Gamma Regression Model with Nuisance Baseline for Tree Growth Data

Abstract

In regression model for longitudinal data such as forest growth, it is important to model the growth behavior and to evaluate the effects of covariates such as the impact of environmental factors on growth behavior. In this paper, we consider a situation where the primary interest is centered on the effects of covariates. Though the time trend of the baseline is non-negligible, it is out of scope for this study. Considering age dependent growth behavior as baseline, we can reconstruct the models to include a nuisance baseline. Then it is possible only to estimate the regression coefficients of covariates without modeling the shape for the baseline growth behavior. The linear regression model assumes normality and homoscedasticity for error terms. However, forest growth data sometimes fail to meet the above assumptions because of data non-negativity. In this paper, we develop a regression model for longitudinal non-negative continuous data, using gamma distribution. We apply the proposed method to a forest growth data on Sugi (Cryptomeria japonica) at Hoshino village in Japan.