Nonlinear Mixed-Effects Models for Repairable Systems Reliability

Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.

Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech（Fagus orientalis Lipsky） in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria： adjusted R^2（R^2_（adj））,root mean square error（RMSE）,relative RMSE（%RMSE）,bias,and relative bias（%bias） criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R^2（0.81）,RMSE（3.7 m）,%RMSE（12.9）,bias（0.8）,%Bias（2.79） than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.

Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities,where variables of interest may include not only scalar(point-like)indicators,but also functional(curve-like)and compositional(pie-like)ones.In many research topics,the variables are also chronologically collected across individuals,which falls into the paradigm of longitudinal analysis.The complicated nature of data,however,increases the difficulty of modeling these variables under the classic longitudinal frame-work.In this study,we investigate the linear mixed-effects model(LMM)for such complex data.Different types of variables arefirst consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them,which gener-alizes the theoretical framework of LMM to complex data analysis.A number of simulation studies indicate the feasibility and effectiveness of the proposed model.We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.

BLUP Estimation of Linear Mixed-effects Models with Measurement Errors and Its Applications to the Estimation of Small Areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.

Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch( Larix olgensis ) plantations in northeast China

Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.

Frequentist model averaging for linear mixed-effects models

Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.

Maximum likelihood estimation of nonlinear mixed-effects models with crossed random effects by combining first-order conditional linearization and sequential quadratic programming

Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well-resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

Aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders:progress of experimental models based on disease pathogenesis

Neuromyelitis optica spectrum disorders are neuroinflammatory demyelinating disorders that lead to permanent visual loss and motor dysfunction.To date,no effective treatment exists as the exact causative mechanism remains unknown.Therefore,experimental models of neuromyelitis optica spectrum disorders are essential for exploring its pathogenesis and in screening for therapeutic targets.Since most patients with neuromyelitis optica spectrum disorders are seropositive for IgG autoantibodies against aquaporin-4,which is highly expressed on the membrane of astrocyte endfeet,most current experimental models are based on aquaporin-4-IgG that initially targets astrocytes.These experimental models have successfully simulated many pathological features of neuromyelitis optica spectrum disorders,such as aquaporin-4 loss,astrocytopathy,granulocyte and macrophage infiltration,complement activation,demyelination,and neuronal loss;however,they do not fully capture the pathological process of human neuromyelitis optica spectrum disorders.In this review,we summarize the currently known pathogenic mechanisms and the development of associated experimental models in vitro,ex vivo,and in vivo for neuromyelitis optica spectrum disorders,suggest potential pathogenic mechanisms for further investigation,and provide guidance on experimental model choices.In addition,this review summarizes the latest information on pathologies and therapies for neuromyelitis optica spectrum disorders based on experimental models of aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders,offering further therapeutic targets and a theoretical basis for clinical trials.

Landslide Susceptibility Mapping Using RBFN-Based Ensemble Machine Learning Models

This study was aimed to prepare landslide susceptibility maps for the Pithoragarh district in Uttarakhand,India,using advanced ensemble models that combined Radial Basis Function Networks(RBFN)with three ensemble learning techniques:DAGGING(DG),MULTIBOOST(MB),and ADABOOST(AB).This combination resulted in three distinct ensemble models:DG-RBFN,MB-RBFN,and AB-RBFN.Additionally,a traditional weighted method,Information Value(IV),and a benchmark machine learning(ML)model,Multilayer Perceptron Neural Network(MLP),were employed for comparison and validation.The models were developed using ten landslide conditioning factors,which included slope,aspect,elevation,curvature,land cover,geomorphology,overburden depth,lithology,distance to rivers and distance to roads.These factors were instrumental in predicting the output variable,which was the probability of landslide occurrence.Statistical analysis of the models’performance indicated that the DG-RBFN model,with an Area Under ROC Curve(AUC)of 0.931,outperformed the other models.The AB-RBFN model achieved an AUC of 0.929,the MB-RBFN model had an AUC of 0.913,and the MLP model recorded an AUC of 0.926.These results suggest that the advanced ensemble ML model DG-RBFN was more accurate than traditional statistical model,single MLP model,and other ensemble models in preparing trustworthy landslide susceptibility maps,thereby enhancing land use planning and decision-making.

Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

Mixed-Effects Parametric Proportional Hazard Model with Generalized Log-Logistic Baseline Distribution

Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.

Prognostic model for esophagogastric variceal rebleeding after endoscopic treatment in liver cirrhosis: A Chinese multicenter study

BACKGROUND Rebleeding after recovery from esophagogastric variceal bleeding(EGVB)is a severe complication that is associated with high rates of both incidence and mortality.Despite its clinical importance,recognized prognostic models that can effectively predict esophagogastric variceal rebleeding in patients with liver cirrhosis are lacking.AIM To construct and externally validate a reliable prognostic model for predicting the occurrence of esophagogastric variceal rebleeding.METHODS This study included 477 EGVB patients across 2 cohorts:The derivation cohort(n=322)and the validation cohort(n=155).The primary outcome was rebleeding events within 1 year.The least absolute shrinkage and selection operator was applied for predictor selection,and multivariate Cox regression analysis was used to construct the prognostic model.Internal validation was performed with bootstrap resampling.We assessed the discrimination,calibration and accuracy of the model,and performed patient risk stratification.RESULTS Six predictors,including albumin and aspartate aminotransferase concentrations,white blood cell count,and the presence of ascites,portal vein thrombosis,and bleeding signs,were selected for the rebleeding event prediction following endoscopic treatment(REPET)model.In predicting rebleeding within 1 year,the REPET model ex-hibited a concordance index of 0.775 and a Brier score of 0.143 in the derivation cohort,alongside 0.862 and 0.127 in the validation cohort.Furthermore,the REPET model revealed a significant difference in rebleeding rates(P<0.01)between low-risk patients and intermediate-to high-risk patients in both cohorts.CONCLUSION We constructed and validated a new prognostic model for variceal rebleeding with excellent predictive per-formance,which will improve the clinical management of rebleeding in EGVB patients.

Exploiting fly models to investigate rare human neurological disorders

Rare neurological diseases,while individually are rare,collectively impact millions globally,leading to diverse and often severe neurological symptoms.Often attributed to genetic mutations that disrupt protein function or structure,understanding their genetic basis is crucial for accurate diagnosis and targeted therapies.To investigate the underlying pathogenesis of these conditions,researchers often use non-mammalian model organisms,such as Drosophila(fruit flies),which is valued for their genetic manipulability,cost-efficiency,and preservation of genes and biological functions across evolutionary time.Genetic tools available in Drosophila,including CRISPR-Cas9,offer a means to manipulate gene expression,allowing for a deep exploration of the genetic underpinnings of rare neurological diseases.Drosophila boasts a versatile genetic toolkit,rapid generation turnover,and ease of large-scale experimentation,making it an invaluable resource for identifying potential drug candidates.Researchers can expose flies carrying disease-associated mutations to various compounds,rapidly pinpointing promising therapeutic agents for further investigation in mammalian models and,ultimately,clinical trials.In this comprehensive review,we explore rare neurological diseases where fly research has significantly contributed to our understanding of their genetic basis,pathophysiology,and potential therapeutic implications.We discuss rare diseases associated with both neuron-expressed and glial-expressed genes.Specific cases include mutations in CDK19 resulting in epilepsy and developmental delay,mutations in TIAM1 leading to a neurodevelopmental disorder with seizures and language delay,and mutations in IRF2BPL causing seizures,a neurodevelopmental disorder with regression,loss of speech,and abnormal movements.And we explore mutations in EMC1 related to cerebellar atrophy,visual impairment,psychomotor retardation,and gain-of-function mutations in ACOX1 causing Mitchell syndrome.Loss-of-function mutations in ACOX1 result in ACOX1 deficiency,characterized by very-long-chain fatty acid accumulation and glial degeneration.Notably,this review highlights how modeling these diseases in Drosophila has provided valuable insights into their pathophysiology,offering a platform for the rapid identification of potential therapeutic interventions.Rare neurological diseases involve a wide range of expression systems,and sometimes common phenotypes can be found among different genes that cause abnormalities in neurons or glia.Furthermore,mutations within the same gene may result in varying functional outcomes,such as complete loss of function,partial loss of function,or gain-of-function mutations.The phenotypes observed in patients can differ significantly,underscoring the complexity of these conditions.In conclusion,Drosophila represents an indispensable and cost-effective tool for investigating rare neurological diseases.By facilitating the modeling of these conditions,Drosophila contributes to a deeper understanding of their genetic basis,pathophysiology,and potential therapies.This approach accelerates the discovery of promising drug candidates,ultimately benefiting patients affected by these complex and understudied diseases.

