Power of Parametric and Semi-parametric Models to Represent Real Life Data Situations

Real-life data situations are not easy to model because of the uncertainty and variation prevailing in the natural system and also due to the presence of the interaction of unknown factors interplaying and governing the entire real-life phenomena. Modelling fish dynamics has been considered as an indispensable area of research by the biologists, bio-researchers, applied and bio-mathematicians to understand the science behind the growth of fish. Valuable contributions in this area are available in different monographs, books and journals. The models prevalent for use are, generally, of two types - deterministic and non-deterministic. The celebrated Von Bertalanffy (VB) model, fitted deterministically, is the main thurst area of research till now to the active biology-modellers and is also considered as the most appropriate one. Non-deterministic models are widely applicable for their inherent capability to provide better representations owing to the fact that these imbibe elements of uncertainty inbuilt in their systems of operation. Efforts in this area call upon using a log transformation on a relationship representing an exponential relationship between the variables, weight and length of fish. The object of data modelling is to generate fitted values as close as possible to the observed values. Longitudinal data modelling can be achieved by parametric and nonparametric modelling. Deterministic fitting of VB equation ensures achieving precision (desired closeness) only up to a certain degree of precision. Precise modular representation of such data comes as a useful complement. This paper deals with non-linear fit (achieved through non-linear optimization), a parametric approach, of the VB model. Also introduced here is the application of distribution free approach, like, nonparametric model fitting, which does not involve parameters (which need to be estimated from the data). Such models assign more importance to data points and the span of the regions surrounding those. This paper exposes the power (in respect of achieving better representation) of non-linear fitting of the celebrated VB model and also of the nonparametric model fitting approaches (spline, loess, kernel), when these have been called upon to represent the growth dynamics of Puntius sophore (Ham), reared in experimental hoopnets. Indeed, these models are found to have more representative power many times, when compared against different performance criteria, to explain and model the real-life data situations. The focus of the paper points to the potentiality of the parametric and semi-parametric models to model many data-situations very closely and appropriately.