Incorporating shape constraints in generalized additive modelling of the height-diameter relationship for Norway spruce

Background： Measurements of tree heights and diameters are essential in forest assessment and modelling. Tree heights are used for estimating timber volume, site index and other important variables related to forest growth and yield, succession and carbon budget models. However, the diameter at breast height （dbh） can be more accurately obtained and at lower cost, than total tree height. Hence, generalized height-diameter （h-d） models that predict tree height from dbh, age and other covariates are needed. For a more flexible but biologically plausible estimation of covariate effects we use shape constrained generalized additive models as an extension of existing h-d model approaches. We use causal site parameters such as index of aridity to enhance the generality and causality of the models and to enable predictions under projected changeable climatic conditions. Methods： We develop unconstrained generalized additive models （GAM） and shape constrained generalized additive models （SCAM） for investigating the possible effects of tree-specific parameters such as tree age, relative diameter at breast height, and site-specific parameters such as index of aridity and sum of daily mean temperature during vegetation period, on the h-d relationship of forests in Lower Saxony, Germany. Results： Some of the derived effects, e.g. effects of age, index of aridity and sum of daily mean temperature have significantly non-linear pattern. The need for using SCAM results from the fact that some of the model effects show partially implausible patterns especially at the boundaries of data ranges. The derived model predicts monotonically increasing levels of tree height with increasing age and temperature sum and decreasing aridity and social rank of a tree within a stand, The definition of constraints leads only to marginal or minor decline in the model statistics like AIC An observed structured spatial trend in tree height is modelled via 2-dimensional surface fitting. Conclusions： We demonstrate that the SCAM approach allows optimal regression modelling flexibility similar to the standard GAM but with the additional possibility of defining specific constraints for the model effects. The longitudinal character of the model allows for tree height imputation for the current status of forests but also for future tree height prediction.

Study of monthly variations in primary production and their relationships with environmental factors in the Daya Bay based on a general additive model

In this study, the horizontal and vertical distribution of primary production(PP) and its monthly variations were described based on field data collected from the Daya Bay in January–December of 2016. The relationships between PP and environmental factors were analyzed using a general additive model(GAM). Significant seasonal differences were observed in the horizontal distribution of PP, while vertical distribution showed a relatively consistent unimodal pattern. The monthly average PP(calculated by carbon) ranged from 48.03 to 390.56 mg/(m~2·h),with an annual average of 182.77 mg/(m~2·h). The highest PP was observed in May and the lowest in November.Additionally, the overall trend in PP was spring>summer>winter>autumn, and spring PP was approximately three times that of autumn PP. GAM analysis revealed that temperature, bottom salinity, phytoplankton, and photosynthetically active radiation(PAR) had no significant relationships with PP, while longitude, depth, surface salinity, chlorophyll a(Chl a) and transparency were significantly correlated with PP. Overall, the results presented herein indicate that monsoonal changes and terrestrial and offshore water systems have crucial effects on environmental factors that are associated with PP changes.

Simulating Potential Distribution of Tamarix chinensis in Yellow River Delta by Generalized Additive Models

There are typical ecosystems of littoral wetlands in the Yellow River Delta.In order to study the relationships between Tamarix chinensis and environmental variables and to predict T.chinensis potential distribution in the Yellow River Delta,641 vegetation samples and 964 soil samples were collected in the area in October of 2004,2005,2006 and 2007.The contents of soil organic matter,total phosphorus,salt,and soluble potassium were determined.Then,the analyzed data were interpolated into spatial raster data by Kriging interpolation method.Meanwhile,the digital elevation model,soil type map and landform unit map of the Yellow River Delta were also collected.Generalized Additive Models(GAMs) were employed to build species-environment model and then simulate the potential distribution of T.chinensis.The results indicated that the distribution of T.chinensis was mainly limited by soil salt content,total soil phosphorus content,soluble potassium content,soil type,landform unit,and elevation.The distribution probability of T.chinensis was produced with a lookup table generated by Grasp Module(based on GAMs) in software ArcView GIS 3.2.The AUC(Area Under Curve) value of validation and cross-validation of ROC(Receive Operating Characteristic) were both higher than 0.8,which suggested that the established model had a high precision for predicting species distribution.

