generalized additive mixed modeling

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R语言实现广义加性模型GeneralizedAdditiveModels（GAM）入门

R语⾔实现⼴义加性模型GeneralizedAdditiveModels（GAM）⼊门转载请说明。

下⾯进⾏⼀个简单的⼊门程序学习。

先新建⼀个txt，叫做 Rice_insect.txt ，内容为：（⽤制表符Tab）Year Adult Day Precipitation1973 27285 15 387.31974 239 14 126.31975 6164 11 165.91976 2535 24 184.91977 4875 30 166.91978 9564 24 146.01979 263 3 24.01980 3600 21 23.01981 21225 13 167.01982 915 12 67.01983 225 17 307.01984 240 40 295.01985 5055 25 266.01986 4095 15 115.01987 1875 21 140.01988 12810 32 369.01989 5850 21 167.01990 4260 39 270.8 Adult为累计蛾量，Day为降⾬持续天数，Precipitation为降⾬量。

输⼊代码：library(mgcv) #加载mgcv软件包，因为gam函数在这个包⾥Data <- read.delim("Rice_insect.txt") #读取txt数据，存到Data变量中Data <- as.matrix(Data) #转为矩阵形式#查看Data数据：Data，查看第2列：Data[,2]，第2⾏：Data[2,]Adult<-Data[,2]Day<-Data[,3]Precipitation<-Data[,4]result1 <- gam(log(Adult) ~ s(Day)) #此时，Adult为相应变量，Day为解释变量summary(result1) #输出计算结果此时可以看到：Family: gaussianLink function: identityFormula:log(Adult) ~ s(Day)Parametric coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 7.9013 0.3562 22.18 4.83e-13 ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Approximate significance of smooth terms:edf Ref.df F p-values(Day) 1.713 2.139 0.797 0.473R-sq.(adj) = 0.0471 Deviance explained = 14.3%GCV score = 2.6898 Scale est. = 2.2844 n = 18Day的影响⽔平p-value=0.473，解释能⼒为14.3%，说明影响不明显。

generalized additive models算法 -回复

generalized additive models算法-回复什么是generalized additive models算法（GAM）？Generalized additive models（GAM）是一种统计模型，常用于探索数据集中观测值和自变量之间的非线性关系。

与传统的线性回归模型相比，GAM允许自变量与响应变量之间的关系不是简单的线性关系，而是通过非线性函数的组合来描述。

这使得GAM能够更好地捕捉数据中的复杂关系。

GAM的基本构成元素是非线性平滑函数。

平滑函数是一种将输入变量映射到响应变量的函数，它可以捕捉到输入变量与响应变量之间的非线性关系。

GAM通过将多个平滑函数相加来构建整个模型，每个平滑函数负责描述某个变量与响应变量之间的关系。

这样，GAM可以将复杂的非线性问题分解为多个简单的非线性问题，从而更好地适应数据的特点。

GAM的优点是它既能够处理连续型自变量，也可以处理类别型自变量。

对于连续型自变量，可以使用平滑函数来建模。

对于类别型自变量，可以将其转化为一组虚拟变量，并分别使用平滑函数描述各个类别与响应变量之间的关系。

在构建GAM时，选择合适的平滑函数以及平滑函数的自由度是非常重要的。

过低的自由度可能导致模型过于简单，无法准确拟合数据；而过高的自由度可能导致模型过度拟合，无法进行准确的预测。

因此，选择适当的平滑函数和自由度需要借助交叉验证等方法进行模型选择。

GAM还可以用于处理缺失数据。

在模型估计过程中，可以利用观测到的数据对模型进行拟合，然后使用拟合的模型对缺失数据进行插补。

这样可以最大程度地利用现有数据来估计缺失数据的值，提高模型的准确性。

另一个GAM的优点是其解释性。

用于建模的平滑函数可以通过绘制曲线来展示，并解释为特定变量对响应变量的影响。

这对于帮助我们理解数据背后的机制和关系非常有帮助。

当然，GAM也有一些限制。

首先，它对于高维数据的建模能力有限。

当输入变量非常多时，GAM的模型复杂度可能变得很高，而且建模的过程也变得困难。

gamm模型的回归代码和方法

gamm模型的回归代码和方法Gamm模型，全称为Generalized Additive Mixed Model，是一种广义可加混合模型。

它结合了广义线性模型（Generalized Linear Model，GLM）和广义可加模型（Generalized Additive Model，GAM），同时考虑了固定效应和随机效应。

Gamm模型在许多实际问题中广泛应用，尤其适用于非线性关系和具有复杂结构的数据。

GAM模型是一种非参数的回归模型，它通过将预测变量的非线性部分用平滑函数来建模。

GAM模型的基本思想是，将自变量的非线性关系分解为一系列平滑的函数，然后将这些函数与线性部分结合起来，以建立预测模型。

通过使用平滑函数，GAM模型能够捕捉到自变量与因变量之间的非线性关系，并且能够较好地适应数据。

GAM模型通常使用的平滑函数有很多种，其中一种常用的平滑函数是样条函数。

样条函数是一种通过在数据上拟合分段多项式来建模非线性关系的方法。

在R语言中，我们可以使用mgcv包来拟合GAM 模型，并使用gam函数来建立模型。

下面是一个使用gamm模型进行回归分析的例子：```R# 导入mgcv包library(mgcv)# 读取数据data <- read.csv("data.csv")# 建立gamm模型model <- gamm(y ~ s(x1) + s(x2) + s(x3) + (1 | random_effect), data = data)# 查看模型结果summary(model)```在这个例子中，我们假设y是因变量，x1、x2、x3是自变量，random_effect是随机效应。

通过使用gamm函数，我们可以将自变量的非线性关系用样条函数来建模，同时考虑随机效应的影响。

在建立模型之后，我们可以使用summary函数来查看模型的结果。

summary函数会给出模型的系数估计值、标准误差、显著性水平等信息，帮助我们评估模型的拟合效果和变量的重要性。

generalized-additive-models算法

generalized additive models算法Generalized Additive Models (GAM), 或者广义可加模型，是统计学中一种常用的非参数回归方法。

它结合了广义线性模型（GLM）和非线性平滑方法，能够适应非线性、非正态分布和非常数方差的数据。

本文将详细介绍GAM算法，并一步一步回答与其相关的问题。

第一部分：GAM算法的介绍1.1 什么是广义可加模型？广义可加模型是一种广义线性模型的扩展形式，它可以处理非线性关系，且不需要假设预测变量之间的交互作用具有线性形式。

广义可加模型通过将预测变量的非线性部分表示为平滑函数的线性组合，从而实现对非线性关系的建模。

1.2 广义可加模型的优点有哪些？广义可加模型具有以下优点：- 不需要假设任何先验形式的数据分布- 可以处理非参数回归问题- 可以通过平滑函数拟合数据的非线性关系- 可以同时考虑多个预测变量的影响第二部分：GAM模型的建立步骤2.1 数据准备首先需要准备用于建模的数据集。

数据集应包含一个响应变量和一个或多个预测变量。

2.2 平滑函数的选择根据数据的特点选择适当的平滑函数，常见的平滑函数包括样条函数（splines）、局部回归（loess）和样条光滑（smoothing splines）等。

