Growth curve models are frequently used in a wide range of disciplines such as biology, ecology, demography, population dynamics etc. Living organisms exhibit different types of growth patterns. To analyze these curves investigators need adequate parametric models. A proper identification of the growth model is very important for the appropriateness of the subsequent analysis. In this paper we develop a natural goodness of fit test for the logistic growth curve model. Bhattacharya et al. (2004, 2008) have provided some interesting approaches based on Hill's method of finite differences (Hill 1968) in case of the exponential and exponential polynomial growth curve models. But in case of the logistic model their approach leads to very complicated and cumbersome mathematics. Basu and Bhattacharj6ee (2006) have presented an alternative method to test the goodness of fit for the exponential growth curve model by directly modeling the relative growth rate rather than the size variable itself. In this paper we extend that approach for testing goodness of fit in case of the logistic growth curve model.
Growth is a fundamental aspect of a living organism. Growth curves play an important role in explaining the complex dynamics of growth trajectories. The development of a large class of growth models provides more choices to explain complex growth dynamics. However, identifying a suitable growth curve from a broad class of growth models becomes a challenging task. Relative Growth Rate (RGR) is the most popular measure in the growth-related study. It serves many purposes in growth curve literature, including constructing any goodness-of-fit index of some growth dynamics. However, the goodness-of-fit test based on RGR is restricted to only simple growth models. This study aims to develop a new growth rate function, instantaneous maturity rate (IMR), which can play an important role in identifying growth models. We have explored that the measure has synergy in mathematical form with IMR. However, unlike the hazard rate, IMR is a random variable when the size/RGR variable is stochastic. We have derived the exact and asymptotic distribution of this measure under the Gaussian setup of both the size and RGR variables. We have constructed a goodness-of-fit test for the extended Gompertz growth model based on the instantaneous maturity rate. We have checked the performance of the test through simulation studies as well as real data. AMS 2010 subject classifications: 62Mxx, 92Bxx, 62P10
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