Additive mixed models to study the effect of tree age and climatic factors on stem radial growth of Eucalyptus trees

The effect of tree age and climatic variables on stem radial growth of two hybrid clones of Eucalyptus was determined using longitudinal data from eastern South Africa.The stem radius of was measured weekly as the response variable.In addition to tree age,average weekly temperature,solar radiation,relative humidity and wind speed were simultaneously recorded with total rainfall at the site.An additive mixed effects model that incorporates a non-parametric smooth function was used.The results of the analysis indicate that the relationship between stem radius and each of the covariates can be explained by nonlinear functions.Models that account for the effect of clone and season together with their interaction in the parametric part of the additive mixed model were also fitted.The interaction between clone and season was not significant in all cases.For analyzing the joint effect all the covariates,additive mixed models that included two or more covariates were fitted.A significant effect of tree age was found in all cases.Although tree age was the key determinant of stem radial growth,weather variables also had a significant effect that was dependent on season.

Modelling tree mortality across diameter classes using mixedeffects zero-inflated models

The mortality of trees across diameter class model is a useful tool for predicting changes in stand structure.Mortality data commonly contain a large fraction of zeros and general discrete models thus show more errors.Based on the traditional Poisson model and the negative binomial model,different forms of zero-inflated and hurdle models were applied to spruce-fir mixed forests data to simulate the number of dead trees.By comparing the residuals and Vuong test statistics,the zero-inflated negative binomial model performed best.A random effect was added to improve the model accuracy;however,the mixed-effects zero-inflated model did not show increased advantages.According to the model principle,the zeroinflated negative binomial model was the most suitable,indicating that the"0"events in this study,mainly from the sample"0",i.e.,the zero mortality data,are largely due to the limitations of the experimental design and sample selection.These results also show that the number of dead trees in the diameter class is positively correlated with the number of trees in that class and the mean stand diameter,and inversely related to class size,and slope and aspect of the site.

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.

Retrospective analysis of chronic hepatitis C in untreated patients with nonlinear mixed effects model

It is well known that viral load of the hepatitis C virus (HCV) is related to the efficacy of interferon therapy. The complex biological parameters that impact on viral load are essentially unknown. The current knowledge of the hepatitis C virus does not provide a mathematical model for viral load dynamics within untreated patients. We car-ried out an empirical modelling to investigate whether different fluctuation patterns exist and how these patterns (if exist) are related to host-specific factors. Data was prospectively col-lected from 147 untreated patients chronically infected with hepatitis C, each contributing be-tween 2 to 10 years of measurements. We pro-pose to use a three parameter logistic model to describe the overall pattern of viral load fluctua-tion based on an exploratory analysis of the data. To incorporate the correlation feature of longitu-dinal data and patient to patient variation, we introduced random effects components into the model. On the basis of this nonlinear mixed ef-fects modelling, we investigated effects of host-specific factors on viral load fluctuation by in-corporating covariates into the model. The pro-posed model provided a good fit for describing fluctuations of viral load measured with varying frequency over different time intervals. The aver-age viral load growth time was significantly dif-ferent between infection sources. There was a large patient to patient variation in viral load as-ymptote.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.

Posterior propriety in nonparametric mixed efects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance compo- nents and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.

Ba（d）^o-Ba（d）^o Mixing and New Physics Effects in a Top Quark Two-Higgs Doublet Model

We calculate the new physics contributions to the neutral Bd^o and Ba^o meson mass splitting △Md and △Ma induced by the box diagrams involving the charged-Higgs bosons in the top quark two-Higgs doublet model （T2HDM）. Using the precision data, we obtain the bounds on the parameter space of the T2HDM： （a） For fixed MH = 400 GeV and 5= [0°, 60°], the upper bound on tan β is tan β≤ 30 after the inclusion of major theoretical uncertainties; （b） For the case of tan β≤ 20, a light charged Higgs boson with a mass around 300 GeV is allowed; and （c） The bounds on tan β and MH are strongly correlated： a smaller （larger） tan β means a lighter （heavier） charged Higgs boson.