平滑函数的选择要考虑数据的特点以及模型的拟合程度。

2.3 模型的拟合与评估通过最小化损失函数来拟合模型，常用的损失函数包括最小二乘法（OLS）和广义最小二乘法（GLS）。

拟合完模型后，需要对模型进行评估，比较观察值和预测值之间的差异。

2.4 平滑度调整根据模型的拟合结果，根据需要调整平滑的程度，以达到最佳的拟合效果。

平滑度的调整可以通过调整平滑参数或者选择不同的平滑函数来实现。

第三部分：GAM模型的应用3.1 连续型响应变量的预测GAM模型在连续型响应变量的预测方面表现出色。

例如，可以使用GAM 模型预测一个人的年龄对其收入的影响，还可以预测某种化学物质的浓度与环境因素之间的关系。

生物药剂学与药物动力学专业词汇

生物药剂学与药物动力学专业词汇※<A>Absolute bioavailability, F 绝对生物利用度Absorption 吸收Absorption pharmacokinetics 吸收动力学Absorption routes 吸收途径Absorption rate 吸收速率Absorption rate constant 吸收速率常数Absorptive epithelium 吸收上皮Accumulation 累积Accumulation factor 累积因子Accuracy 准确度Acetylation 乙酰化Acid glycoprotein 酸性糖蛋白Active transport 主动转运Atomic absorption spectrometry 原子吸收光谱法Additive 加和型Additive errors 加和型误差Adipose 脂肪Administration protocol 给药方案Administration route 给药途径Adverse reaction 不良反应Age differences 年龄差异Akaike’s information criterion, AIC AIC判据Albumin 白蛋白All-or-none response 全或无效应Amino acid conjugation 氨基酸结合Analog 类似物Analysis of variance, ANOVA ANOVA方差分析Anatomic Volume 解剖学体积Antagonism 拮抗作用Antiproliferation assays 抑制增殖法Apical membrane 顶端表面Apoprotein 载脂蛋白脱辅基蛋白Apparatus 仪器Apparent volume of distribution 表观分布容积Area under the curve, AUC 曲线下面积Aromatisation 芳构化Artery 动脉室Artifical biological membrane 人工生物膜Aryl 芳基Ascorbic acid 抗坏血酸维生素C Assistant in study design 辅助实验设计Average steady-state plasma drug concentration 平均稳态血浆药物浓度Azo reductase 含氮还原酶※<B>Backward elimination 逆向剔除Bacteria flora 菌丛Basal membrane 基底膜Base structural model 基础结构模型Basolateral membrane 侧底膜Bayesian estimation 贝易斯氏评估法Bayesian optimization 贝易斯优化法Bile 胆汁Billiary clearance 胆汁清除率Biliary excretion 胆汁排泄Binding 结合Binding site 结合部位Bioactivation 生物活化Bioavailability, BA 生物利用度Bioequivalence, BE 生物等效性Biological factors 生理因素Biological half life 生物半衰期Biological specimen 生物样品Biomembrane limit 膜限速型Biopharmaceutics 生物药剂学Bioequivalency criteria 生物等效性判断标准Biotransformation 生物转化Biowaiver 生物豁免Blood brain barrier, BBB BBB血脑屏障Blood clearance 血液清除率Blood flow rate-limited models 血流速度限速模型Blood flux in tissue 组织血流量Body fluid 体液Buccal absorption of drug 口腔用药的吸收Buccal mucosa 口腔粘膜颊粘膜Buccal spray formulation 口腔喷雾制剂※<C>Capacity limited 容量限制Carrier mediated transport 载体转运Catenary model 链状模型Caucasion 白种人Central compartment 中央室Characteristic 特点Chelate 螯合物Chinese Traditional medicine products 中药制剂Cholesterol esterase 胆固醇酯酶Chromatogram 色谱图Circulation 循环Classification 分类Clearance 清除率Clinical testing in first phase I期临床试验Clinical testing in second phase Ⅱ期临床试验Clinical testing in third phase Ⅲ期临床试验Clinical trial 临床试验Clinical trial simulation 临床实验计划仿真Clockwise hysteresis loop 顺时针滞后回线Collection 采集Combined administration 合并用药Combined errors 结合型误差Common liposomes, CL 普通脂质体Compartment models 隔室模型Compartments 隔室Competitive interaction 竞争性相互作用Complements 补体Complex 络合物Confidential interval 置信区间Conjugation with glucuronic acid 葡萄糖醛酸结合Controlled-release preparations 控释制剂Control stream 控制文件Conventional tablet 普通片Convergence 收敛Convolution 卷积Corresponding relationship 对应关系Corticosteroids 皮质甾体类Counter-clockwise hysteresis loop 逆时针滞后回线Countermeasure 对策Course in infusion period 滴注期间Covariance 协方差Covariates 相关因素Creatinine 肌酐Creatinine clearance 肌酐清除率Cytochrome P450, CYP450 细胞色素P450 Cytoplasm 细胞质Cytosis 胞饮作用Cytosol 胞浆胞液质※<D>Data File 数据文件Data Inspection 检视数据Deamination 脱氨基Deconvolution 反卷积Degree of fluctuation, DF DF波动度Delayed release preparations 迟释制剂Desaturation 降低饱和度Desmosome 桥粒Desulfuration 脱硫Detoxication 解毒Diagnosis 诊断Diffusion 扩散作用Dietary factors 食物因素Displacement 置换作用Disposition 处置Dissolution 溶解作用Distribution 分布Dosage adjustment 剂量调整Dosage form 剂型Dosage form design 剂型设计Dosage regimen 给药方案Dose 剂量dose-proportionality study 剂量均衡研究Dropping pills 滴丸Drug absorption via eyes 眼部用药物的吸收Drug binding 药物结合Drug concentration in plasma 血浆中药物浓度Drug Delivery System, DDS 药物给药系统Drug interaction 药物相互作用Drug-plasma protein binding ratio 药物—血浆蛋白结合率Drug-Protein Binding 药物蛋白结合Drug transport to foetus 胎内转运※<E>Efficient concentration range 有效浓度范围Efflux 外排Electrolyte 电解质Electro-spray ionization, ESI 电喷雾离子化Elimination 消除Elimination rate constant 消除速度常数Elongation 延长Emulsion 乳剂Endocytosis 入胞作用Endoplasmic reticulum 内质网Enterohepatic cycle 肠肝循环Enzyme 酶Enzyme induction 酶诱导Enzyme inhibition 酶抑制Enzyme-linked immunosorbent assays ELISA 酶联免疫法Enzymes or carrier-mediated system 酶或载体—传递系统Epithelium cell 上皮细胞Epoxide hydrolase 环化物水解酶Erosion 溶蚀Excretion 排泄Exocytosis 出胞作用Exons 外显子Experimental design 实验设计Experimental procedures 实验过程Exponential errors 指数型误差Exposure-response studies 疗效研究Extended least squares, ELS 扩展最小二乘法Extended-release preparations 缓控释制剂Extent of absorption 吸收程度External predictability 外延预见性Extraction ratio 抽取比Extract recovery rate 提取回收率Extrapolation 外推法Extravascular administration 血管外给药※<F>F test F检验Facilitated diffusion 促进扩散Factors of dosage forms 剂型因素Fasting 禁食Fibronectin 纤粘连蛋白First order rate 一级速度First Moment 一阶矩First order absorption 一级吸收First-order conditional estimation, FOCE 一级条件评估法First-order estimation, FO 一级评估法Fiest-order kinetics 一级动力学First pass effect 首过作用首过效应Fixed-effect parameters 固定效应参数Flavoprotein reductaseNADPH－细胞色素还原酶附属黄素蛋白还原酶Flow-through cell dissolution method 流室法Fluorescent detection method 荧光检测法Fraction of steady-state plasma drug concentration 达稳分数Free drug 游离药物Free drug concentration 游离药物浓度※<G>Gap junction 有隙结合Gas chromatography, GC 气相色谱法Gasrtointestinal tract, GI tract 胃肠道Gender differences 性别差异Generalized additive modeling, GAM 通用迭加模型化法Glimepiride 谷胱甘肽Global minimum 整体最小值Glomerular filtration 肾小球过滤Glomerular filtration rate, GFR 肾小球过滤率Glucuonide conjugation 葡萄糖醛酸结合Glutathione conjugation 谷胱甘肽结合Glycine conjugation 甘氨酸结合Glycocalyx 多糖—蛋白质复合体Goodness of Fit 拟合优度Graded response 梯度效应Graphic method 图解法Gut wall clearance肠壁清除率※<H>Half life 半衰期Health volunteers 健康志愿者Hemodialysis 血液透析Hepatic artery perfusion administration 肝动脉灌注给药Hepatic clearance, Clh 肝清除率Hierarchical Models 相同系列药物动力学模型High performance liquid chromatography, HPLC 高效液相色谱Higuchi equation Higuchi 方程Homologous 类似Human liver cytochrome P450 人类肝细胞色素P450 Hydrolysis 水解Hydroxylation 羟基化Hysteresis 滞后Hysteresis of plasma drug concentration 血药浓度滞后于药理效应Hysteresis of response 药理效应滞后于血药浓度※<I>Immunoradio metrec assays, IRMA 免疫放射定量法Incompatibility 配伍禁忌Independent 无关，独立Individual parameters 个体参数Individual variability 个体差异Individualization of drug dosage regimen 给药方案的个体化Inducer 诱导剂Induction 诱导Infusion 输注Inhibition 抑制Inhibitor 抑制剂Initial dose 速释部分Initial values 初始值Injection sites 注射部位Insulin 胰岛素Inter-compartmental clearance 隔室间清除率Inter-individual model 个体间模型Inter-individual random effects 个体间随机效应Inter-individual variability 个体间变异性Intermittence intravenous infusion 间歇静脉输液Internal predictability 内延预见性Inter-occasion random effects 实验间随机效应Intestinal bacterium flora 肠道菌丛Intestinal metabolism 肠道代谢Intra-individual model 个体内模型Intra-individual variability 个体内变异性Intramuscular administration 肌内给药Intramuscular injection 肌内注射Intra-peritoneal administration 腹腔给药Intravenous administration 静脉给药Intravenous infusion 静脉输液Intravenous injection 静脉注射Intrinsic clearance固有清除率内在清除率Inulin 菊粉In vitro experiments 体外试验In vitro–In vivo correlation, IVIVC 体外体内相关关系In vitro mean dissolution time, MDT vitro 体外平均溶出时间In vivo Mean dissolution time, MDT vivo 体内平均溶出时间Ion exchange 离子交换Isoform 异构体Isozyme 同工酶※<K>Kerckring 环状皱褶Kidney 肾※<L>Lag time 滞后时间Laplace transform 拉普拉斯变换Lateral intercellular fluid 侧细胞间隙液Lateral membrane 侧细胞膜Least detection amount 最小检测量Linearity 线性Linear models 线性模型Linear regression method 线性回归法Linear relationship 线性关系Lipoprotein 脂蛋白Liposomes 脂质体Liver flow 肝血流Local minimum 局部最小值Loading dose 负荷剂量Logarithmic models 对数模型Long circulation time liposomes 长循环脂质体Loo-Riegelman method Loo-Riegelman法Lowest detection concentration 最低检测浓度Lowest limit of quantitation 定量下限Lowest steady-state plasma drug concentration 最低稳态血药浓度Lung clearance 肺清除率Lymphatic circulation 淋巴循环Lymphatic system 淋巴系统※<M>Maintenance dose 维持剂量Mass balance study 质量平衡研究Masticatory mucosa 咀嚼粘膜Maximum likelihood 最大似然性Mean absolute prediction error, MAPE 平均绝对预测误差Mean absorption time, MAT 平均吸收时间Mean disintegration time, MDIT 平均崩解时间Mean dissolution time, MDT 平均溶出时间Mean residence time, MRT 平均驻留时间Mean sojourn time 平均逗留时间Mean squares 均方Mean transit time 平均转运时间Membrane-limited models 膜限速模型Membrane-mobile transport 膜动转运Membrane transport 膜转运Metabolism 代谢Metabolism enzymes 代谢酶Metabolism locations 代谢部位Metabolites 代谢物Metabolites clearance, Clm 代谢物清除率Method of residuals 残数法剩余法Methylation 甲基化Michaelis-Menten equation 米氏方程Michaelis-Menten constant 米氏常数Microbial assays 微生物检定法Microsomal P－450 mixed-function oxygenases 肝微粒体P-450混合功能氧化酶Microspheres 微球Microvilli 微绒毛Minimum drug concentration in plasma 血浆中最小药物浓度Mixed effects modeling 混合效应模型化Mixed-function oxidase, MFO 混合功能氧化酶Models 模型Modeling efficiency 模型效能Model validation 模型验证Modified release preparations 调释制剂Molecular mechanisms 分子机制Mono-exponential equation 单指数项公式Mono-oxygenase 单氧加合酶Mucous membrane injury 粘膜损伤Multi-compartment models 多室模型延迟分布模型Multi-exponential equation 多指数项公式Multifactor analysis of variance, multifactor ANOVA 多因素方差分析Multiple dosage 多剂量给药Multiple-dosage function 多剂量函数Multiple-dosage regimen 多剂量给药方案Multiple intravenous injection 多次静脉注射Myoglobin 肌血球素※<N>Naive average data, NAD 简单平均数据法Naive pool data, NPD 简单合并数据法Nanoparticles 纳米粒Nasal cavity 鼻腔Nasal mucosa 鼻粘膜National Institute of Health 美国国立卫生研究所Nephron 肾原Nephrotoxicity 肾毒性No hysteresis 无滞后Non-compartmental analysis, NCA 非隔室模型法Non-compartmental assistant Technology 非隔室辅助技术Nonionized form 非离子型Nonlinear mixed effects models, NONMEM 非线性混合效应模型Nonlinear pharmacokinetics 非线性药物动力学Non-linear relationship 非线性关系Nonparametric test 非参数检验※<O>Objective function, OF 目标函数Observed values 观测值One-compartment model 一室模型（单室模型）Onset 发生Open randomized two-way crossover design 开放随机两路交叉实验设计Open crossover randomized design 开放交叉随机设计Oral administration 口服给药Ordinary least squares, OLS 常规最小二乘法Organ 器官Organ clearance 器官清除率Original data 原始数据Osmosis 渗透压作用Outlier 偏离数据Outlier consideration 异常值的考虑Over-parameterized 过度参数化Oxidation 氧化Oxidation reactions 氧化反应※<P>Paracellular pathway 细胞旁路通道Parameters 参数Passive diffusion 被动扩散Pathways 途径Patient 病人Peak concentration 峰浓度Peak concentration of drug in plasma 血浆中药物峰浓度Poly-peptide 多肽Percent of absorption 吸收百分数Percent of fluctuation, PF 波动百分数Perfused liver 灌注肝脏Period 周期Peripheral compartments 外周室Peristalsis 蠕动Permeability of cell membrane 细胞膜的通透性P-glycoprotein, p-gp P-糖蛋白Phagocytosis 吞噬Pharmaceutical dosage form 药物剂型pharmaceutical equivalents 药剂等效性Pharmacokinetic models 药物动力学模型Pharmacokinetic physiological models 药物动力学的生理模型Pharmacological effects 药理效应Pharmacologic efficacy 药理效应Pharmacokinetics, PK 药物动力学Pharmacokinetic/pharmacodynamic link model 药物动力学-药效动力学统一模型Pharmacodynamics, PD 药效动力学Pharmacodynamic model 药效动力学模型Phase II metabolism 第II相代谢Phase I metabolism 第I相代谢pH-partition hypothesis pH分配假说Physiological function 生理功能Physiological compartment models 生理房室模型Physiological pharmacokinetic models 生理药物动力学模型Physiological pharmacokinetics 生理药物动力学模型Pigment 色素Physicochemical factors 理化因素Physicochemical property of drug 药物理化性质Physiological factors 生理因素Physiology 生理Physiological pharmacokinetic models 生理药物动力学模型Pinocytosis 吞噬Plasma drug concentration 血浆药物浓度Plasma drug concentration－time curve 血浆药物浓度-时间曲线Plasma drug-protein binding 血浆药物蛋白结合Plasma metabolite concentration 血浆代谢物浓度Plasma protein binding 血浆蛋白结合Plateau level 坪浓度Polymorphism 多态性Population average pharmacokinetic parameters 群体平均动力学参数Population model 群体模型Population parameters 群体参数Population pharmacokinetics 群体药物动力学Post-absorptive phase 吸收后相Post-distributive phase 分布后相Posterior probability 后发概率practical pharmacokinetic program 实用药代动力学计算程序Precision 精密度Preclinical 临床前的Prediction errors 预测偏差Prediction precision 预测精度Predicted values 拟合值Preliminary structural model 初始结构模型Primary active transport 原发性主动转运Principle of superposition 叠加原理Prior distribution 前置分布Prodrug 前体药物Proliferation assays 细胞增殖法Proportional 比例型Proportional errors 比例型误差Prosthehetic group 辅基Protein 蛋白质Pseudo-distribution equilibrium 伪分布平衡Pseudo steady state 伪稳态Pulmonary location 肺部Pulsatile drug delivery system 脉冲式释药系统※<Q、R>QQuality controlled samples 质控样品Quality control 质量控制Quick tissue 快分布组织RRadioimmuno assays, RIA 放射免疫法Random error model 随机误差模型Rapid intravenous injection 快速静脉注射Rate constants 速度常数Rate method 速度法Re-absorption 重吸收Receptor location 受体部位Recovery 回收率Rectal absorption 直肠吸收Rectal blood circulation 直肠部位的血液循环Rectal mucosa 直肠黏膜Reductase 还原酶Reduction 还原Reductive metabolism 还原代谢Reference individual 参比个体Reference product 参比制剂Relative bioavailability, Fr 相对生物利用度Release 释放Release medium 释放介质Release standard 释放度标准Renal 肾的Renal clearance, Clr 肾清除率Renal excretion 肾排泄Renal failure 肾衰Renal impairment 肾功能衰竭Renal tubular 肾小管Renal tubular re-absorption 肾小管重吸收Renal tubular secretion 肾小管分泌Repeatability 重现性Repeated one-point method 重复一点法Requirements 要求Research field 研究内容Reside 驻留Respiration 呼吸Respiration organ 呼吸器官Response 效应Residuals 残留误差Residual random effects 残留随机效应Reversal 恢复Rich Data 富集数据Ritschel one-point method Ritschel 一点法Rotating bottle method 转瓶法Rough surfaced endoplasmic reticulum 粗面内质网Routes of administration 给药途径※<S、T>SSafety and efficacy therapy 安全有效用药Saliva 唾液Scale up 外推Scale-Up/Post-Approval Changes, SUPAC 放大/审批后变化Second moment 二阶矩Secondary active transport 继发性主动转运Secretion 分泌Sensitivity 灵敏度Serum creatinine 血清肌酐Sigma curve 西格玛曲线Sigma-minus method 亏量法（总和减量法）Sigmoid curve S型曲线Sigmoid model Hill’s方程Simulated design 模拟设计Single-dose administration 单剂量（单次）给药Single dose response 单剂量效应Sink condition 漏槽条件Skin 皮肤Slow Tissue 慢分布组织Smooth surfaced endoplasmic reticulum 滑面内质网Soluble cell sap fraction 可溶性细胞液部分Solvent drag effect 溶媒牵引效应Stability 稳定性Steady-state volume of distribution 稳态分布容积Sparse data 稀疏数据Special dosage forms 特殊剂型Special populations 特殊人群Specialized mucosa 特性粘膜Species 种属Species differences 种属差异Specificity 特异性专属性Square sum of residual error 残差平方和Stagnant layer 不流动水层Standard curve 标准曲线Standard two stage, STS 标准两步法Statistical analysis 统计分析Statistical moments 统计矩Statistical moment theory 统计矩原理Steady state 稳态Steady state plasma drug concentration 稳态血药浓度Stealth liposomes, SL 隐形脂质体Steroid 类固醇Steroid-sulfatases 类固醇－硫酸酯酶Structure 结构Structure and function of GI epithelial cells 胃肠道上皮细胞的构造与功能Subcutaneous injections 皮下注射Subgroup 亚群体Subjects 受试者Sublingual administration 舌下给药Sublingual mucosa 舌下粘膜Subpopulation 亚群Substrate 底物Sulfate conjugation 硫酸盐结合Sulfation 硫酸结合Sum of squares 平方和Summation 相加Superposition method 叠加法Susceptible subject 易受影响的患者Sustained-release preparations 缓释制剂Sweating 出汗Synergism 协同作用Systemic clearance 全身清除率TTargeting 靶向化Taylor expansion 泰勒展开Tenous capsule 眼球囊Test product 试验制剂Therapy drug monitoring, TDM 治疗药物监测Therapeutic index 治疗指数Thermospray 热喷雾Three-compartment models 三室模型Though concentration 谷浓度Though concentration during steady state 稳态谷浓度Thromboxane 血栓素Tight junction 紧密结合Tissue 组织Tissue components 组织成分Tissue interstitial fluid 组织间隙Tolerance 耐受性Topping effect 尖峰效应Total clearance 总清除率Toxication and emergency treatment 中毒急救Transcellular pathway 经细胞转运通道Transdermal absorption 经皮肤吸收Transdermal drug delivery 经皮给药Transdermal penetration 经皮渗透Transport 转运Transport mechanism of drug 药物的转运机理Trapezoidal rule 梯形法Treatment 处理Trial Simulator 实验计划仿真器Trophoblastic epithelium 营养上皮层Two-compartment models 二室模型Two one sided tests 双单侧t检验Two period 双周期Two preparations 双制剂Two-way crossover bioequivalence studies 双周期交叉生物等效性研究Typical value 典型值※<U~Z>UUnwanted 非预期的Uniformity 均一性Unit impulse response 单位刺激反应Unit line 单位线Urinary drug concentration 尿药浓度Urinary excretion 尿排泄Urinary excretion rate 尿排泄速率VVagina 阴道Vaginal Mucosa 阴道黏膜Validation 校验Variance of mean residence time, VRT 平均驻留时间的方差Vein 静脉室Villi 绒毛Viscre 内脏Volumes of distribution 分布容积volunteers or patients studies 人体试验WWagner method Wagner法Wagner-Nelson method Wagner-Nelson法Waiver requirements 放弃（生物等效性研究）要求Washout period 洗净期Weibull distribution function Weibull分布函数Weighted Least Squares WLS加权最小二乘法Weighted residuals 加权残留误差XXenobiotic 外源物, 异生素ZZero Moment 零阶矩Zero-order absorption 零级吸收Zero-order kinetics 零级动力学Zero order rate 零级速度Zero-order release 零级释放。

