Extended spatial logit models of deforestation due to population and relief energy in East Asia

Tanaka and Nishii (2005) figured out that deforestation can be elucidated quantitatively by nonlinear logit regression models in four East Asian test fields: forest areal rate F as a target variable, and human population size (N) and relief energy (R: difference of minimum altitude from the maximum in a sampled area) as explanatory variables, whose functional forms had been suggested by step functions fitted to one-kilometer square high precision grid-cell data firstly in Japan (n=6825): log F/1-F = β₀ + g(N) + h(R) + error, where g(N) and h(R) are regression functions of explanatory variables N and R, respectively. Likelihood functions with spatial dependency were derived, and several deforestation models were selected for the application to four regions in East Asia by calculating relative appropriateness to data. For the measure of appropriateness, Akaike's Information Criterion (AIC) was used. To formulate East-Asian dataset, landcover dataset estimated from NOAA observations available at UNEP, Tsukuba for F, gridded population of the world of CIESIN, US for N, and GTOPO30 of USGS for R, were used. The resolutions were matched by taking their common multiple of 20 minute square. Tanaka and Nishii (ibid.) omitted the data with F = 0.0 and F = 1.0 to employ the logit models. Unfortunately the reduction of the data size for regression led to instability of parameter estimation. As for the test field in Harbin, China, n = 76 for 0.0 < F < 1.0, but n = 504 for 0.0 ≤ F ≤ 1.0. In this study, we therefore compare the models based on all data, especially with F = 1.0, by the following extended logit transformation with two additional positive parameters of κ and λ: log F+κ/1-F+λ = β₀ + g(N) + h(R) + error. Obvious improvements in terms of relative appropriateness to data are observed in extended logit models.