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STS486 R. Ayesha A. et al.
                  can help mitigate model overfit. In the empirical analysis, the BIC associated
                  with the penalized and unpenalized models were similar, but the penalized
                  model  was  much  simpler  and  could  be  explained  from  an  ecological
                  perspective.
                     Potential improvements to model selection consistency could be attained
                  by using an adjusted BIC. For example, Hui et al. (2015) suggest the extended
                  regularization information criteria (ERIC), a modification of the BIC, where the
                  model complexity term is also a function of ̃. Although we studied network
                  sizes motivated by ecological network sizes, extending the framework to the
                  high dimensional setting where K≫N likely only requires another modification
                  of  the  BIC,  tailored  specifically  for  the  high  dimensional  case.  Regardless,
                  regularized grouped DM regression is a  useful tool for ecologists and can
                  provide insights into the functional traits driving species’ interactions.

                  References
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                  4.  Crea, C. (2017). Variable Selection for Grouped DM regression,
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