gamm 目标函数

Gamm 目标函数引言在数学和优化领域，目标函数（Objective Function）是指在数学模型中表示一个最优化问题的目标的数学函数。

目标函数的值描述了待优化变量的性能和效果。

在本文中，我们将探讨一个特定的目标函数——Gamm 目标函数。

什么是 Gamm 目标函数Gamm 目标函数是一种非凸目标函数，它在统计建模和机器学习中广泛应用。

Gamm 是 Generalized Additive Mixed Models（广义加性混合模型）的缩写。

Gamm 目标函数结合了广义线性模型（Generalized Linear Model，GLM）和非参数平滑技术，能够更好地拟合复杂数据中的非线性关系。

Gamm 目标函数的定义Gamm 目标函数可以表示如下形式：其中，y 是响应变量，β0 是常数项，fi 是非参数的非线性平滑函数，xi 是输入变量，ε 是误差项。

Gamm 目标函数的关键在于使用非线性平滑函数 fi 来拟合各个输入变量与响应变量之间的非线性关系。

Gamm 目标函数的优势Gamm 目标函数相比传统的线性模型具有以下优势：1.灵活性：Gamm 可以处理非线性关系，对于复杂数据集具有更好的灵活性。

2.可解释性：Gamm 模型将不同的输入变量与响应变量关系拆分成多个平滑函数，每一个平滑函数对应一个输入变量。

这使得模型的可解释性更强，可以更好地理解不同因素对响应变量的影响。

3.鲁棒性：Gamm 对异常值和噪声有较好的鲁棒性，能够更好地适应复杂数据中的异常情况。

Gamm 目标函数的求解Gamm 目标函数的求解是一个非凸优化问题，通常使用迭代算法进行求解。

常用的求解方法有广义交替最小二乘（Generalized Alternating Least Squares, GALS）和基于样条函数的方法。

Gamm 目标函数在实际应用中的案例Gamm 目标函数在许多领域中得到了广泛应用。

以下是一些实际应用案例：1. 医学研究在医学研究中，研究人员常常需要分析多个生物标志物对某种疾病的影响关系。

generalize additive model

generalize additive model
广义加性模型（Generalized Additive Model，GAM）是回归分析中的一种模型，用于处理非参数或半参数的回归问题。

它是一种灵活的建模工具，能够处理多种类型的数据，包括连续变量、分类变量和有序分类变量。

在广义加性模型中，响应变量与解释变量之间的关系被假定为光滑函数的加权和。

这些光滑函数可以是线性、多项式、样条、指数等函数形式，通过选择适当的函数形式来描述响应变量与解释变量之间的关系。

广义加性模型允许解释变量对响应变量的影响是非线性的，这使得它非常适合处理复杂的非线性关系。

在广义加性模型中，模型的参数被假定为未知的，需要通过某种优化算法来估计。

常用的优化算法包括梯度下降法、牛顿-拉夫森方法等。

通过最小化损失函数或残差平方和，优化算法可以找到最佳的参数估计值。

广义加性模型可以应用于各种领域，包括生物医学、经济学、环境科学、金融学等。

在生物医学领域中，它可以用于预测疾病风险、药物反应等；在经济学中，它可以用于预测股票价格、消费行为等；在环境科学中，它可以用于预测气候变化、环境污染等。

总之，广义加性模型是一种强大的非参数和半参数回归分析工具，可以应用于各种领域的数据分析中。

它能够处理复杂的非线性关系，提供更准确的预测结果，并为决策提供有力的支持。

物种分布模型的发展及评价方法

物种分布模型的发展及评价方法许仲林;彭焕华;彭守璋【摘要】物种分布模型已被广泛地应用于以保护区规划、气候变化对物种分布的影响等为目的的研究.回顾了已经得到广泛应用的多种物种分布模型,总结了评价模型性能的方法.基于物种分布模型的发展和应用以及性能评价中尚存在的问题,本文认为:在物种分布模型中集成样本选择模块能够避免模型预测过程中的过度拟合及欠拟合,增加变量选择模块可评估和降低变量之间自相关性的影响,增加生物因子以及将物种对环境的适应性机制(及扩散行为特征)和潜在分布模型进行结合,是提高模型预测性能的可行方案;在模型性能的评价方面,采用赤池信息量可对模型的预测性能进行客观评价.相关建议可为物种分布建模提供参考.【期刊名称】《生态学报》【年(卷),期】2015(035)002【总页数】11页(P557-567)【关键词】物种分布模型;性能评价;阈值相关;阈值无关【作者】许仲林;彭焕华;彭守璋【作者单位】新疆大学资源与环境科学学院,乌鲁木齐830046;新疆大学智慧城市与环境建模重点实验室,乌鲁木齐830046;中国科学院武汉植物园,武汉430074;草地农业生态系统国家重点实验室,兰州大学生命科学学院,兰州730000【正文语种】中文物种分布模型(Species Distribution Models, SDMs)，是将物种的分布样本信息和对应的环境变量信息进行关联得出物种的分布与环境变量之间的关系，并将这种关系应用于所研究的区域，对目标物种的分布进行估计的模型。

