Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

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.

Effect of climate factors on the incidence of hand, foot, and mouth disease in Malaysia: A generalized additive mixed model

Climate change is one of the critical determinants affecting life cycles and transmission of most infectious agents,including malaria,cholera,dengue fever,hand,foot,and mouth disease(HFMD),and the recent Corona-virus pandemic.HFMD has been associated with a growing number of outbreaks resulting in fatal complications since the late 1990s.The outbreaks may result from a combination of rapid population growth,climate change,socioeconomic changes,and other lifestyle changes.However,the modeling of climate variability and HFMD remains unclear,particularly in statistical theory development.The statistical relationship between HFMD and climate factors has been widely studied using generalized linear and additive modeling.When dealing with time-series data with clustered variables such as HFMD with clustered states,the independence principle of both modeling approaches may be violated.Thus,a Generalized Additive Mixed Model(GAMM)is used to investigate the relationship between HFMD and climate factors in Malaysia.The model is improved by using a first-order autoregressive term and treating all Malaysian states as a random effect.This method is preferred as it allows states to be modeled as random effects and accounts for time series data autocorrelation.The findings indicate that climate variables such as rainfall and wind speed affect HFMD cases in Malaysia.The risk of HFMD increased in the subsequent two weeks with rainfall below 60 mm and decreased with rainfall exceeding 60 mm.Besides,a two-week lag in wind speeds between 2 and 5 m/s reduced HFMD's chances.The results also show that HFMD cases rose in Malaysia during the inter-monsoon and southwest monsoon seasons but fell during the northeast monsoon.The study's outcomes can be used by public health officials and the general public to raise awareness,and thus,implement effective preventive measures.

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.

Modelling the population fluctuation of winter moth and mottled umber moth in central and northern Germany

Background: Winter moth(Operophtera brumata) and mottled umber moth(Erannis defoliaria) are forest Lepidoptera species characterized by periodic high abundance in a 7–11 year cycle. During outbreak years they cause severe defoliation in many forest stands in Europe. In order to better understand the spatio-temporal dynamics and elucidate possible influences of weather, stand and site conditions, a generalized additive mixed model was developed. The investigated data base was derived from glue band catch monitoring stands of both species in Central and North Germany. From the glue bands only female moth individuals are counted and a hazard code is calculated. The model can be employed to predict the exceedance of a warning threshold of this hazard code which indicates a potential severe defoliation of oak stands by winter moth and mottled umber in the coming spring.Results: The developed model accounts for specific temporal structured effects for three large ecoregions and random effects at stand level. During variable selection the negative model effect of pest control and the positive model effects of mean daily minimum temperature in adult stage and precipitation in early pupal stage were identified.Conclusion: The developed model can be used for short-term predictions of potential defoliation risk in Central and North Germany. These predictions are sensitive to weather conditions and the population dynamics. However, a future extension of the data base comprising further outbreak years would allow for deeper investigation of the temporal and regional patterns of the cyclic dynamics and their causal influences on abundance of winter moth and mottled umber.

The Additive Hazard Mixing Models

This paper is concerned with the aging and dependence properties in the additive hazard mixing models including some stochastic comparisons. Further, some useful bounds of reliability functions in additive hazard mixing models are obtained.

含竞争指标的广义可加混合效应树高-胸径模型

广义可加混合效应模型(GAMM)兼具参数模型与非参数模型的优点,同时适于处理多层次分组数据。通过运用广义可加混合效应模型模拟胸径及树高之间关系,加入竞争因子作为辅助变量,并与传统非线性混合效应模型进行比较,能够为建立树高曲线及提高模型精度提供新方法。根据吉林省汪清林业局金沟岭林场2块100 m×100 m次生混交林样地中的实测单木数据,按照7∶3比例随机划分建模与验证数据。随机效应设定为林木分级,辅助变量选择大于对象木胸高断面积之和(B_(AL))或简单竞争指数(Hegyi指数,H_(EG)),根据随机效应的设定位置共构建15个广义可加混合效应模型,对照模型以Logistic及Richard方程为基础模型,共构建6个非线性混合效应树高-胸径模型。结果表明:所有广义可加混合效应模型均能较好地描述自变量与树高之间的关系,决定系数(R^(2))为0.8897~0.8998,相对均方根误差(R_(RMSE))为17.87%~18.74%,平均绝对误差(M_(AE))为1.7881~1.8745 m,赤池信息量(A_(IC))为4120.42~4162.23,均优于相同自变量下的非线性混合模型,R^(2)平均提高0.005,相对均方根误差、平均绝对误差、赤池信息量分别平均降低0.46%、0.0587 m、41.49。对于验证数据的预测可以看出,模型5具有最小的预测相对均方根误差,为20.28%,同时具有最小的预测平均绝对误差,为2.1038 m。但部分广义可加混合效应模型的预测表现略差于非线性混合模型。综合考虑参数与非参数估计显著性、模型估计精度及预测能力,所有模型中的最优模型为模型5,即以B_(AL)为辅助变量,考虑唯一全局平滑函数并以具有相同扭曲程度的分组水平平滑函数为基础添加随机效应。竞争因子选择B AL作为辅助变量能够提升树高模型的精度,而选择Hegyi指数为辅助变量的促进效果不明显。研究建立的广义可加混合效应树高胸径模型相较于传统非线性混合效应模型具有更高的估计精度及预测效果,B AL适宜作为树高模型的辅助变量来反映林木竞争状况的影响。