Probabilistic Precipitation Forecasting Based on Ensemble Output Using Generalized Additive Models and Bayesian Model Averaging

A probabilistic precipitation forecasting model using generalized additive models （GAMs） and Bayesian model averaging （BMA） was proposed in this paper. GAMs were used to fit the spatial-temporal precipitation models to individual ensemble member forecasts. The distributions of the precipitation occurrence and the cumulative precipitation amount were represented simultaneously by a single Tweedie distribution. BMA was then used as a post-processing method to combine the individual models to form a more skillful probabilistic forecasting model. The mixing weights were estimated using the expectation-maximization algorithm. The residual diagnostics was used to examine if the fitted BMA forecasting model had fully captured the spatial and temporal variations of precipitation. The proposed method was applied to daily observations at the Yishusi River basin for July 2007 using the National Centers for Environmental Prediction ensemble forecasts. By applying scoring rules, the BMA forecasts were verified and showed better performances compared with the empirical probabilistic ensemble forecasts, particularly for extreme precipitation. Finally, possible improvements and a^plication of this method to the downscaling of climate change scenarios were discussed.

Longitudinal height-diameter curves for Norway spruce, Scots pine and silver birch in Norway based on shape constraint additive regression models

Background： Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce （Piceo abies （L.） Karst.）, Scots pine （Pinus sylvestris L.） and silver birch （Betula pendula Roth） in Norwa are presented. The Norwegian National Forest Inventory （NFI） is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputatio in forest inventories as well as future tree height predictions in growth and yield scenario simulations. Methods： Generalized additive mixed models （gamm） are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand ag as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models （scare） were fit tc incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity. Results： Model comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. / two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatial correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive. Conclusions： In this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scare may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.

Modeling deformation resistance for hot rolling based on generalized additive model

A model of deformation resistance during hot strip rolling was established based on generalized additive model.Firstly,a data modeling method based on generalized additive model was given.It included the selection of dependent variable and independent variables of the model,the link function of dependent variable and smoothing functional form of each independent variable,estimating process of the link function and smooth functions,and the last model modification.Then,the practical modeling test was carried out based on a large amount of hot rolling process data.An integrated variable was proposed to reflect the effects of different chemical compositions such as carbon,silicon,manganese,nickel,chromium,niobium,etc.The integrated chemical composition,strain,strain rate and rolling temperature were selected as independent variables and the cubic spline as the smooth function for them.The modeling process of deformation resistance was realized by SAS software,and the influence curves of the independent variables on deformation resistance were obtained by local scoring algorithm.Some interesting phenomena were found,for example,there is a critical value of strain rate,and the deformation resistance increases before this value and then decreases.The results confirm that the new model has higher prediction accuracy than traditional ones and is suitable for carbon steel,microalloyed steel,alloyed steel and other steel grades.

RCV-based error density estimation in the ultrahigh dimensional additive model

In this paper,we mainly study how to estimate the error density in the ultrahigh dimensional sparse additive model,where the number of variables is larger than the sample size.First,a smoothing method based on B-splines is applied to the estimation of regression functions.Second,an improved two-stage refitted crossvalidation(RCV)procedure by random splitting technique is used to obtain the residuals of the model,and then the residual-based kernel method is applied to estimate the error density function.Under suitable sparse conditions,the large sample properties of the estimator,including the weak and strong consistency,as well as normality and the law of the iterated logarithm,are obtained.Especially,the relationship between the sparsity and the convergence rate of the kernel density estimator is given.The methodology is illustrated by simulations and a real data example,which suggests that the proposed method performs well.

Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters

This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

Grouping tree species to estimate basal area increment in temperate multispecies forests in Durango,Mexico

Multispecies forests have received increased scientific attention,driven by the hypothesis that biodiversity improves ecological resilience.However,a greater species diversity presents challenges for forest management and research.Our study aims to develop basal area growth models for tree species cohorts.The analysis is based on a dataset of 423 permanent plots(2,500 m^(2))located in temperate forests in Durango,Mexico.First,we define tree species cohorts based on individual and neighborhood-based variables using a combination of principal component and cluster analyses.Then,we estimate the basal area increment of each cohort through the generalized additive model to describe the effect of tree size,competition,stand density and site quality.The principal component and cluster analyses assign a total of 37 tree species to eight cohorts that differed primarily with regard to the distribution of tree size and vertical position within the community.The generalized additive models provide satisfactory estimates of tree growth for the species cohorts,explaining between 19 and 53 percent of the total variation of basal area increment,and highlight the following results:i)most cohorts show a"rise-and-fall"effect of tree size on tree growth;ii)surprisingly,the competition index"basal area of larger trees"had showed a positive effect in four of the eight cohorts;iii)stand density had a negative effect on basal area increment,though the effect was minor in medium-and high-density stands,and iv)basal area growth was positively correlated with site quality except for an oak cohort.The developed species cohorts and growth models provide insight into their particular ecological features and growth patterns that may support the development of sustainable management strategies for temperate multispecies forests.

Optimization of environmental variables in habitat suitability modeling for mantis shrimp Oratosquilla oratoria in the Haizhou Bay and adjacent waters

Habitat suitability index(HSI)models have been widely used to analyze the relationship between species abundance and environmental factors,and ultimately inform management of marine species.The response of species abundance to each environmental variable is different and habitat requirements may change over life history stages and seasons.Therefore,it is necessary to determine the optimal combination of environmental variables in HSI modelling.In this study,generalized additive models(GAMs)were used to determine which environmental variables to be included in the HSI models.Significant variables were retained and weighted in the HSI model according to their relative contribution(%)to the total deviation explained by the boosted regression tree(BRT).The HSI models were applied to evaluate the habitat suitability of mantis shrimp Oratosquilla oratoria in the Haizhou Bay and adjacent areas in 2011 and 2013–2017.Ontogenetic and seasonal variations in HSI models of mantis shrimp were also examined.Among the four models(non-optimized model,BRT informed HSI model,GAM informed HSI model,and both BRT and GAM informed HSI model),both BRT and GAM informed HSI model showed the best performance.Four environmental variables(bottom temperature,depth,distance offshore and sediment type)were selected in the HSI models for four groups(spring-juvenile,spring-adult,falljuvenile and fall-adult)of mantis shrimp.The distribution of habitat suitability showed similar patterns between juveniles and adults,but obvious seasonal variations were observed.This study suggests that the process of optimizing environmental variables in HSI models improves the performance of HSI models,and this optimization strategy could be extended to other marine organisms to enhance the understanding of the habitat suitability of target species.

Linearity extensions of the market model:a case of the top 10 cryptocurrency prices during the pre‑COVID‑19 and COVID‑19 periods

This research investigates the appropriateness of the linear specification of the market model for modeling and forecasting the cryptocurrency prices during the pre-COVID-19 and COVID-19 periods.Two extensions are offered to compare the performance of the linear specification of the market model(LMM),which allows for the measurement of the cryptocurrency price beta risk.The first is the generalized additive model,which permits flexibility in the rigid shape of the linearity of the LMM.The second is the time-varying linearity specification of the LMM(Tv-LMM),which is based on the state space model form via the Kalman filter,allowing for the measurement of the time-varying beta risk of the cryptocurrency price.The analysis is performed using daily data from both time periods on the top 10 cryptocurrencies by adjusted market capitalization,using the Crypto Currency Index 30(CCI30)as a market proxy and 1-day and 7-day forward predictions.Such a comparison of cryptocurrency prices has yet to be undertaken in the literature.The empirical findings favor the Tv-LMM,which outperforms the others in terms of modeling and forecasting performance.This result suggests that the relationship between each cryptocurrency price and the CCI30 index should be locally instead of globally linear,especially during the COVID-19 period.