物种分布模型的理论基础，是生态位的概念，生态位被定义为生态系统中的种群在时间和空间上所占据的位置及其与其他种群之间的关系与作用[1]。

Hutchinson以数学方式描述了生态位的概念: 在由多个环境变量定义的多维空间内，能够维持稳定种群的“超体积(Hyper-volume)”[1]。

围绕如何界定“超体积”，生态学家进行了各种尝试并依据不同的界定方法，发展了不同的物种分布模型。

generalized additive models算法 -回复

generalized additive models算法-回复Generalized Additive Models (GAMs) Algorithm: A Step-by-Step GuideIntroduction:Generalized Additive Models (GAMs) is a popular algorithm used in statistical modeling and machine learning. It extends the concept of linear regression by allowing for nonlinear relationships between the dependent variable and the predictor variables. This algorithm has gained significant attention due to its flexibility and ability to handle various data types. In this article, we will provide astep-by-step guide to understanding and implementing GAMs.1. Understanding the Foundations:Before diving into GAMs, it is essential to grasp the fundamentals of linear regression. Linear regression assumes a linear relationship between the dependent variable Y and predictor variables X. However, real-world data often exhibit nonlinearity. GAMs address this limitation by introducing smoothing functions to model these nonlinear relationships.2. Identifying the Components:GAMs consist of three main components: a systematic component, a link function, and a random component. The systematic component includes predictor variables and their corresponding smooth functions. The link function connects the systematic component to the random component. Lastly, the random component captures the residual or unexplained variability.3. Selecting the Predictor Variables:Choose the predictor variables that are expected to have an impact on the dependent variable. These variables may be continuous or categorical. Categorical variables can be encoded using dummy or one-hot encoding before proceeding with the GAM implementation.4. Preprocessing the Data:Prepare the data by handling missing values, outliers, and scaling the variables if necessary. GAMs are relatively robust to missing values, but it is advisable to impute them using appropriate techniques based on the nature of the dataset.5. Choosing the Smoothing Functions:For each predictor variable, determine the smoothing function thatmodels its relationship with the dependent variable. Commonly used smoothing functions include splines, polynomial functions, and Gaussian processes. The choice of smoothing function depends on the type of data, the expected relationship, and the complexity desired in the model.6. Estimating the Model:Estimate the GAM by fitting the chosen smoothing functions to the data. This involves finding the optimal smoothing parameters that minimize a specified loss function. Cross-validation techniques, such as k-fold cross-validation, can help in identifying the best model fit and avoiding overfitting.7. Assessing the Model Fit:Evaluate the model's performance using appropriate metrics such as mean squared error, R-squared, or deviance. These metrics measure the goodness-of-fit and quantify how well the model explains the variability in the data. Additionally, visually inspecting diagnostic plots, such as residuals vs. fitted values or Q-Q plots, can provide further insights into the model's performance.8. Interpreting the Results:Interpreting GAMs can be challenging due to the flexibility of smooth functions. However, one can gain insights by examining the estimated smooth functions' shape and significance. Plotting the estimated functions against the predictor variables can reveal the relationships between predictors and the response variable, accounting for nonlinearity.9. Handling High-Dimensional Data:GAMs can handle high-dimensional data by employing variable selection techniques or dimension reduction methods such as principal component analysis (PCA) or partial least squares (PLS). These methods help in reducing the number of predictor variables and improving model interpretability.10. Advantages and Limitations of GAMs:GAMs offer several advantages, including flexibility in handling nonlinear relationships, interpretability through smooth functions, and robustness against missing values. However, they come with limitations such as difficulty in selecting appropriate smoothing functions, potential overfitting if not properly regularized, and potential computational challenges when dealing with large datasets.Conclusion:Generalized Additive Models (GAMs) provide a powerful tool for modeling nonlinear relationships between predictors and the response variable. By incorporating smoothing functions, GAMs offer flexibility, interpretability, and robustness. With a step-by-step understanding of the algorithm, practitioners can effectively implement GAMs and gain valuable insights from their data.。

generalized additive model (gam)

generalized additive model (gam)1. 引言1.1 概述在现实生活中，我们经常需要通过建立统计模型来对各种问题进行预测和解释。

然而，传统的线性模型往往无法准确地拟合复杂的非线性关系。

为了克服这个问题，广义可加模型（Generalized Additive Model, GAM）应运而生。

GAM是一种灵活的非参数统计模型，通过将多个光滑函数组合在一起，能够更好地捕捉变量之间的非线性关系。

与传统的线性回归模型相比，GAM不再依赖于线性假设，可以更准确地对数据进行建模和预测。

1.2 文章结构本文将对GAM进行深入探讨。

首先，在第2部分中，我们将介绍GAM的定义和原理，并探讨其在不同领域中的应用情况。

然后，在第3部分中，我们将详细讨论GAM模型的主要组成部分，包括广义可加性假设、成分变量和光滑函数以及模型参数估计方法等。

接下来，在第4部分中，我们将通过实际案例分析来展示如何应用GAM进行数据建模和解释结果。

最后，在第5部分中，我们将总结本文的主要发现，并展望未来研究方向。

1.3 目的本文的目的是介绍GAM这一强大的统计建模工具，并展示其在实际应用中的优势和局限性。

通过深入理解GAM的原理和应用方法，读者可以更好地掌握GAM 模型在数据分析与预测中的作用，为实际问题提供更准确、更可靠的解决方案。

同时，我们还将展望未来有关GAM领域的研究方向，以推动该领域更加广泛和深入的发展。

2. Generalized Additive Model (GAM)2.1 定义和原理广义可加模型（Generalized Additive Model，简称GAM）是一种灵活的非线性统计模型，由各个部分函数的和构成。

它是从广义线性模型（Generalized Linear Model，简称GLM）扩展而来的。

GAM可以捕捉自变量与因变量之间的非线性关系，同时允许控制其他协变量的影响。

GAM采用一个附加到线性预测器上的非参数光滑函数来描述自变量与因变量之间的关系。

gamm模型的回归代码和方法

gamm模型的回归代码和方法GAMM（Generalized Additive Mixed Models）是一种广义可加混合模型，结合了广义可加模型（GAM）和混合效应模型（Mixed Effects Models）的特点，用于处理非线性关系和非正态分布的数据。

在回归分析中，GAMM模型能够更准确地描述因变量和自变量之间的关系，同时考虑到不同个体之间的差异。

GAMM模型的回归代码主要使用R语言的mgcv包。

首先，我们需要安装并加载mgcv包，然后使用gamm()函数建立GAMM模型。

接下来，我们将介绍GAMM模型的建模过程和常用的参数设置。

我们需要加载mgcv包，可以使用以下代码完成：```Rinstall.packages("mgcv") # 安装mgcv包library(mgcv) # 加载mgcv包```在加载mgcv包之后，我们可以开始建立GAMM模型。

使用gamm()函数可以建立GAMM模型，其基本语法如下：```Rmodel <- gamm(formula, data, random = random, method = method)其中，formula表示模型的公式，data表示数据集，random表示随机效应的公式，method表示估计方法。

在GAMM模型中，我们可以通过formula来指定因变量和自变量之间的关系。

例如，如果我们要建立一个只包含一个自变量的GAMM模型，可以使用以下代码：```Rmodel <- gamm(y ~ s(x), data = mydata)```在上述代码中，y表示因变量，x表示自变量，s()函数表示平滑项。

通过s()函数，我们可以对自变量进行平滑处理，以捕捉非线性关系。

在GAMM模型中，还可以使用其他函数来表示不同的平滑项，如te()函数表示二维平滑项，ti()函数表示时间平滑项等。

除了自变量的平滑项之外，GAMM模型还可以包含随机效应。

R语言 mgcv包 gam()函数中文帮助文档(中英文对照)

Generalized additive models with integrated smoothness estimation广义加性模型与集成的平滑估计描述----------Description----------Fits a generalized additive model (GAM) to data, the term "GAM" being taken to include any quadratically penalized GLM. The degree of smoothness of model terms is estimated as part of fitting. gam can also fit any GLM subject to multiple quadratic penalties (including estimation of degree of penalization). Isotropic or scale invariant smooths of any number of variables are available as model terms, as are linear functionals of such smooths; confidence/credible intervals are readily available for any quantity predicted using a fitted model; gam is extendable: users can add smooths.适合一个广义相加模型（GAM）的数据，“GAM”被视为包括任何二次处罚GLM。