Nonparametric Estimation in Linear Mixed Models with Uncorrelated Homoscedastic Errors

Today, Linear Mixed Models (LMMs) are fitted, mostly, by assuming that random effects and errors have Gaussian distributions, therefore using Maximum Likelihood (ML) or REML estimation. However, for many data sets, that double assumption is unlikely to hold, particularly for the random effects, a crucial component in which assessment of magnitude is key in such modeling. Alternative fitting methods not relying on that assumption (as ANOVA ones and Rao’s MINQUE) apply, quite often, only to the very constrained class of variance components models. In this paper, a new computationally feasible estimation methodology is designed, first for the widely used class of 2-level (or longitudinal) LMMs with only assumption (beyond the usual basic ones) that residual errors are uncorrelated and homoscedastic, with no distributional assumption imposed on the random effects. A major asset of this new approach is that it yields nonnegative variance estimates and covariance matrices estimates which are symmetric and, at least, positive semi-definite. Furthermore, it is shown that when the LMM is, indeed, Gaussian, this new methodology differs from ML just through a slight variation in the denominator of the residual variance estimate. The new methodology actually generalizes to LMMs a well known nonparametric fitting procedure for standard Linear Models. Finally, the methodology is also extended to ANOVA LMMs, generalizing an old method by Henderson for ML estimation in such models under normality.

用Mixed和Nlmixed过程建立混合生长模型

本文用5块不同密度样地的树高生长资料,根据线性和非线性混合模型理论,利用SAS的Mixed过程和Nlmixed过程,分别拟合线性混合模型和非线性混合树高生长模型。根据预测值和固定效应同时绘制出不同密度下的高生长曲线和平均高生长曲线,充分显示了混合模型的优势,即它可以同时反映总体的平均变化趋势和个体之间的差异。

双反应变量重复测量资料分析及MIXED过程实现

目的探讨双反应变量重复测量资料的分析原理与方法及SAS软件PROCMIXED过程的应用。方法结合双反应变量重复测量数据的特点,采用SAS软件的MIXED过程对其进行分析,建立线性混合效应模型。结果该模型不仅考虑了每个变量多次重复测量结果之间的相关性,也考虑了两个变量之间的相关性,同时还引入固定效应和随机效应,结合数据特征分析,结果更为可信。结论对双反应变量非独立重复测量资料,可以把数据之间的相关性分解为重复测量间相关性和变量间相关性两部分,采用MIXED过程不仅可对其相关性做出明晰深入的分析,且可保证数据分析结果解释更符合实际。

基于SAS NLMIXED的广义线性混合效应模型在发病率数据Meta分析中的应用

目的:介绍利用SAS软件中的PROC NLMIXED过程步实现发病率数据的META分析方法。方法:基于广义线性混合效应模型(GLMM)的二项式-正态模型(BN)和泊松-正态模型(PNM)等,可方便地实现发病率数据的随机效应Meta分析,尤其当Meta分析纳入含0事件研究时。以Schutz等发表的血管内皮生长因子受体酪氨酸激酶抑制剂治疗的癌症患者发生致命不良事件风险的系统评价作为实例数据,利用SAS软件实现发病率数据的META分析,并提供编程代码。结果:对于含0事件研究,使用PNM模型进行Meta分析,无需进行连续校正法。删除0事件研究对于PNM模型影响较大。与标准正态模型相比,PNM和BNM模型给出的效应值更高,而P值则更小,具有更好的灵敏性。结论:基于广义线性混合效应模型,利用SAS的PROCNLMIXED实现发病率数据Meta分析是优选的方法。

Toward managing mixed-species stands： from parametrization to prescription

A better understanding and a more quantitative design of mixed-species stands will contribute to more integrative and goal-oriented research in mixed-species forests. Much recent work has indicated that the structure and growth of mixed species forests may fundamentally differ from monocultures. Here we suggest how to progress from the present accumulation of phenomenological findings to a design of mixed-species stands and advanced silvicultural prescriptions by means of modelling. First, the knowledge of mixing effects on the structure and growth at the stand, species, and individual tree level is reviewed, with a focus on those findings that are most essential for suitable modelling and silvicultural designs and the regulation of mixed stands as opposed to monocultures. Then, the key role of growth models, stand simulators, and scenario assessments for designing mixed species stands is discussed The next section illustrates that existing forest stand growth models require some fundamental modifications to become suitable for both monocultures and mixed-species stands. We then explore how silvicultural prescriptions derived from scenario runs would need to be both quantified and simplified for transfer to forest management and demonstrated in training plots. Finally, we address the main remaining knowledge gaps that could be remedied through empirical research.

Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η ≡ η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η ∝ R_λ^(1.39) obtained from the numerical data.

Credit Risk Model Taking Account of Inflation and Its Contribution to Macroeconomic Discussion on Effect of Inflation on Output Growth

We use Extended Merton model(EMM)for estimating the firm’s credit risks in the presence of inflation.We show quantitatively that inflation is an influential factor making either a benign or adverse effect on the firm’s survival,supporting at the microeconomic level New Keynesian findings of the nonlinear inflation effect on output growth.Lower inflation increasing the firm’s expected rate of return can raise its mean year returns and decrease its default probability.Higher inflation,decreasing the expected rate return,makes the opposite effect.The magnitude of the adverse effect depends on the firm strength:for a steady firm,this effect is small,whereas for a weaker firm,it can be fatal.EMM is the only model taking account of inflation.It can be useful for banks or insurance companies estimating credit risks of commercial borrowers over the debt maturity,and for the firm’s management planning long-term business operations.

Can a multistage approach improve individual tree mortality predictions across the complex mixed-species and managed forests of eastern North America?

Tree mortality plays a fundamental role in the dynamics of forest ecosystems,yet it is one of the most difficult phenomena to accurately predict.Various modeling strategies have been developed to improve individual tree mortality predictions.One less explored strategy is the use of a multistage modeling approach.Potential improvements from this approach have remained largely unknown.In this study,we developed a novel multistage approach and compared its performance in individual tree mortality predictions with a more conventional approach using an identical individual tree mortality model formulation.Extensive permanent plot data(n=9442)covering the Acadian Region of North America and over multiple decades(1965–2014)were used in this study.Our results indicated that the model behavior with the multistage approach better depicted the observed mortality and showed a notable improvement over the conventional approach.The difference between the observed and predicted numbers of dead trees using the multistage approach was much smaller when compared with the conventional approach.In addition,tree survival probabilities predicted by the multistage approach generally were not significantly different from the observations,whereas the conventional approach consistently underestimated mortality across species and overestimated tree survival probabilities over the large range of DBH in the data.The new multistage approach also predictions of zero mortality in individual plots,a result not possible in conventional models.Finally,the new approach was more tolerant of modeling errors because it based estimates on ranked tree mortality rather than error-prone predicted values.Overall,this new multistage approach deserves to be considered and tested in future studies.

The Assessment of Non-Linear Effects in Clinical Research

Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusions: 1) Logit and probit transformations are often successfully used to mimic a linear model. Logistic regression, Cox regression, Poisson regression, and Markow modeling are examples of logit transformation;2) Either the x- or y-axis or both of them can be logarithmically transformed. Also Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data;3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis;4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

Competitive effect, but not competitive response, varies along a climatic gradient depending on tree species identity

Background: Understanding the role of species identity in interactions among individuals is crucial for assessing the productivity and stability of mixed forests over time. However, there is limited knowledge concerning the variation in competitive effect and response of different species along climatic gradients. In this study, we investigated the importance of climate, tree size, and competition on the growth of three tree species: spruce(Picea abies), fir(Abies alba), and beech(Fagus sylvatica), and examined their competitive response and effect along a climatic gradient.Methods: We selected 39 plots distributed across the European mountains with records of the position and growth of 5,759 individuals. For each target species, models relating tree growth to tree size, climate and competition were proposed. Competition was modelled using a neighbourhood competition index that considered the effects of inter-and intraspecific competition on target trees. Competitive responses and effects were related to climate.Likelihood methods and information theory were used to select the best model.Results: Our findings revealed that competition had a greater impact on target species growth than tree size or climate. Climate did influence the competitive effects of neighbouring species, but it did not affect the target species? response to competition. The strength of competitive effects varied along the gradient, contingent on the identity of the interacting species. When the target species exhibited an intermediate competitive effect relative to neighbouring species, both higher inter-than intraspecific competitive effects and competition reduction occurred along the gradient. Notably, species competitive effects were most pronounced when the target species' growth was at its peak and weakest when growing conditions were far from their maximum.Conclusions: Climate modulates the effects of competition from neighbouring trees on the target tree and not the susceptibility of the target tree to competition. The modelling approach should be useful in future research to expand our knowledge of how competition modulates forest communities across environmental gradients.