  A mediation analysis approach is proposed for multiple exposures, multiple
mediators, and a continuous scalar outcome under the linear structural equation
modeling framework. It assumes that there exist orthogonal components that
demonstrate parallel mediation mechanisms on the outcome, and thus is named
Principal Component Mediation Analysis (PCMA). Likelihood-based estimators are
introduced for simultaneous estimation of the component projections and effect
parameters. The asymptotic distribution of the estimators is derived for
low-dimensional data. A bootstrap procedure is introduced for inference.
Simulation studies illustrate the superior performance of the proposed
approach. Applied to a proteomics-imaging dataset from the Alzheimer's Disease
Neuroimaging Initiative (ADNI), the proposed framework identifies protein
deposition - brain atrophy - memory deficit mechanisms consistent with existing
knowledge and suggests potential AD pathology by integrating data collected
from different modalities.