模型计算的平滑度估计作为拟合的一部分。

gam也可以适用于任何GLM多个二次处罚（包括估计程度的处罚）。

各向同性或规模不变平滑的任意数量的变量的模型计算，这样的线性泛函平滑的信心/可信区间都是现成的使用拟合模型预测任何数量，“gam是可扩展的：用户可以添加平滑。

pspline.inference 1.0.4 软件包用户指南说明书

Package‘pspline.inference’October14,2022Title Estimation of Characteristics of Seasonal and SporadicInfectious Disease Outbreaks Using Generalized AdditiveModeling with Penalized Basis SplinesDate2021-01-18Version1.0.4Description Inference of infectious disease outcomes using generalized additive (mixed)models with penalized basis splines(P-Splines).See<https:///cgi/content/short/2020.07.14.20138180v1>. Depends R(>=3.4.0)Imports stats,utils,mgcv,dplyr,magrittr,assertthat,plyr,reshape2,plotrix,rlangSuggests import,ggplot2,data.table,ggstance,knitr,rmarkdown,roxygen2,kableExtra,doParallel,parallel,stringr,scales,testthatLicense Apache License2.0Encoding UTF-8LazyData trueVignetteBuilder knitrRoxygenNote7.1.0URL https:///weinbergerlab/pspline.inferenceBugReports https:///weinbergerlab/pspline.inference/issues NeedsCompilation noAuthor Ben Artin[aut,cre,cph]Maintainer Ben Artin<**************>Repository CRANDate/Publication2021-01-1915:10:02UTC12pspline.estimate.scalars R topics documented:pspline.estimate.scalars (2)pspline.estimate.timeseries (3)pspline.inference (4)pspline.outbreak.calc.cumcases (6)pspline.outbreak.cases (7)pspline.outbreak.cumcases (7)pspline.outbreak.cumcases.relative (8)pspline.outbreak.thresholds (8)pspline.validate.scalars (9)Index10pspline.estimate.scalarsCalculates conﬁdence intervals for scalars estimated from generalizedadditive(mixed)model of an outbreakDescriptionThis function performs Monte Carlo sampling of a GAM/GAMM outbreak model.For each sam-pled curve,it calls outcomess to calculate scalar outcomes It then calculates and returns the conﬁ-dence interval of each scalar outcomeUsagepspline.estimate.scalars(model,predictors,outcomes,samples=100,level=0.95)Argumentsmodel model returned by gam or gammpredictors data.frame of predictor values at which the model will be evaluatedoutcomes function returning calculated scalar outcomes,as described abovesamples number of samples of outcomes to drawlevel conﬁdence level for estimatespspline.estimate.timeseries3DetailsThe outcomes function must accept(model,params,predictors)and return a one-row data framein which each column lists the value of a single scalar outcome calculated from the model estimates.A typical implementation of the outcomes function would call predict on model and predictorsto obtain model variable estimates at predictor values,then calculate the scalar outcomes of interestand return them in a data frame.For example,to calculate the time of outbreak peak,you might use this function for outcomes:calc_peak=function(model,params,time){incidence=predict(model,data.frame(time=time), type="response")data.frame(peak=time[which.max(incidence)])}The data frame returned by pspline.estimate.scalars contains three columns for each outcomecalculated by outcomes:for outcome x returned by outcomes,pspline.estimate.scalars re-turns columns x.lower,x.median,and x.upper,corresponding to lower conﬁdence limit,median,and upper conﬁdence limit of x.Valuedata frame of estimates,as described abovepspline.estimate.timeseriesCalculates conﬁdence intervals for time series sampled from general-ized additive(mixed)model of an outbreakDescriptionThis function performs a series of Monte Carlo simulations of a GAM/GAMM outbreak model.For each simulated outbreak,it calls outcome to calculate a time series for the simulated outbreak(for example,the number of cumulative cases vs time).It then calculates and returns the conﬁdenceinterval of the simulated time series at each time point across all simulationsUsagepspline.estimate.timeseries(model,predictors,outcome,samples=1000,level=0.95)Argumentsmodel model returned by gam or gamm,with a single parameter(time)predictors data frame of predictor values at which the model will be evaluatedoutcome function returning calculated outcome time series,as described abovesamples number of simulations to runlevel conﬁdence level for returned estimatesDetailsThe outcome function must accept(model,params,time)and return a vector containing the out-come time series obtained by evaluating the model at the time points given in time and using themodel parameters given in params.A typical implementation of the outcome function would call predict on model and time to obtainthe linear predictor matrix,and then post-multiply that matrix by params.Having thus obtainedmodel prediction at every time point,it would calculate the desired time series outcome and returnit in a vector.For example,to calculate the time series of theﬁrst derivative of incidence,you might use thisfunction for outcome:calc_deriv=function(model,params,time){eps=0.001predictors=predict(model,data.frame(time=time type="lpmatrix")fit=model$family$linkinv(predictors predictors_eps=predict(model,data.frame(time=time+eps),type="lpmatrix")fit_eps=model$family$linkinv(predictors_eps(fit_eps-fit)/eps}The data frame returned by pspline.estimate.timeseries contains three columns and one rowfor each time point in time.The columns are lower,median,and upper,containing the medianand the conﬁdence interval for the computed outcome time series at each time point.Valuedata frame of estimates,as described abovepspline.inference Inference using penalized basis splines(P-splines)in a generalizedadditive model(GAM),with applications in infectious disease out-break modelingDescriptionThis package lets you make point and interval estimates of outcomes modeled with a non-linearP-spline GAM.DetailsApplications in infectious disease outbreak modeling include estimating of outbreak onset,peak,oroffset,as well as outbreak cumulative incidence over time.The package can model two types of outcomes:scalar outcomes,which are single-value outcomemeasures(for example,timing of outbreak peak)and time series characteristics,which are functionsof time(for example,infection incidence over time)For each outcome measure,the package produces median and conﬁdence interval estimates.Typical use of this package begins by using the package mgcv to obtain a GAM/GAMM model ofthe process under investigation(such as an infectious disease outbreak),followed by calling eitherpspline.estimate.scalars or pspline.estimate.timeseries to obtain conﬁdence intervalson the desired outcome measureBoth pspline.estimate.scalars and pspline.estimate.timeseries allow computation of ar-bitrary outcome measures,by passing a function that calculates the desired outcome measure intopspline.estimate.scalars or pspline.estimate.timeseries.For convenience,this package also includes several utilities speciﬁcally aimed at modeling of in-fectious disease outbreaks,such as pspline.outbreak.cases and pspline.outbreak.cumcases(for estimation of incidence and cumulative incidence),and pspline.outbreak.thresholds,forestimation of outbreak onset and offset.Author(s)Ben Artin<**************>Examples#Simulate an outbreak for analysiscases=data.frame(time=seq(0,51),cases=rpois(52,c(rep(1,13),seq(1,50,length.out=13),seq(50,1,length.out=13),rep(1,13))) )#Generate GAM model for outbreak;see mgcv for detailslibrary(mgcv)model=gam(cases~s(time,k=10,bs="cp",m=3),family=poisson,data=cases)#Generate time series at which model will be evaluated for estimates#Usually you want this to be the same as the time interval that your observations are in,except #divided into small increments(here,eps).Using a smaller eps gives more accurate estimates, #but takes longer to run.A value smaller than0.5would be better for final analysiseps=0.5estTimes=data.frame(time=seq(min(cases$time)-0.5,max(cases$time)+0.5-eps,by=eps))#Estimate incidenceestCases=pspline.estimate.timeseries(model,estTimes,pspline.outbreak.cases,#Using a large number of samples makes the analysis more robust;#using only15samples makes this example run fast(default is2000)samples=15,level=.95)#Estimate time when outbreak crosses5\%and95\%of cumulative case countonsetThreshold=0.025offsetThreshold=1-onsetThresholdthresholds=pspline.estimate.scalars(model,estTimes,pspline.outbreak.thresholds(onset=onsetThreshold,offset=offsetThreshold),#Using a large number of samples makes the analysis more robust;#using only15samples makes this example run fast(default is2000)samples=15,level=.95)#Plot cumulative incidence estimates and threshold estimateslibrary(ggplot2)ggplot()+geom_ribbon(data=estCases,aes(x=time,ymin=cases.lower,ymax=cases.upper),fill=grey(.75))+ geom_line(data=estCases,aes(x=time,y=cases.median))+geom_point(data=cases,aes(x=time,y=cases))+annotate("rect",xmin=thresholds$onset.lower,xmax=thresholds$onset.upper,ymin=-Inf,ymax=Inf,alpha=.25)+annotate("rect",xmin=thresholds$offset.lower,xmax=thresholds$offset.upper,ymin=-Inf,ymax=Inf,alpha=.25)+labs(x="Time",y="Incidence")pspline.outbreak.calc.cumcasesCalculate cumulative incidence time series from incidence time seriesDescriptionCorrectly handles accumulating over time intervals different from1Usagepspline.outbreak.calc.cumcases(time,cases)Argumentstime vector of timescases vector of corresponding incidencesValuevector of corresponding cumulative incidencespspline.outbreak.casesCalculate cumulative incidence for an outbreakDescriptionThis is useful as outcome for pspline.estimate.timeseries.Usagepspline.outbreak.cases(model,data)Argumentsmodel model returned by gam or gamm,with a single parameter(time)data data frame of predictor values at which the model will be evaluatedValuedata frame of predictor values with corresponding cumulative incidence estimates in$cumcasespspline.outbreak.cumcasesCalculate cumulative incidence for an outbreakDescriptionThis is useful as outcome for pspline.estimate.timeseries.Usagepspline.outbreak.cumcases(model,data)Argumentsmodel model returned by gam or gamm,with a single parameter(time)data data frame of predictor values at which the model will be evaluatedValuedata frame of predictor values with corresponding cumulative incidence estimates in$cumcases8pspline.outbreak.thresholdspspline.outbreak.cumcases.relativeCalculate relative incidence for an outbreakDescriptionThis is useful as outcome for pspline.estimate.timeseries.Usagepspline.outbreak.cumcases.relative(model,data)Argumentsmodel model returned by gam or gamm,with a single parameter(time)data data frame of predictor values at which the model will be evaluatedValuedata frame of predictor values with corresponding relative cumulative incidence estimates in$cumcases.relativepspline.outbreak.thresholdsCalculate outbreak thresholds for an outbreakDescriptionThe result of calling this is useful as outcomes for pspline.estimate.scalars.Usagepspline.outbreak.thresholds(onset=NA,offset=NA)Argumentsonset onset threshold(as fraction of total outbreak case count)offset offset threshold(as fraction of total outbreak case count)Valuefunction suitable as outcome estimator parameter of pspline.estimate.scalarspspline.validate.scalars9pspline.validate.scalarsRun a simulation study to validate a scalar estimatorDescriptionRun a simulation study to validate a scalar estimatorUsagepspline.validate.scalars(fun.truth,n.truths,fun.observations,n.observations,fun.model,fun.outcomes,n.samples,level)Argumentsfun.truth function that generates a true state of the system.Takes no arguments,returns data frame of true values for model variablesn.truths number of different truths to generate for simulation studyfun.observationsfunction that generates a set of observations from truth.Takes one argument(truth data frame)and returns data frame of observationsn.observations number of sets of observations to generate for each truth in the simulation study fun.model function that returns a model to be used for estimation.Takes one argument (observations data frame)and returns the modelfun.outcomes function that calculates the outcomes of interest.Same as outcomes function in pspline.estimate.scalars.n.samples number of samples to use for estimation.See pspline.estimate.scalars.level conﬁdence level to use for estimation.See pspline.estimate.scalars.Valuelist of summary(which is a data frame specifying the fraction of true values that were contained in their estimated conﬁdence interval)and results(which is a data frame specifying the quantile of the true value in the estimated sampled distribution for each simulation)Indexgam,2,3,7,8gamm,2,3,7,8mgcv,5pspline.estimate.scalars,2,5,8,9pspline.estimate.timeseries,3,5,7,8 pspline.inference,4pspline.outbreak.calc.cumcases,6pspline.outbreak.cases,5,7pspline.outbreak.cumcases,5,7pspline.outbreak.cumcases.relative,8 pspline.outbreak.thresholds,5,8pspline.validate.scalars,910。