A promising approach for quantifying focal stroke modeling and assessing stroke progression:optical resolution photoacoustic microscopy photothrombosis

To investigate the mechanisms underlying the onset and progression of ischemic stroke,some methods have been proposed that can simultaneously monitor and create embolisms in the animal cerebral cortex.However,these methods often require complex systems and the effect of age on cerebral embolism has not been adequately studied,although ischemic stroke is strongly age-related.In this study,we propose an optical-resolution photoacoustic microscopy-based visualized photothrombosis methodology to create and monitor ischemic stroke in mice simultaneously using a 532 nm pulsed laser.We observed the molding process in mice of different ages and presented age-dependent vascular embolism differentiation.Moreover,we integrated optical coherence tomography angiography to investigate age-associated trends in cerebrovascular variability following a stroke.Our imaging data and quantitative analyses underscore the differential cerebrovascular responses to stroke in mice of different ages,thereby highlighting the technique's potential for evaluating cerebrovascular health and unraveling age-related mechanisms involved in ischemic strokes.

LoRa Sense:Sensing and Optimization of LoRa Link Behavior Using Path-Loss Models in Open-Cast Mines

The Internet of Things(IoT)has orchestrated various domains in numerous applications,contributing significantly to the growth of the smart world,even in regions with low literacy rates,boosting socio-economic development.This study provides valuable insights into optimizing wireless communication,paving the way for a more connected and productive future in the mining industry.The IoT revolution is advancing across industries,but harsh geometric environments,including open-pit mines,pose unique challenges for reliable communication.The advent of IoT in the mining industry has significantly improved communication for critical operations through the use of Radio Frequency(RF)protocols such as Bluetooth,Wi-Fi,GSM/GPRS,Narrow Band(NB)-IoT,SigFox,ZigBee,and Long Range Wireless Area Network(LoRaWAN).This study addresses the optimization of network implementations by comparing two leading free-spreading IoT-based RF protocols such as ZigBee and LoRaWAN.Intensive field tests are conducted in various opencast mines to investigate coverage potential and signal attenuation.ZigBee is tested in the Tadicherla open-cast coal mine in India.Similarly,LoRaWAN field tests are conducted at one of the associated cement companies(ACC)in the limestone mine in Bargarh,India,covering both Indoor-toOutdoor(I2O)and Outdoor-to-Outdoor(O2O)environments.A robust framework of path-loss models,referred to as Free space,Egli,Okumura-Hata,Cost231-Hata and Ericsson models,combined with key performance metrics,is employed to evaluate the patterns of signal attenuation.Extensive field testing and careful data analysis revealed that the Egli model is the most consistent path-loss model for the ZigBee protocol in an I2O environment,with a coefficient of determination(R^(2))of 0.907,balanced error metrics such as Normalized Root Mean Square Error(NRMSE)of 0.030,Mean Square Error(MSE)of 4.950,Mean Absolute Percentage Error(MAPE)of 0.249 and Scatter Index(SI)of 2.723.In the O2O scenario,the Ericsson model showed superior performance,with the highest R^(2)value of 0.959,supported by strong correlation metrics:NRMSE of 0.026,MSE of 8.685,MAPE of 0.685,Mean Absolute Deviation(MAD)of 20.839 and SI of 2.194.For the LoRaWAN protocol,the Cost-231 model achieved the highest R^(2)value of 0.921 in the I2O scenario,complemented by the lowest metrics:NRMSE of 0.018,MSE of 1.324,MAPE of 0.217,MAD of 9.218 and SI of 1.238.In the O2O environment,the Okumura-Hata model achieved the highest R^(2)value of 0.978,indicating a strong fit with metrics NRMSE of 0.047,MSE of 27.807,MAPE of 27.494,MAD of 37.287 and SI of 3.927.This advancement in reliable communication networks promises to transform the opencast landscape into networked signal attenuation.These results support decision-making for mining needs and ensure reliable communications even in the face of formidable obstacles.

