massive studies rely on highly interdisciplinary teams that collect extremely diverse types of data across numerous systems and scales of measurement (e.g., genetics, brain structure, behavior, and demographics). Such large, complex, and heterogeneous data requires relatively simple methods that allow for exibility in analyses without the loss of the inherent properties of various data types. Here we introduce a method designed * Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu/).As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at http://adni.loni.ucla.edu/wpcontent/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf specically to address these problems: partial least squares-correspondence analysisregression (PLS-CA-R). PLS-CA-R generalizes PLS regression for use with virtually any data type (e.g., continuous, ordinal, categorical, non-negative values). Though the primary emphasis here is on a PLS-regression approach generalized for data types, we also show that PLS-CA-R leads to additional generalizations of many routine twotable multivariate techniques and their respective algorithms, such as various PLS approaches, canonical correlation analysis, and redundancy analysis (a.k.a. reduced rank regression).

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“…It is similar to the canonical correlation analysis (CCA) used in our previous study (Tibon et al, 2021), which instead maximizes the correlation between the latent variables. Although both CCA and PLS are useful to characterize relationships between two datasets, PLS has been suggested as a more appropriate tool for mixed datasets (Grellmann et al, 2015;Beaton et al, 2019), as is in our case, with the continuous and ordinal nature of the HMM and sleep data, respectively. All variables were z-scored before being subjected to the PLS analysis.…”

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“…It is similar to the canonical correlation analysis (CCA) used in our previous study (Tibon et al, 2021), which instead maximizes the correlation between the latent variables. Although both CCA and PLS are useful to characterize relationships between two datasets, PLS has been suggested as a more appropriate tool for mixed datasets (Beaton et al, 2019;Grellmann et al, 2015), as is in our case, with the continuous and ordinal nature of the HMM and sleep data, respectively. All variables were z-scored before being subjected to the PLS analysis.…”