Generalizedadditivemixedmodels

Generalized Additive Mixed ModelsInitial data-exploratory analysis using scatter plots indicated a non linear dependence of the response on predictor variables. To overcome these difficulties, Hastie and Tibshirani (1990) proposed generalized additive models (GAMs). GAMs are extensions of generalized linear models (GLMs) in which a link function describing the total explained variance is modeled as a sum of the covariates. The terms of the model can in this case be local smoothers or simple transformations with fixed degrees of freedom (e.g. Maunder and Punt 2004). In general the model has a structure of:Where and has an exponential family distribution. is a response variable, isa row for the model matrix for any strictly parametric model component, is the correspondingparameter vector, and the are smooth functions of the covariates, .In regression studies, the coefficients tend to be considered fixed. However, there are cases in which it makes sense to assume some random coefficients. These cases typically occur in situations where the main interest is to make inferences on the entire population, from which some levels are randomly sampled. Consequently, a model with both fixed and random effects (so called mixed effects models) would be more appropriate. In the present study, observations were collected from the same individuals over time. It is reasonable to assume that correlations exist among the observations from the same individual, so we utilized generalized additive mixed models (GAMM) to investigate the effects of covariates on movement probabilities. All the models had the probability of inter-island movement obtained from the BBMM as the dependent term, various covariates (SST, Month, Chlorophyll concentration, maturity stage, and wave energy) as fixed effects, and individual tagged sharks as the random effect. The GAMM used in this study had Gaussian error, identity link function and is given as:Where k = 1, …q is an unknown centered smooth function of the k th covariate andis a vector of random effects following All models were implemented using the mgcv (GAM) and the nlme (GAMM) packages in R (Wood 2006, R Development Core Team 2011).Spatially dependent or environmental data may be auto-correlated and using models that ignore this dependence can lead to inaccurate parameter estimates and inadequate quantification of uncertainty (Latimer et al., 2006). In the present GAMM models, we examined spatial autocorrelation among the chosen predictors by regressing the consecutive residuals against each other and testing for a significant slope. If there was auto-correlation, then there should be a linear relationship between consecutive residuals. The results of these regressions showed no auto-correlation among the predictors.Predictor terms used in GAMMsPredictor Type Description Values Sea surface Continuous Monthly aver. SST on each of the grid cells 20.7° - 27.5°C Chlorophyll a Continuous Monthly aver. Chlo each of grid cells 0.01 – 0.18 mg m-3 Wave energy Continuous Monthly aver. W. energy on each of grid cells 0.01 – 1051.2 kW m-1Month Categorical Month the Utilization Distributionwas generated January to December (1-12)Maturity stage Categorical Maturity stage of shark Mature male TL> 290cmMature female TL > 330cmDistribution of residual and model diagnosticsThe process of statistical modeling involves three distinct stages: formulating a model, fitting the model to data, and checking the model. The relative effect of each x j variable over the dependent variable of interest was assessed using the distribution of partial residuals. The relative influence of each factor was then assessed based on the values normalized with respect to the standard deviation of the partial residuals. The partial residual plots also contain 95% confidence intervals. In the present study we used the distribution of residuals and the quantile-quantile (Q-Q) plots, to assess the model fits. The residual distributions from the GAMM analyses appeared normal for both males and females.MalesResiduals distribution ResidualsF r e q u e n c y-202402004006008001000120-4-2024-2024Q-Q plotTheorethical quantilesS a m p l e q u a n t i l e sFemalesHastie, T.J., and R.J. Tibshirani. 1990. Generalized Additive Models. CRC press, Boca Raton,FL. Latimer, A. M., Wu, S., Gelfand, A. E., and Silander, J. A. 2006. Building statistical models toanalyze species distributions. Ecological Applications, 16: 33–50. Maunder, M.N., and A.E. Punt. 2004. Standardizing catch and effort: a review of recentapproaches. Fisheries Research 70: 141-159. Wood, S.N. 2006. Generalized Additive Models: an introduction with R. Boca Raton, CRCPress.。

广义可加混合模型在婴幼儿生长发育研究中的应用

发育研究中的应用ꎮ 方法采用出生队列随访资料ꎬ通过Ｒ语言软件ｍｇｃｖ包拟合广义可加混合模型ꎮ 结果本研究共
纳入儿童８１９名ꎬ儿童体重的影响因素包括:月龄( Ｆ＝５１６１７ꎬＰ < ０００１) ꎬ出生体重( Ｆ＝１３１９ꎬＰ < ０００１) ꎬ辅食添加频
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generalized additive models

generalized additive modelsGeneralized additive models (GAMs) are a type of regression model used for modeling nonlinear relationships. They are an extension oflinear regression that allows for nonlinearities in the response variable, by introducing additional terms (smoothing functions) into the model. In contrast to other nonlinear models, the residuals of a GAM are independent and identically distributed, which is an important assumption for making valid statistical inferences.GAMs are a flexible approach and can be used to model a variety of data types, such as discrete, continuous, and categorical data. Theyalso offer more accuracy than linear models, allowing for better prediction. In addition, GAMs are less prone to overfitting compared to other nonlinear models.The key advantage of GAMs is that they allow for complex nonlinear relationships to be modeled, while still using the same linear model framework and terminology. This makes it easier to interpret the results, as opposed to more complex nonlinear methods.Another benefit of GAMs is that they have fewer parameters thanother nonlinear methods, making them more efficient. Additionally, GAMs can be used in conjunction with regularization techniques such as ridge regression, which further helps to improve model performance.Overall, GAMs are an effective and versatile approach for modeling nonlinear relationships. They are fairly easy to implement and offer better accuracy than linear models. However, it is important to keep in mind that GAMs are still an approximation, and must be used with caution when dealing with large datasets.。