Reduced mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor contributes to neurodegeneration in a model of spinal and bulbar muscular atrophy pathology

Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen receptor protein,characterized by polyglutamine expansion,is prone to misfolding and forms aggregates in both the nucleus and cytoplasm in the brain in spinal and bulbar muscular atrophy patients.These aggregates alter protein-protein interactions and compromise transcriptional activity.In this study,we reported that in both cultured N2a cells and mouse brain,mutant androgen receptor with polyglutamine expansion causes reduced expression of mesencephalic astrocyte-de rived neurotrophic factor.Overexpressio n of mesencephalic astrocyte-derived neurotrophic factor amelio rated the neurotoxicity of mutant androgen receptor through the inhibition of mutant androgen receptor aggregation.Conversely.knocking down endogenous mesencephalic astrocyte-derived neurotrophic factor in the mouse brain exacerbated neuronal damage and mutant androgen receptor aggregation.Our findings suggest that inhibition of mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor is a potential mechanism underlying neurodegeneration in spinal and bulbar muscular atrophy.

Physiology and health assessment,risk balance,and model for endstage liver disease scores:Postoperative outcome of liver transplantation

BACKGROUND Liver transplantation aims to increase the survival of patients with end-stage liver diseases and improve their quality of life.The number of organs available for transplantation is lower than the demand.To provide fair organ distribution,predictive mortality scores have been developed.AIM To compare the Acute Physiology and Chronic Health Evaluation IV(APACHE IV),balance of risk(BAR),and model for end-stage liver disease(MELD)scores as predictors of mortality.METHODS Retrospective cohort study,which included 283 adult patients in the postoperative period of deceased donor liver transplantation from 2014 to 2018.RESULTS The transplant recipients were mainly male,with a mean age of 58.1 years.Donors were mostly male,with a mean age of 41.6 years.The median cold ischemia time was 3.1 hours,and the median intensive care unit stay was 5 days.For APACHE IV,a mean of 59.6 was found,BAR 10.7,and MELD 24.2.The 28-day mortality rate was 9.5%,and at 90 days,it was 3.5%.The 28-day mortality prediction for APACHE IV was very good[area under the curve(AUC):0.85,P<0.001,95%CI:0.76-0.94],P<0.001,BAR(AUC:0.70,P<0.001,95%CI:0.58–0.81),and MELD(AUC:0.66,P<0.006,95%CI:0.55-0.78),P<0.008.At 90 days,the data for APACHE IV were very good(AUC:0.80,P<0.001,95%CI:0.71–0.90)and moderate for BAR and MELD,respectively,(AUC:0.66,P<0.004,95%CI:0.55–0.77),(AUC:0.62,P<0.026,95%CI:0.51–0.72).All showed good discrimination between deaths and survivors.As for the best value for liver transplantation,it was significant only for APACHE IV(P<0.001).CONCLUSION The APACHE IV assessment score was more accurate than BAR and MELD in predicting mortality in deceased donor liver transplant recipients.

Modeling and Comprehensive Review of Signaling Storms in 3GPP-Based Mobile Broadband Networks:Causes,Solutions,and Countermeasures

Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.

Generalized or general mixed-effect modelling of tree morality of Larix gmelinii subsp.principis-rupprechtii in Northern China

Tree mortality models play an important role in predicting tree growth and yield,but existing mortality models for Larix gmelinii subsp.principis-rupprechtii,an important species used for regeneration and afforestation in northern China,have overlooked potential regional influences on tree mortality.This study used data acquired from 102 temporary sample plots(TSPs)in natural stands of Prince Rupprecht larch in the state-owned Guandi Mountain Forest(n=67)and state-owned Boqiang Forest(n=35)in northern China.To model stand-level tree mortality,we compared seven model forms of county data.Three continuous(dominant height,plot mean diameter,and basal area per hectare)and one dummy variable with two levels(region)were used as fixed effects variables.Tree morality variations caused by forest blocks were accounted for using forest blocks as a random effect in selected models.Results showed that tree mortality significantly positively correlated with stand basal area and dominant height,but negatively correlated with stand mean diameter.Incorporating both the dummy variables and random effects into the tree mortality models significantly increased the fitting improvements,and Hurdle Poisson mixed-effects model showed the most attractive fit statistics(largest R^(2)and smallest RMSE)when employing leave-one-out cross-validation.These mixed-effects dummy variable models will be useful for accurately predicting Larix tree mortality in different regions.