Diagnostics in generalized nonlinear models based on maximum L_q-likelihood estimation

In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

Tree mortality and biomass loss in drought-aff ected forests of East Texas,USA

Changes in tree mortality due to severe drought can alter forest structure,composition,dynamics,ecosystem services,carbon fl uxes,and energy interactions between the atmosphere and land surfaces.We utilized long-term(2000‒2017,3 full inventory cycles)Forest Inventory and Analysis(FIA)data to examine tree mortality and biomass loss in drought-aff ected forests for East Texas,USA.Plots that experienced six or more years of droughts during those censuses were selected based on 12-month moderate drought severity[Standardized Precipitation Evaporation Index(SPEI)-1.0].Plots that experienced other disturbances and inconsistent records were excluded from the analysis.In total,222 plots were retained from nearly 4000 plots.Generalized nonlinear mixed models(GNMMs)were used to examine the changes in tree mortality and recruitment rates for selected plots.The results showed that tree mortality rates and biomass loss to mortality increased overall,and across tree sizes,dominant genera,height classes,and ecoregions.An average mortality rate of 5.89%year−1 during the study period could be incited by water stress created by the regional prolonged and episodic drought events.The overall plot and species-group level recruitment rates decreased during the study period.Forest mortality showed mixed results regarding basal area and forest density using all plots together and when analyzed the plots by stand origin and ecoregion.Higher mortality rates of smaller trees were detected and were likely compounded by densitydependent factors.Comparative analysis of drought-induced tree mortality using hydro-meteorological data along with drought severity and length gradient is suggested to better understand the eff ects of drought on tree mortality and biomass loss around and beyond East Texas in the southeastern United States.

Model-based estimation of above-ground biomass in the miombo ecoregion of Zambia

Background：Information on above-ground biomass（AGB） is important for managing forest resource use at local levels,land management planning at regional levels,and carbon emissions reporting at national and international levels.In many tropical developing countries,this information may be unreliable or at a scale too coarse for use at local levels.There is a vital need to provide estimates of AGB with quantifiable uncertainty that can facilitate land use management and policy development improvements.Model-based methods provide an efficient framework to estimate AGB.Methods：Using National Forest Inventory（NFI） data for a^1,000,000 ha study area in the miombo ecoregion,Zambia,we estimated AGB using predicted canopy cover,environmental data,disturbance data,and Landsat 8 OLI satellite imagery.We assessed different combinations of these datasets using three models,a semiparametric generalized additive model（GAM） and two nonlinear models（sigmoidal and exponential）,employing a genetic algorithm for variable selection that minimized root mean square prediction error（RMSPE）,calculated through cross-validation.We compared model fit statistics to a null model as a baseline estimation method.Using bootstrap resampling methods,we calculated 95% confidence intervals for each model and compared results to a simple estimate of mean AGB from the NFI ground plot data.Results：Canopy cover,soil moisture,and vegetation indices were consistently selected as predictor variables.The sigmoidal model and the GAM performed similarly;for both models the RMSPE was -36.8 tonnes per hectare（i.e.,57% of the mean）.However,the sigmoidal model was approximately 30% more efficient than the GAM,assessed using bootstrapped variance estimates relative to a null model.After selecting the sigmoidal model,we estimated total AGB for the study area at 64,526,209 tonnes（＋/- 477,730）,with a confidence interval 20 times more precise than a simple designbased estimate.Conclusions：Our findings demonstrate that NFI data may be combined with freely available satellite imagery and soils data to estimate total AGB with quantifiable uncertainty,while also providing spatially explicit AGB maps useful for management,planning,and reporting purposes.