poptrend软件包说明书

Package‘poptrend’November22,2023Title Estimate Smooth and Linear Trends from Population Count SurveyDataVersion0.2.0Description Functions to estimate and plot smooth or linear population trends,or population indices, from animal or plant count survey data.Depends R(>=3.1.2)License GPL-3LazyData trueImports mgcv(>=1.7.0),stats,graphicsRoxygenNote7.1.2URL https:///jknape/poptrendBugReports https:///jknape/poptrend/issuesNeedsCompilation noAuthor Jonas Knape[aut,cre]Maintainer Jonas Knape<******************>Repository CRANDate/Publication2023-11-2213:50:02UTCR topics documented:change (2)checkFit (3)goldcrest (4)greenﬁnch (4)hessBootstrap (5)plot.trend (6)poptrend (7)print.trend (8)ptrend (8)simTrend (10)summary.trend (11)trend (12)12change Index13change Compute the change in the population over a time interval.DescriptionComputes the estimated percentual change in the population between two given time points,and an approximate conﬁdence interval for the change.Usagechange(trend,start,end,alpha=0.05)Argumentstrend Aﬁtted object of class trend.start Start time for the comparison.end End time for the comparison.alpha alpha-level for approximate conﬁdence interval.DetailsThe function computes the estimated change between two chosen time points.When random effects are present,the change is computed for the underlying linear or smooth trend term.For index mod-els,the change is estimated from the difference between indices.Changes can only be computed between time points that were included in the trendGrid argument to ptrend,if the two time points are not included the nearest points in the grid are chosen.Conﬁdence intervals are computed using quantiles of the bootstrapped trends.ValueA list containing the estimated change,and start and end points.NoteIf start or end are not contained in the trendgrid argument of the ptrend function,the change is computed between the values in the grid that are closest to these points.Author(s)Jonas KnapecheckFit3 Examples##Simulate a data set with10sites and30yearsdata=simTrend(30,10)##Fit a smooth trend with fixed site effects,random time effects,##and automatic selection of degrees of freedomtrFit=ptrend(count~trend(year,type="smooth")+site,data=data)##Check the estimated percent change from year2to20change(trFit,10,20)checkFit Check goodness ofﬁt of a trend model.DescriptionProduces various goodness ofﬁt plots and diagnostic measures.UsagecheckFit(trend,residuals=TRUE,...)Argumentstrend Aﬁtted object of class trend.residuals Should residuals be plotted?...Further arguments passed to plot.gam.DetailsThe function simply calls plot.gam and gam.check on the underlying gam model for checking good-ness ofﬁt.Author(s)Jonas KnapeSee Alsoplot.gam,gam.check4greenﬁnch goldcrest Data for goldcrest from the Swedish Bird Survey.DescriptionTransect count survey data for goldcrest from the Swedish Bird Survey from1998to2012.UsagegoldcrestFormatA data frame with5728rows and9columns.•count Total transect count.•site Site identity.•year Year of the survey.•observerAge Age of the observer.•day Day of season.•ﬁrstSurvey A binary variable which is1if the route was surveyed for theﬁrst time by the observer in that year,and0otherwise.•latitude Latitude of the transect.•lineCov The percentage of the transect that was surveyed.Sourcehttp://www.fageltaxering.lu.se/englishgreenfinch Data for greenﬁnch from the Swedish Bird Survey.DescriptionTransect count survey data for greenﬁnch from the Swedish Bird Survey from1998to2012.UsagegreenfinchhessBootstrap5FormatA data frame with5728rows and9columns.•count Total transect count.•site Site identity.•year Year of the survey.•observerAge Age of the observer.•day Day of season.•ﬁrstSurvey A binary variable which is1if the route was surveyed for theﬁrst time by the observer in that year,and0otherwise.•latitude Latitude of the transect.•lineCov The percentage of the transect that was surveyed.Sourcehttp://www.fageltaxering.lu.se/englishhessBootstrap Compute bootstrap conﬁdence intervals based on sampling from thevariance-covariance matrix.DescriptionDraws bootstrap samples using the estimated variance matrix of theﬁtted gam model.UsagehessBootstrap(trend,nBoot=500)Argumentstrend An object of class trend.nBoot The number of bootstrap samples to draw.DetailsThis function is used by ptrend and would typically not be called directly.Bootstrap samples are drawn using the estimated coefﬁcients and covariance matrix vcov.gam of theﬁtted gam model.The default values of vcov.gam which gives the Bayesian posterior covariance matrix.Bootstrapped samples computed in this way do not account for any uncertainty in the selection of degrees of freedom.ValueA trend object with the bootstrapped trend estimates appended.6plot.trendAuthor(s)Jonas Knapeplot.trend Plot an estimated trend.DescriptionThe function plots an estimated trend or index,as well as estimates of any temporal random effects included in the trend term.Usage##S3method for class trendplot(x,ciBase=NULL,alpha=0.05,ylab="abundance index",trendCol="black",lineCol=adjustcolor("black",alpha.f=0.05),shadeCol=adjustcolor("#0072B2",alpha.f=0.4),incCol="#009E73",decCol="#D55E00",plotGrid=TRUE,plotLines=FALSE,ranef="pointCI",secDeriv=TRUE,...)Argumentsx Aﬁtted object of class trend.ciBase A time point or function used to compute the baseline of the trend.If the ar-gument is numeric,the point in the trendGrid argument of the function ptrendclosest to this value will be taken as the baseline(i.e.the estimated trend will be1at this point).If the argument is a function,the function is applied to trendsand the resulting value is used as the baseline.By default,theﬁrst time point istaken as the reference.alpha The alpha level of conﬁdence intervals.ylab The label of the y-axis.trendCol The color of the trend line.lineCol The color of bootstrapped trend lines,if plotted.shadeCol The color of the conﬁdence region.poptrend7 incCol The color of regions where theﬁrst or second derivative is signiﬁcantly increas-ing.decCol The color of regions where theﬁrst or second derivative is signiﬁcantly decreas-ing.plotGrid If true,grid lines are plotted.plotLines If true,the bootstrapped trends are plotted.ranef String indicating whether to plot point estimates and/or conﬁdence intervals for random effects.One of’pointCI’,’point’,’CI’or’no’.secDeriv If true,coloured boxes at the bottom of the plot shows segments where the sec-ond derivative of the smooth is signiﬁcantly different from zero....Further arguments passed to plot.default.DetailsTrends and indexes are relative measures and therefore are compared against some reference value.By default,theﬁrst observed time point is used as the reference value.If the estimated trend contains bootstrap samples,conﬁdence intervals are plotted as well.For smooth trend models,time periods where the trend is signiﬁcantly declining or increasing are marked with a different color(set by arguments decCol and incCol).Periods where the second derivative is signiﬁcantly positive or negative are marked by coloured boxes at the bottom of the plot.There is an additional option of plotting each of the bootstrapped trends.Author(s)Jonas Knapepoptrend Analyze population trends from survey count data.DescriptionThe package provides functions forﬁtting and analysing trend models of data obtained from popu-lation count surveys.DetailsThe package provides functions for estimating smooth trends with generalized additive mixed mod-els,as well as linear trends and population indices.It is intended as a simple interface to basic trend estimation,allowing estimation of trends accounting for effects of covariates in the form of both smooth terms and random effects.The modelﬁtting engine is the function gam of package mgcv.Background for the package is given in Knape(2016).ReferencesKnape,J.2016.Decomposing trends in Swedish bird populations using generalized additive mixed models.Journal of Applied Ecology,53:1852-1861.DOI:10.1111/1365-2664.12720.print.trend Print a trend object.DescriptionPrints basic information about a trend object.Usage##S3method for class trendprint(x,...)Argumentsx A trend object....Not used.DetailsPrints the family,formula and type of trend.Author(s)Jonas Knapeptrend Fit a smooth or linear trend to count survey data.DescriptionThe function estimates a trend from count survey data.Usageptrend(formula,data=list(),family=quasipoisson(),nGrid=500,nBoot=500,bootType="hessian",gamModel=TRUE,engine="gam",...)Argumentsformula A trend formula.This is a GAM formula with an extra term trend describing the time variable and properties of the trend.All terms except the trend termare treated as covariates.Effect of temporal variation in these covariates are notincluded in the calculation of the trend.data A data frame containing response variables and covariates.family The distributional family of the response.The family most use a log-link,it defaults to a quasi-Poisson.nGrid The number of grid points over which to compute the trend.If the length of the argument is one,an equally spaced grid over the survey period of length nGridis set up.nGrid can also be a vector of length3,in which case theﬁrst element isthe number of grid points and the second and third elements give,respectively,the start and endpoints of the grid.nBoot The number of bootstrap samples to draw.bootType Only one method,"hessian",currently implemented.Type"hessian",draws bootstrap samples using the Bayesian covariance matrix of the parameters(seevcov.gam).gamModel If true,theﬁt of the underlying gam model is saved in the output.May be set to FALSE to save memory,but with the side effect that theﬁt of the gam modelcannot be checked.engine If’gam’,the default,modelﬁtting is done via gam.If’bam’,modelﬁtting is done via bam,which is less memory hungry and can be faster for large data sets....Further arguments passed to gam.DetailsThe function estimates smooth or loglinear population trends,or indexes from simple design count survey data.It is essentially a wrapper around a call to gam,processing its output using predict.gam to produce a trend estimate.For smooth trends,cubic regression splines for the temporal variable are set up by the term s(var,k=k,fx=fx,bs="cr")where var is theﬁrst argument to trend in the formula.For loglinear trends,the identity of var is used,and for index models a factor variable is constructed from var.Temporal random effects are set up by converting the temporal variable supplied to trend to a factor variable and adding this factor variable to the data supplied to gam.Bootstrap conﬁdence intervals are computed by drawing normally distributed random variable with means equal to the estimated coefﬁcients and covariance matrix equal to the Bayesian posterior covariance matrix(see vcov.gam).ValueAn object of class trend.Author(s)Jonas Knape10simTrendExamples##Simulate a data set with15sites and25yearsdata=simTrend(15,25)##Fit a smooth trend with fixed site effects,random time effects,##and automatic selection of degrees of freedomtrFit=ptrend(count~trend(year,tempRE=TRUE,type="smooth")+site,data=data) ##Check the model fitcheckFit(trFit)##Plot the trendplot(trFit)summary(trFit)##Check the estimated percent change from year8to25change(trFit,8,25)##Fit a loglinear trend model with random site effects and random time effects##to the same data set.trLin=ptrend(count~trend(year,tempRE=TRUE,type="loglinear")+s(site,bs="re"),data=data)plot(trLin)summary(trLin)##Fit an index model with fixed site effects and an(unrelated)continous covariate ##as a smooth effect.#Simulate mock covariate unrelated to data.cov=rnorm(nrow(data))trInd=ptrend(count~trend(year,type="index")+site+s(cov),data=data)plot(trInd)summary(trInd)simTrend Simulate population survey data.DescriptionSimulates count survey data with a non-linear trend,and site and temporal random effects.The logistic function is used to create a trend the reduces the expected population size to half its initial value over the time period.UsagesimTrend(nyear=30,nsite=40,mu=3,timeSD=0.1,siteSD=0.3)Argumentsnyear The number of years in the simulated survey.nsite The number of sites in the simulated surveymu The expected mean of the counts at the start of the survey.timeSD Standard deviation(at log-scale)of annual mean deviation from the trend.siteSD Standard deviation(at log-scale)of simulated among site variation.summary.trend11ValueA data frame containing simulated data.Author(s)Jonas Knapesummary.trend Summary of trend estimatesDescriptionComputes a trend or index estimate for each time point in the survey.Usage##S3method for class trendsummary(object,ciBase=NULL,alpha=0.05,...)Argumentsobject A trend object returned by ptrend.ciBase A time point or function used to compute the baseline of the trend.If the argu-ment is numeric,the point in the trendGrid argument of the function ptrendclosest to this value will be taken as the baseline(i.e.the estimated trend will be1at this point).If the argument is a function,the function is applied to trendsand the resulting value is used as the baseline.By default,theﬁrst time point istaken as the reference.alpha alpha level for approximate conﬁdence intervals....Not used.DetailsFor a smooth or loglinear trend model the function computes an estimate of the trend value for each time point in the survey.By default,the reference value is theﬁrst time point.Note that if the trend model wasﬁtted with random effects,the random effects are not included in the estimate.Thus the estimate refers to the long-term component.For an index trend model the index at each time point is computed.If bootstrap samples are available,bootstrap conﬁdence intervals for the trend or index values are also computed.Author(s)Jonas Knape12trend trend Deﬁne a trend component.DescriptionThe function is used to set up the trend component used in ptrend formulas.Usagetrend(var,tempRE=FALSE,type="smooth",by=NA,k=-1,fx=FALSE) Argumentsvar A numeric time variable over which a trend or index will be computed.tempRE If TRUE,this will set up random time effects.The random effects will be con-structed by converting the var argument to a factor.Note that this yields a ran-dom effect level for each unique value in var.If this is not appropriate,analternative is to set tempRE to false and manually add temporal random effectsin the trend formula(using s(...,bs="re")).Temporal random effects cannot beused with index estimation.type The type of trend to be estimated.One of"smooth","loglinear"or"index".by Currently ignored.k The dimension of the basis for the cubic regression spline of smooth trendﬁts.fx If true,automatic selection of degrees of freedom are used for smooth trends. DetailsThe function extracts information about the trend component of a formula supplied to ptrend.It re-turns a list containing variable names,information,and s components as strings used in subsequent calls to gam.ValueA list containing information to set up the trend.Author(s)Jonas KnapeExamples##Simulate a data set with15sites and25yearsdata=simTrend(15,25)##Fit a smooth trend with fixed site effects,but no random time effects,##and fixed degrees of freedomtrFit=ptrend(count~trend(year,tempRE=FALSE,k=8,fx=FALSE,type="smooth")+ site,data=data)plot(trFit)Index∗datasetsgoldcrest,4greenfinch,4bam,9change,2checkFit,3gam,7,9gam.check,3goldcrest,4greenfinch,4hessBootstrap,5mgcv,7plot.default,7plot.gam,3plot.trend,6poptrend,7predict.gam,9print.trend,8ptrend,2,5,6,8,11s,12simTrend,10summary.trend,11trend,9,12vcov.gam,5,913。

generalized additive mixed modeling

generalized additive mixed modeling摘要：I.简介- 介绍generalized additive mixed modeling（GAMM）- 解释GAMM 在数据建模中的作用II.GAMM 的原理- 详细介绍GAMM 的建模原理- 阐述GAMM 与其他建模方法的区别III.GAMM 的应用领域- 举例说明GAMM 在各个领域的应用- 强调GAMM 在复杂数据集处理方面的优势IV.GAMM 的局限性与未来展望- 分析GAMM 在实际应用中的局限性- 探讨GAMM 未来的研究方向和前景正文：I.简介Generalized additive mixed modeling（GAMM）是一种强大的数据建模方法，它结合了广义线性模型（GLM）和additive mixed modeling （AMM）的优点，能够有效地处理各种类型的数据。

GAMM 广泛应用于各种领域，如生物学、社会科学、医学等，为研究者提供了丰富的信息。

II.GAMM 的原理GAMM 的建模原理主要包括两部分：广义线性模型（GLM）和additive mixed modeling（AMM）。

GLM 是一种用于分析连续或离散响应变量的线性模型，可以处理各种分布的响应变量，如正态分布、泊松分布等。

AMM 则是一种用于处理复杂数据结构的建模方法，可以同时处理分类和连续变量。

GAMM 将这两部分结合起来，形成了一个统一的建模框架。

它允许研究者使用各种类型的数据，并提供了强大的建模能力。

此外，GAMM 还具有可扩展性，可以根据需要添加新的函数和分布。

III.GAMM 的应用领域GAMM 在各个领域都有广泛的应用。

在生物学中，GAMM 可以用于分析基因表达数据，寻找关键基因和生物标志物。

在社会科学中，GAMM 可以用于分析问卷调查数据，探讨各种社会现象之间的关系。

在医学中，GAMM 可以用于分析患者的临床数据，为疾病诊断和治疗提供依据。

glm的名词解释

glm的名词解释经典的广义线性模型（Generalized Linear Model，简称GLM）是统计学中一种非常重要的模型，它是线性回归模型的一种泛化形式，适用于各种类型的响应变量。

GLM的提出主要是为了应对线性回归模型对响应变量分布的假设限制，从而更好地适应实际问题。

GLM的本质是建立一个联系函数（link function）和一个线性预测函数之间的关系，联系函数的作用是将线性预测值映射到响应变量的预测值上。

同时，GLM还引入了一个协方差函数（variance function），用于描述响应变量的变异性。

通过这三个关键部分的组合，GLM可以分别应对高斯分布、伯努利分布、多项分布等不同类型的响应变量。

首先，让我们来了解一下GLM的联系函数。

联系函数的作用是将线性预测函数的结果映射到响应变量的预测值上。

这意味着GLM可以适用于非线性关系的建模。

常见的联系函数有标识函数、逻辑函数、逆函数等。

例如，在二分类问题中，我们可以使用逻辑函数作为联系函数，将线性预测值映射到一个[0,1]区间上的概率值，从而进行分类预测。

其次，GLM的线性预测函数是由一组解释变量（也称为自变量或特征）的线性组合构成的。

这个线性组合可以使用多个组合方式，例如，可以通过特征的加权求和、交互项的引入等方式构建。

线性预测函数的构建过程是非常灵活的，这使得GLM可以适应各种类型的数据情况。

最后，GLM的协方差函数用于描述响应变量的变异性。

不同的响应变量类型通常对应不同的协方差函数。

例如，在高斯分布情况下，协方差函数可以取恒等函数；在伯努利分布情况下，可以取为二项分布的方差函数。

通过引入协方差函数，GLM可以准确描述响应变量的分布特征，从而更好地进行参数估计和推断。

总的来说，GLM通过引入联系函数、线性预测函数和协方差函数，可以适应各种类型的响应变量，并且克服了线性回归模型对响应变量分布的假设限制。

GLM在统计学中应用广泛，尤其是在医学、经济学、生态学等领域。

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generalized additive mixed modeling1. 引言1.1 概述在统计建模中，回归模型是一种常见的分析工具，用于研究变量之间的关系。

