Motivated by our work in pediatric research, a new partial least squares regression (PLSR) model is proposed to analyze the relationship between multiple collinear fitness and health outcomes and a series of collinear predictors, including compositional data related to daily physical activity. We develop a probabilistic version of PLSR that uses heavy tailed distributions to specify the likelihood function. The model parameters are estimated using an EM algorithm. This PLSR model is extended to tensor variate data, using the Tucker product and a variation of the multilinear tensor regression model. This extension allows us to model our collaborators' data longitudinally. All our models are implemented in Julia, a dynamic and high performance numerical computing language.