A Natural Goodness-of-Fit Testing Procedure for the Logistic Growth Curve Model

Abstract

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.