基于广义加性混合模型(GAMM)的沙柳特征因子动态变化

【目的】对沙柳特征因子的动态变化进行研究,分析环境因子影响下的地径、枝高动态变化过程。【方法】采用样地调查、样本采集、气象数据收集等手段,基于广义加性混合模型(GAMM),以灌丛、枝条以及二者的嵌套作为随机效应,探究灌木地径、枝高与土壤水分(SM)、年平均降水量(MAP)、年平均气温(MAT)及年龄等影响因子的动态变化规律。【结果】1)对于不考虑随机效应的广义加性模型(GAM),灌木地径与影响因子呈较强的非线性关系(有效自由度E均大于8.20,且P<0.001),枝高仅与时间呈非线性关系,与其他影响因子均为线性关系。2)相较于GAM,GAMM在随机效应的影响下,地径与各影响因子之间非线性显著降低(E变小),但在以灌丛为随机效应的模型中,地径与年平均气温趋于线性关系(E为1),而枝高与时间的非线性关系更强,与其余影响因子仍呈线性关系。3)考虑随机效应的GAMM比GAM的拟合结果更优,且嵌套模式下的GAMM拟合效果最好。【结论】沙柳不同特征因子对环境因子的响应有差异,而相比枝高,地径的变化程度更大。研究结果有助于掌握沙柳特征因子的动态变化对环境因素的响应机制,为进一步探究沙地生境变化过程中植物种群变化、植被演替及植被管理提供科学依据。

中国城市能源电力转型发展战略影响因素量化模型及分析

随着国家碳达峰、碳中和目标的提出,作为二氧化碳主要排放源的城市能源电力消耗,其转型面临着极大的挑战。由于影响因素的指标计算存在极大的主观差异,该文根据中国296个地级市和4个直辖市的面板数据,基于信息熵提出了中国城市能源电力转型的影响因素指标体系。为解决传统线性统计学模型对城市能源电力转型影响因素的解释存在局限性的问题,该文提出了“基于SHAP值神经网络-个体随机效应-时间固定效应的混合模型”,分析了中国城市能源电力转型战略影响因素,阐述了中国城市能源电力转型的特征,并分析了不同区域、不同发展规模等级的城市能源电力转型影响因素的差异性特征和产生原因,提出了有针对性的发展战略建议,为能源电力转型战略的制定提供了理论基础。

考虑时空自相关性的共享电动汽车出行选择影响因素分析

共享电动汽车作为新兴的低碳出行方式,探究其时空分布规律及影响因素,有助于优化交通资源配置,推动城市交通系统的可持续发展。本文首先研究了共享电动汽车订单量的时空自相关特征;其次,基于对传统区域聚合方法的改进,结合对兴趣点(POI)空间分布模式(密度、邻近性、集聚性)的精细化定义,本文建立了综合考虑时空特征、站点属性及建成环境特征的“S-T+S+T+5D”影响因素量化体系;最后,通过构建并对比多个识别模型,本文揭示了各因素的影响程度和作用机理。结果表明:(1)相较于广义线性模型及随机森林模型,考虑地理交互效应的广义可加混合模型能更准确地识别影响因素,有效解释了服务需求的空间依赖特征。(2)影响因素中,站点属性的影响程度最高;车位容量表现出阈值效应,即区域容量高于70会抑制出行需求;站点间的过近距离会加剧内部竞争。(3)共享电动汽车在补充城市公共交通服务不足方面具有一定潜力,尤其在地铁入口2 km外的服务薄弱区域和大型客运枢纽周边。(4)土地混合利用强度呈现倒U型的非线性关系,娱乐场所密度、高校邻近性和医疗场所集聚性均对共享电动汽车出行产生促进作用。研究结果可为运营商进行短期站点优化及长期布局规划提供理论支撑。

基于遗传算法的计算机配色优化模型

针对不透明制品配色外观美观度和市场竞争力问题,提出一种基于遗传算法的计算机配色优化模型,通过模拟自然界中基因进化过程来寻找最优颜色搭配。该模型将颜色搭配问题转化为一个遗传搜索问题,通过不断地迭代和优化,寻找出最佳的色彩组合。依据不同波长不同浓度下着色剂的K/S值、计算机配色理论K-M光学模型以及CIELAB色差计算公式,采用基于遗传算法的计算机配色优化模型,对样品的配方进行细致分析,充分发挥MATLAB对于不同数据处理的优劣,快速、准确地完成数据的处理且寻找配方时循环遍历的思想运用恰当,操作简便且易于推广。

测边网坐标平差的加性乘性混合型误差模型解算

在大地测量数据处理领域,已有加性乘性混合型误差模型参数估计方法的有效性和适用性研究都是建立在模拟算例基础之上,尚无对加性乘性混合误差模型实际测量数据处理应用方面做出研究.文中首次将加性乘性混合型误差模型的参数估计方法应用到测边网平差中,推导基于该模型的平差公式.最后通过算例验证推导的公式在处理大地测量领域实际数据应用中的有效性和可行性.

热带温带玉米群体产量性状遗传力及遗传方差分量的剖析

【目的】评估2个热带群体和7个温带群体的育种价值,并在这些群体之间寻找新的杂种优势模式,为利用这些种质提供有用的科学信息。【方法】采用9个群体的双列杂交设计,得到36个杂交组合;2002～2003年分别在河南省安阳和湖北省十堰进行田间鉴定,获取产量相关性状的试验数据,用混合线性(AD)模型和MINQUE(1)法(minimum norm quadratic unbiased estimation,最小范数二阶无偏估算法)对各性状遗传力、遗传方差分量及其占总表型变异的比率、群体的加性遗传效应和显性遗传效应进行剖析。【结果】联合分析结果显示:各性状的大多数遗传效应值都达到显著(P≤0.05)或极显著水平(P≤0.01)。各遗传方差分量的效应对小区产量贡献大小是显性>显性与环境互作>加性与环境互作>加性;各性状狭义遗传力大小为穗行数>行粒数>穗长>出籽率>百粒重>小区产量,加性效应最好的4个群体是Suwan1(31.69)、Stay green c4(25.44),WBM C4(14.15)和中综4号(10.29);而显性效应比较好的4个组合为3×6(883.65)、1×3(572.20)、1×2(404.2376)和6×7(384.59)。【结论】在温带玉米育种中Suwan1和Stay green c4是最有利用价值的外来种质,它们都与BSSS C9构成杂种优势模式。在育种实践中,可以把Suwan1和Stay green c4杂交重组,并与BSSS C9构成一对温带和热带种质的杂种优势模式,可以进一步进行相互轮回选择。

水稻抽穗期上位效应和QE互作效应的分析

抽穗期是水稻的重要农艺性状,深入了解其遗传效应对水稻育种实践具有重要现实意义。本研究利用基于明恢86×佳辐占、广陆矮×佳辐占两个重组自交系构建的SSR遗传图谱,应用混合线性模型方法对2003年晚季和2005年早季获得的两季水稻抽穗期数据进行QTL定位,并作加性效应、加性×加性上位互作效应及环境互作效应分析。两个群体共检测到10个控制抽穗期的QTL,分别位于1、2、3、6、7和10号染色体上,仅qHD10(广佳重组自交系中为qHD10-1)在两个群体中同时检测到,另检测到11对具有上位效应的互作位点,其中有5个是加性效应显著的QTL。环境互作检测中,发现明佳重组自交系的qHD10和广佳重组自交系的qHD7与环境存在显著互作,贡献率分别为0.34%和2.32%。本研究表明:两群体的抽穗期性状的遗传受环境因素影响较小,特别是明佳组合,较适合作为分子辅助育种的研究材料。

基于AMMI模型的烤烟品种丰产性和稳定性评价

对2010年湖南省烤烟品种区域试验结果进行方差分析,利用AMMI模型进行品种稳定性分析,发现HY-9J、C6212两品种在3个试验点产量均较高,具有稳定丰产的特性,品种HY-5X有较好的丰产性,对各地的适应性很好,HY-9X和HY-9CH丰产性和稳定性较差,利用价值不大;湖南农业大学基地环境对品种的鉴别力较高,而永州烟科所环境对品种的适应性较强。