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.

A spatially-explicit count data regression for modeling the density of forest cockchafer(Melolontha hippocastani) larvae in the Hessian Ried(Germany)

Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are

Inference Procedures on the Generalized Poisson Distribution from Multiple Samples: Comparisons with Nonparametric Models for Analysis of Covariance (ANCOVA) of Count Data

Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.

Subgroup Analysis for Longitudinal Data via Semiparametric Additive Mixed Effects Model

This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal data,thus it could reveal which covariate contributes to the existence of subgroups among population.A backfitting combined with k-means algorithm was developed to detect subgroup structure on each covariate and estimate each semiparametric additive component across subgroups.A Bayesian information criterion is employed to estimate the actual number of groups.The efficacy and accuracy of the proposed procedure in identifying the subgroups and estimating the regression functions are illustrated through numerical studies.In addition,the authors demonstrate the usefulness of the proposed method with applications to PBC data and Industrial Portfolio's Return data and provide meaningful partitions of the populations.

Infl uence of altitude and tree class on climate-growth relationships in a larch plantation in subtropical China

Precise quantifi cation of climate-growth relationships can make a major contribution to scientifi c forest management.However,whether diff erences in the response of growth to climate at diff erent altitudes remains unclear.To answer this,264 trees of Larix kaempferi from 88 plots,representing diff erent altitudinal ranges(1000-2100 m)and tree classes were sampled and used to develop tree-ring chronologies.Tree-ring growth(TRG)was either positively(dominant)or negatively(intermediate and suppressed)correlated with climate in diff erent tree classes at diff erent altitudes.TRG was strongly correlated with growing season at low altitudes,but was less sensitive to climate at middle altitudes.It was mainly limited by precipitation and was highly sensitive to climate at low altitudes.Climate-growth relationships at high altitudes were opposite compared to those at low altitudes.TRG of dominant trees was more sensitive to climate change compared to intermediate and suppressed trees.Climate factors(annual temperatures;moisture,the number of frost-free days)had diff erent eff ects on tree-ring growth of diff erent tree classes along altitudinal gradients.It was concluded that the increase in summer temperatures decreased water availability,resulting in a signifi cant decline in growth rates after 2005 at lower altitudes.L.kaempferi is suitable for planting in middle altitudes and dominant trees were the best sampling choice for accurately assessing climate-growth relationships.

A Review of Residual Stress and Deformation Modeling for Metal Additive Manufacturing Processes

A metal additive manufacturing process results in a nearly net-shaped fabrication of parts directly from digital data.A local heat source melts the deposited material,and a part is built layer-by-layer.Residual stress and de-formation are critical issues experienced by additively manufactured parts.Modeling the additive manufacturing process provides important insights and can help determine an optimal build plan so as to minimize residual stress formation.Various approaches have been used for modeling of residual stresses,ranging from high-fidelity models to simplified models,for quicker results.This paper provides a state-of-the-art review of the approaches used to numerically model residual deformation and stresses in structures built using additive manufacturing.Fur-thermore,it describes the physical causes of residual-stress generation in an additively manufactured structure.

Growth and form of Quercus robur and Fraxinus excelsior respond distinctly different to initial growing space: results from 24-year-old Nelder experiments

