Empirical detection of parameter variation in growth curve models using interval specific estimators

Quantitative assessment of the growth of biological organisms has produced many mathematical equations, and over time, it has become an independent research area. Many efforts have been given on statistical identification of the correct growth model from a given data set, and have generated many model selection criteria as well. Every growth equation is unique in terms of mathematical structure; however, one model may serve as a close approximation of another equation by some appropriate choice of the parameter(s). It is still an interesting problem to select the best estimating model from a set of models whose shapes are similar in nature. In this manuscript, we utilize an existing model selection criterion which reduces the number of model fitting exercises substantially. By using continuous transformation of parameters, interconnections between many existing equations can be made. We consider four basic models, namely, exponential, logistic, confined exponential, and theta-logistic, as a starting point. Starting with these basic models, we utilize the idea of interval-specific rate parameter (ISRP), proposed by Bhowmick et al. (J. Biol. Phys., Vol 40, pp. 71–95, 2014) to obtain the best model for real data sets. The ISRP profiles of the parameters of simpler models indicate the nature of variation in parameters as a function of time, enabling the experimenter to extrapolate the inference to more complex models. Our proposed methodology significantly reduces the efforts involved in model fitting exercises. Connections have been built amongst many growth equations, which were studied independently to date by researchers. We believe that this work will be helpful for practitioners in the field of growth study. The proposed idea is verified by using simulated, and real data sets.