Growth Analysis Using Nuisance Baseline

Abstract

Abstract:In the growth analysis, when the research focus is environmental factor, the longitudinal growth part is essential but not our main interest. In such a situation, by regarding age dependent growth behavior as baseline, we can reconstruct the models to include a nuisance baseline. Such an approach makes it possible only to estimate parameters of interest (environmental factors) without information about the nuisance baseline. After estimating the main parameters, we can graph the baseline trend, nonparametrically. In this paper, the growth model was generated using data on Sugi (Cryptomeria Japonica) at Hoshino village in Japan. The results from this study showed an inverse relationship between altitude and tree growth, without modeling for longitudinal growth, i.e., higher altitude resulted in less tree growth. In practice the results can be explained by our knowledge based on two established facts. The first is based on the direction of water and nutrients flow from a higher elevation and accumulates at a lower elevation, and the second can be explained by the fact that trees are suppressed by strong winds at higher elevations. By using this data, we compared our model with traditionally used parametric growth models which are constructed without nuisance baseline. In statistical terms, both the variance of residual and the standard error for parameters in the proposed model were found to be the smallest among the other parametric alternatives. This implies that the estimate is stable in our model that is one of the advantage for statistical inference aspect.

Gamma Regression Model with Nuisance Baseline for Tree Growth Data

“…Thus, DBH growth tends to decrease with increasing altitude and the relative ratio of DBH growth against one-unit difference in scaled altitude is estimated as: exp(−0.177) ≈ 0.838. This result is similar to those of Kamo et al (2017). In their paper, they indicated two reasons for the negative effect of altitude: water and nutrients flow (Sands and Mulligan 1990), and strong winds in high altitude areas (King 1986).…”

“…Note that the gamma distribution can be approximated by normal distribution with mean µ and variance ϕ for large shape parameter ν (or small dispersion parameter ϕ). Therefore, from the growth data of tree height, it is also possible to fit a regression model with normal error in Kamo et al (2017).…”

“…It can be seen that the variances of DBH and volume increase with age. This fails to meet the assumption in Kamo et al (2017). We adopt the altitude for explanatory variable as in Kamo et al (2017) and analyze the growth behaviors of these three variables using the proposed regression model: [11]…”

“…Satoh and Tonda (2016) introduced nuisance baseline in growth curve models (Kollo and von Rosen, 2005). Kamo et al (2017) proposed regression model with nuisance baseline for forest growth data. These approaches were based on linear regression models using data on continuous outcomes.…”