Initial growing space is of critical importance to growth and quality development of individual trees. We investigated how mortality, growth （diameter at breast height, total height）, natural pruning （height to first dead and first live branch and branchiness） and stem and crown form of 24-year-old pedunculate oak （Quercus robur [L.]） and European ash （Fraxinus excelsior [L.]） were affected by initial spacing. Data were recorded from two replicate single-species Nelder wheels located in southern Germany with eight initial stocking regimes varying from 1,020 to 30,780 seedlings·ha？1. Mortality substantially decreased with increasing initial growing space but significantly differed among the two species, averaging 59% and 15% for oak and ash plots, respectively. In contrast to oak, the low self-thinning rate found in the ash plots over the investigated study period resulted in a high number of smaller intermediate or suppressed trees, eventually retarding individual tree as well as overall stand development. As a result, oak gained greater stem dimensions throughout all initial spacing regimes and the average height of ash significantly increased with initial growing space. The survival of lower crown class ashes also appeared to accelerate self-pruning dynamics. In comparison to oak, we observed less dead and live primary branches as well as a smaller number of epicormic shoots along the first 6 m of the lower stem of dominant and co-dominant ashes in all spacing regimes. Whereas stem form of both species was hardly affected by initial growing space, the percentage of brushy crowns significantly increased with initial spacing in oak and ash. Our findings suggest that initial stockings of ca. 12,000 seedlings per hectare in oak and 2,500 seedlings per hectare in ash will guarantee a sufficient number of at least 300 potential crop trees per hectare in pure oak and ash plantations at the end of the self-thinning phase, respectively. If the problem of epicormic shoots and inadequate self-pruning can be controlled with trainer species, the initial stocking may be reduced significantly in oak.

National-scale data-driven rainfall induced landslide susceptibility mapping for China by accounting for incomplete landslide data

China is one of the countries where landslides caused the most fatalities in the last decades. The threat that landslide disasters pose to people might even be greater in the future, due to climate change and the increasing urbanization of mountainous areas. A reliable national-scale rainfall induced landslide susceptibility model is therefore of great relevance in order to identify regions more and less prone to landsliding as well as to develop suitable risk mitigating strategies. However, relying on imperfect landslide data is inevitable when modelling landslide susceptibility for such a large research area. The purpose of this study is to investigate the influence of incomplete landslide data on national scale statistical landslide susceptibility modeling for China. In this context, it is aimed to explore the benefit of mixed effects modelling to counterbalance associated bias propagations. Six influencing factors including lithology, slope,soil moisture index, mean annual precipitation, land use and geological environment regions were selected based on an initial exploratory data analysis. Three sets of influencing variables were designed to represent different solutions to deal with spatially incomplete landslide information: Set 1(disregards the presence of incomplete landslide information), Set 2(excludes factors related to the incompleteness of landslide data), Set 3(accounts for factors related to the incompleteness via random effects). The variable sets were then introduced in a generalized additive model(GAM: Set 1 and Set 2) and a generalized additive mixed effect model(GAMM: Set 3) to establish three national-scale statistical landslide susceptibility models: models 1, 2 and 3. The models were evaluated using the area under the receiver operating characteristics curve(AUROC) given by spatially explicit and non-spatial cross-validation. The spatial prediction pattern produced by the models were also investigated. The results show that the landslide inventory incompleteness had a substantial impact on the outcomes of the statistical landslide susceptibility models. The cross-validation results provided evidence that the three established models performed well to predict model-independent landslide information with median AUROCs ranging from 0.8 to 0.9.However, although Model 1 reached the highest AUROCs within non-spatial cross-validation(median of 0.9), it was not associated with the most plausible representation of landslide susceptibility. The Model 1 modelling results were inconsistent with geomorphological process knowledge and reflected a large extent the underlying data bias. The Model 2 susceptibility maps provided a less biased picture of landslide susceptibility. However, a lower predicted likelihood of landslide occurrence still existed in areas known to be underrepresented in terms of landslide data(e.g., the Kuenlun Mountains in the northern Tibetan Plateau). The non-linear mixed-effects model(Model 3) reduced the impact of these biases best by introducing bias-describing variables as random effects. Among the three models, Model 3 was selected as the best national-scale susceptibility model for China as it produced the most plausible portray of rainfall induced landslide susceptibility and the highest spatially explicit predictive performance(median AUROC of spatial cross validation 0.84) compared to the other two models(median AUROCs of 0.81 and 0.79, respectively). We conclude that ignoring landslide inventory-based incompleteness can entail misleading modelling results and that the application of non-linear mixed-effect models can reduce the propagation of such biases into the final results for very large areas.