然而，传统的回归模型通常对数据的线性关系做出了限制，无法很好地拟合复杂的非线性关系。

为了解决这个问题，广义可加混合模型（Generalized Additive Mixed Modeling, GAMM）应运而生。

GAMM是一种灵活而强大的统计建模方法，它结合了广义可加模型（Generalized Additive Model, GAM）和混合效应模型（Mixed Effects Model）。

通过引入非线性平滑函数和随机效应，GAMM能够更准确地描述变量之间的复杂关系，并考虑到数据中可能存在的随机变异。

本文将详细介绍GAMM的理论基础、模型框架和参数估计方法。

同时，我们还将探讨GAMM在各个领域中的应用，并与传统回归模型以及混合效应模型进行比较和评估。

最后，我们将总结目前对于GAMM方法的认识，并提出未来研究方向。

1.2 文章结构本文共分为五个部分。

首先，在引言部分概述了GAMM的背景和研究意义。

接下来，第二部分将介绍GAMM的理论基础、模型框架和参数估计方法。

第三部分将详细探讨GAMM在生态学、社会科学和医学研究中的应用案例。

第四部分将与其他回归模型和传统混合模型进行比较，并对GAMM方法的优缺点及局限性进行讨论。

最后，在第五部分中，我们将总结全文的主要内容，并提出对未来研究方向的建议。

1.3 目的本文旨在全面介绍广义可加混合模型（GAMM）这一统计建模方法，以及其在不同领域中的应用。

通过对GAMM的理论基础、模型框架和参数估计方法进行详细描述，读者可以了解到该方法如何解决传统回归模型无法处理非线性关系问题的局限性。

同时，通过实际案例研究，读者可以进一步了解GAMM在生态学、社会科学和医学研究等领域中的应用效果。

此外，通过与其他回归模型和传统混合模型进行比较，本文还旨在评估GAMM方法的优势和局限性。

最后，本文将总结当前对于GAMM方法的认识，并提出未来研究的方向和建议。

2. Generalized Additive Mixed Modeling (GAMM)2.1 理论基础:Generalized Additive Mixed Modeling (GAMM)是一种灵活且广泛应用于统计建模的方法。

它结合了广义可加模型（Generalized Additive Models，GAM）和混合效应模型（Mixed Effects Models）的优势，能够处理复杂、非线性和非正态数据的建模问题。

在GAMM中，我们考虑了两个核心组成部分：广义可加模型和混合效应模型。

广义可加模型通过使用非线性平滑函数来描述自变量与因变量之间的关系，并允许捕捉到数据中潜在的非线性结构。

混合效应模型则考虑了随机效应，用于建模数据中存在的随机变化，并通过引入随机项来进一步提高模型的灵活性和准确性。

2.2 模型框架:GAMM可以被表达为如下形式的数学公式：Y = Xβ+ f₁(X₁) + ... + fₖ(Xₖ) + Zb + ɛ其中，Y表示响应变量，X是固定效应参数向量，f₁(X₁)到fₖ(Xₖ)是平滑函数用于描述自变量X₁到Xₖ与响应变量之间的关系，Z是设计矩阵用于描述随机效应的结构，b是随机效应参数向量，ɛ代表误差项。

2.3 模型参数估计方法:在GAMM中，模型参数通常通过最大似然估计方法进行估计。

求解模型的最大似然估计可以通过迭代算法实现，其中一种常用的方法是基于广义线性混合模型（Generalized Linear Mixed Models, GLMM）和广义可加模型（GAM）之间的循环迭代过程。

在GAMM中，平滑函数的平滑度也需要进行选择和调整。

通常使用交叉验证、信息准则（如AIC或BIC）、广义交互验证等方法来评估和比较不同平滑度下模型的拟合能力，并选择最佳的平滑度参数。

总之，GAMM提供了一种灵活且强大的统计建模方法，可以用于分析复杂、非线性和非正态数据。

它的理论基础涵盖了广义可加模型和混合效应模型，并采用最大似然估计方法进行参数估计。

通过适当选择平滑函数及其平滑度参数，我们可以更好地探索数据中潜在的非线性结构，并获得更准确和全面的统计推断结果。

3. 应用领域和案例研究3.1 生态学研究中的应用Generalized Additive Mixed Modeling (GAMM)在生态学研究中有着广泛的应用。

生态系统的复杂性通常导致数据呈现出非线性关系，并且存在许多潜在影响因素。

由于GAMM可以捕捉到非线性和非平稳关系，因此它成为了解决生态系统数据分析挑战的强大工具。

例如，在森林生态学研究中，研究人员可以利用GAMM来探索树木物种多样性与环境变量之间的关系。

他们可以通过建立一个包含非线性平滑项、随机效应和固定效应的模型，来评估气候变量、土壤特征等因素对于树木物种多样性的影响。

3.2 社会科学研究中的应用社会科学领域广泛使用GAMM来分析和预测各种社会现象。

例如，在经济学研究中，GAMM可以被用来建立预测通货膨胀率或股票市场波动性的模型。

研究人员可以结合时间序列数据和其他相关因素，如利率、失业率等，来进行预测分析。

此外，在社会心理学研究中，GAMM也可以用于探索人类行为与各种心理因素之间的关系。

例如，研究人员可以使用GAMM来分析社交媒体数据，以了解社交媒体使用量与个人幸福感之间是否存在非线性的关联。

3.3 医学研究中的应用医学研究中的数据通常具有复杂的结构和多层次特征。

GAMM提供了一种强大的方法来处理这些多层次数据，并且能够捕捉到各种影响因素之间复杂的关系。

例如，在流行病学研究中，研究人员可以利用GAMM来分析和预测疾病发生率及其与环境因素之间的关系。

他们可以通过结合空间和时间上的非线性平滑项来对传染病传播模式进行建模，并评估不同环境因素对于传染病风险的影响。

此外，在临床试验中，GAMM也被用于分析患者治疗效果和生存率等指标与治疗方案、患者特征等因素之间的关系。

研究人员可以利用GAMM来探索治疗效果在不同患者子群中是否存在差异，并定量评估各种影响因素对于治疗结果的贡献程度。

综上所述，GAMM在生态学、社会科学和医学研究领域都有广泛的应用。

其能够处理具有复杂结构和非线性特征的数据，为研究人员提供了一种强大而灵活的建模工具，以揭示出数据背后隐藏的关系和规律。

4. 方法比较和评估4.1 与其他回归模型的比较在这一部分，我们将介绍广义可加混合模型（Generalized Additive Mixed Modeling，GAMM）与其他常见的回归模型进行比较。

首先是与线性回归模型的比较。

线性回归模型假设自变量和因变量之间的关系是线性的，而GAMM则允许非线性关系的存在。

这意味着GAMM可以更准确地捕捉到自变量对因变量的影响。

此外，同样在拟合非线性函数方面，GAMM相对于多项式回归、样条回归等方法具有更高的灵活性。

其次是与广义线性混合模型（Generalized Linear Mixed Model, GLMM）的比较。

GLMM是将随机效应引入广义线性模型中，用于处理具有非正态误差结构或离散因变量的数据。

相对于GLMM来说，GAMM不仅可以处理类似问题，还能处理具有非线性关系或连续响应变量问题。

另外一个值得比较的模型是Generalized Additive Models (GAMs)。

尽管在名称上看起来与GAMM很相似，但它们有着一些重要区别。

GAM使用加性非线性函数模拟自变量和因变量之间的关系，而不涉及混合效应。

相比之下，GAMM 引入了随机效应，使得模型更适用于处理来自多层次结构或者重复测量的数据。

4.2 与传统混合模型的比较在这一部分，我们将讨论GAMM与传统混合模型（Traditional Mixed Effect Models）的比较。

传统混合模型是指固定效应和随机效应的叠加，在处理相关数据时具有较强的实用性。

然而，传统混合模型对于非线性关系的建模能力相对有限。

与此相反，GAMM通过引入广义可加属性解决了这个问题，并增强了对非线性关系建模的能力。

因此，在涉及到非线性关系建模时，GAMM可能是更好的选择。

4.3 优缺点讨论与局限性分析在本节中，我们将综合讨论与GAMM相关的优点、缺点以及其局限性。

首先是GAMM的优点。

首先，GAMM具有很高的灵活性，可以捕捉到因变量和自变量之间更复杂、非线性且非常态分布的关系。

其次，GAMM还具有无参数设定的优势，避免了对分布形式的假设。

此外，GAMM还能够很好地处理来自多层次结构或重复测量的数据。

然而，GAMM也存在一些缺点和局限性。

首先是对大样本数据的计算复杂性。

由于GAMM中模型参数估计的计算成本较高，当面临大规模数据集时，可能需要更多时间和计算资源。

其次是GAMM在解释因果关系方面相对困难。

由于GAMM着重于描述变量之间的关系而非因果关系，对因果推断意义有限。

综上所述，GAMM作为一种灵活、非线性建模工具，在许多领域都获得了广泛应用。

然而，在使用和解释GAMM时，我们需要认识到其优点、缺点以及局限性，并结合具体研究问题进行判断和选择。

5. 结论和展望5.1 结论总结:综上所述，本文对广义可加混合模型（GAMM）进行了详细介绍和分析。

在引言部分我们概述了文章的目的和结构。

随后我们阐述了GAMM的理论基础并介绍了其模型框架和参数估计方法。

接着，我们探讨了GAMM在生态学、社会科学和医学研究中的应用。

此外，我们还比较了GAMM与其他回归模型以及传统混合模型之间的差异，并讨论了其优缺点和局限性。

在应用领域方面，生态学研究中使用GAMM可以更准确地分析环境因素对物种多样性或群落组成的影响。

社会科学研究中，GAMM可以帮助解决非线性关系问题，例如探索收入水平、教育程度等变量对人们幸福感的影响。

而在医学研究方面，GAMM可用于建立与时间相关的疾病预测模型。

通过与其他回归模型进行比较，我们发现GAMM能够更好地捕捉非线性关系，并通过非参数平滑函数灵活地建模。

相比传统混合模型，GAMM在处理非线性效应时表现更出色。

然而，GAMM也存在一些局限性，例如对大样本数据的计算复杂性较高。

5.2 对未来研究方向的建议:在未来的研究中，我们建议进一步探索以下方向以推动广义可加混合模型（GAMM）的发展：1. 开发更高效的参数估计算法：当前推断GAMM模型的方法多数基于迭代算法，计算复杂度较高。

未来可以探索并开发更高效的参数估计算法，以提升模型拟合速度和准确性。

2. 扩展适用场景：虽然GAMM已经被广泛应用于生态学、社会科学和医学领域，并取得了显著成果，但仍有其他领域有待探索其潜力。