Goodness-of-fit testing for the Gompertz growth curve model

Abstract

In this paper we develop some natural “goodness-of-fit” tests for the Gompertz growth curve model (GGCM) based on the empirical estimate of relative growth rate (RGR). Existing approaches of goodness-of-fit tests for growth curve models are mainly based on finite differences of the size data (Bhattacharya et al., Commun Stat Theory Methods 38:340–363, 2009). In growth curve studies the underlying model is often better identified through the rate profile than the size profile (Zotin, Can Bull Fish Aquat Sci 213:27–37, 1985; Bhattacharya et al., J Appl Probab Stat, 4:239–253, 2009; Sibly et al., Science 309:607–610, 2005). The parameters of the GGCM are easily interpretable and a test based on the RGR can be derived more easily by assuming a simple correlation structure among RGRs, rather than modeling the size variable directly (White and Brisbin, Growth 44:97–111, 1980; Sandland and McGilchrist, Biometrics 35:255–271, 1979). We therefore expect that a goodness-of-fit test for the GGCM based on the RGR will have substantial practical value. The tests for the GGCM developed here are based on the finite differences of appropriate functions of the empirical relative growth rate. The performance of the theory developed is illustrated through simulation and with several sets of real data.