包含加法模型和混合模型的指数分析体系

统计指数体系分析方法的一个较大不足就是局限于乘法形式的经济方程式,然而经济现象之间的相互联系是多种多样的,目前的统计指数体系分析方法难以应用于形式多样的复杂经济现象的因素分析。本文把基于乘法方式的指数体系称之为指数体系的"乘法模型",并以此为基础,将传统的只包含乘法关系的经济方程式加以扩展,将其推广到可以应用于加减运算的"加法模型"和包含全部四则运算的"混合模型",建立了"广义指数分析模型"。该模型不仅保留了传统统计指数体系的基本结构和基本分析方法,还可以提高统计指数分析的深度和广度,由此可以基本解决统计指数体系分析方法的局限性问题。

316L不锈钢循环特性的有限元分析及疲劳寿命预测

针对316L奥氏体不锈钢进行了低周疲劳试验,采用有限元方法针对材料的循环特性进行了模拟计算。试验结果表明,该材料在不同应变范围下均表现出了明显的循环附加硬化,且硬化程度随着应变范围的增加而更为明显。在Abaqus模拟计算中,使用非线性随动强化与各向同性强化的混合模型描述材料弹塑性行为。不同应变范围下,模拟得到的第二周次下的应力应变曲线与实验结果吻合较好,模拟得到的前20周的最大应力与实验结果的误差与应变范围有关,最大平均误差为3.20%。基于实验结果和模拟结果,采用能量方法进行疲劳寿命预测,预测结果均位于两倍分散带内。

应用基因型与播期互作效应分析水稻光温敏核不育系对光周期和温度的育性敏感性

应用AMMI模型、线性回归模型和系统聚类分析方法分析了9个水稻光温敏核不育系和2个对照不育系(培矮64S,浙农大11S),在9个播期环境下花粉和种子育性的变化动态。从AMMI两维图可直观看到基因型与播期的交互模式,根据最大互作效应主成分轴IPCA1值和花粉育性平均值将不育系分成3个集团。第1集团是培矮64S(1)、浙大21S(10)和浙大22S(11),具有较低花粉育性平均值和较高IPCA1值,表明它们对温度变化比较敏感,且有较大的负向互作效应。第2集团是浙农大11S(2)、浙大4S(3)、浙大5S(4)、浙大7S(6)、浙大8S(7)和浙大9S(8),其花粉育性平均值和互作值相对较低,变动在0.013～0.276间,暗示花粉育性对播期敏感度低。第3集团是浙大6S(5)和浙大10S(9),花粉育性平均值高,互作效应大,该2个不育系尚有分离,且花粉育性对播期反映敏感度高。对光敏型和温敏型不育系而言,基因型IPCA值大小主要反映它们对光周期和温度敏感性强弱。花粉和种子育性在基因型、播期及其互作效应上都存在极显著差异。本文还提出利用育性相对稳定性的定量指标Di界定光温敏核不育系的育性稳定性,分析表明,Di值与育种实践结果较为接近。基于AMMI模型的基因型主效应和互作效应分析可以明确划分不育系的不育期、育性转换期和可育期,并将水稻光敏型与温敏型不育系区分开,因而该模型可为不育系应用于种子生产提供信息和依据。

LKW-Ⅱ温拌剂对橡胶/SBS复合改性沥青流变性能的影响

为研究LKW-Ⅱ温拌对橡胶粉/SBS改性沥青流变性能的影响,通过傅里叶红外光谱(FTIR)实验、动态剪切流变(DSR)试验、多应力重复蠕变恢复(MSCR)实验以及低温弯曲梁流变(BBR)实验,分析LKW-Ⅱ温拌剂对其流变性能的影响。实验结果表明:LKW-Ⅱ温拌剂能够有效控制高温条件下流变性能,当掺量为0.1%时,改善效果最好,实验中其余掺量改善性能较为接近;掺加温拌剂后改性沥青的弹性恢复能力更好,在12.8 kPa应力下,0.1%LKW-Ⅱ掺量不会出现结构损伤,且对应力敏感性最小;LKW-Ⅱ温拌剂能够改善低温条件下流变性能,相同温度下0.3%LKW-Ⅱ掺量内部产生应力最小,应力松弛能力最好。LKW-Ⅱ温拌剂掺量少,能够有效控制高温流变和改善低温流变性能。