A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units - Héctor Echavarria-Heras; Cecilia Leal-Ramirez; Enrique Villa-Diharce; Juan Ramón Castro-Rodríguez (Applied Sciences, 2019)
(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi−Sugeno−Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols.