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Abstract:
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In regression analysis of the market share data four main models are prevalent: multinomial logistic regression, attraction models, Dirichlet covariance models, and compositional regression. We extend this with a completely novel regression perspective, labelled combinatorial regression, based on combining n-tuplets of sampling units into groups and treating them in abstract simplicial complex spaces. The novel perspective, estimated in combination with Multivariate Distance Matrix Regression approach, allows extensive number of perspectives in the analysis for any n-tuplet and using as measure of disparity between the units (to construct regressors) different divergence measures. It also allows applications to very small datasets as the number of units can be expressed in terms of factorial products of units of original sample. We provide the analysis of new approach for different n-tuple combinations using generalized Jensen-Shannon divergence measures and explore the approach using asymptotic analysis and Monte Carlo simulation. We present application to sessile hard-substrate marine organisms image data from Italian coast areas which allows extension to relative abundance data.
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