分类：广义线性模型代写

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

Posted on 2023年5月30日2023年5月30日 by statistics-lab_01, statistics-lab_01

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

广义线性模型（GLiM，或GLM）是John Nelder和Robert Wedderburn在1972年制定的一种高级统计建模技术。它是一个包含许多其他模型的总称，它允许响应变量y具有除正态分布以外的误差分布。

statistics-lab™ 为您的留学生涯保驾护航在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

These variance estimators are referred to as HAC variance estimators because they are heteroskedasticity- and autocorrelation-consistent estimates of the variances (of parameter estimators). A weighted sandwich estimate of variance calculates a (possibly) different middle of the sandwich. Instead of using only the usual score contributions, a weighted sandwich estimate of variance calculates a weighted mean of score contributions and lagged score contributions.
Newey and West (1987) discuss a general method for combining the contributions for each considered lag. The specific implementation then assigns a weight to each lagged score contribution. In related sections, we present various weight functions for use with this general approach.

In the following, let $n$ be the number of observations, $p$ be the number of predictors, $G$ be the maximum lag, $C$ be an overall scale factor, and $q$ be the prespecified bandwidth (number of lags for which the correlation is nonzero). The overall scale factor is usually defined as one but could be defined as $n /(n-p)$ to serve as a small sample scale factor adjustment.

$\begin{aligned} \widehat{V}{\mathrm{NW}} & =\widehat{V}_H^{-1} \widehat{B}{\mathrm{NW}} \widehat{V}H^{-1} \ \widehat{B}{\mathrm{NW}} & =C\left{\widehat{\Omega}0+\sum{j=1}^G \omega\left(\frac{j}{q+1}\right)\left(\widehat{\Omega}j+\widehat{\Omega}_j^{\prime}\right)\right} \ \widehat{\Omega}_j & =\sum{i=j+1}^n x_i \widehat{r}i^S \widehat{T}{i-j}^S x_i^T \ \omega(z) & =\text { sandwich weights } \ \widehat{r}_i^S & =\text { score residuals (see section 4.4.9) }=\nabla_i\left(y_i-\mu_i\right) / v_i\end{aligned}$

统计代写|广义线性模型代写generalized linear model代考|Jackknife

The jackknife estimate of variance estimates variability in fitted parameters by comparing results from leaving out one observation at a time in repeated estimations. Jackknifing is based on a data resampling procedure in which the variability of an estimator is investigated by repeating an estimation with a subsample of the data. Subsample estimates are collected and compared with the full sample estimate to assess variability. Introduced by Quenouille (1949) , an excellent review of this technique and extensions is available in Miller (1974).
The sandwich estimate of variance is related to the jackknife. Asymptotically, it is equivalent to the one-step and iterated jackknife estimates, and as shown in Efron (1981), the sandwich estimate of variance is equal to the infinitesimal jackknife.
There are two general methods for calculating jackknife estimates of variance. One approach is to calculate the variability of the individual estimates from the full sample estimate. We supply formulas for this approach. A less conservative approach is to calculate the variability of the individual estimates from the average of the individual estimates. You may see references to this approach in other sources. Generally, we prefer the approach outlined here because of its more conservative nature.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

这些方差估计量被称为HAC方差估计量，因为它们是方差(参数估计量)的异方差和自相关一致估计。加权三明治方差估计计算一个(可能)不同的三明治中间。加权三明治方差估计不是只使用通常的分数贡献，而是计算分数贡献和滞后分数贡献的加权平均值。
Newey和West(1987)讨论了一种综合考虑每个滞后的贡献的一般方法。然后，具体的实现为每个滞后的分数贡献分配一个权重。在相关章节中，我们将介绍与这种通用方法一起使用的各种权重函数。

在下文中，设$n$为观测数，$p$为预测数，$G$为最大滞后，$C$为总体比例因子，$q$为预先指定的带宽(相关性非零的滞后数)。总体比例因子通常定义为1，但也可以定义为$n /(n-p)$作为小样本比例因子调整。

统计代写|广义线性模型代写generalized linear model代考|Jackknife

方差的折刀估计是通过比较在重复估计中每次省略一个观测值的结果来估计拟合参数的可变性。jackkifing基于数据重采样过程，其中通过对数据的子样本重复估计来研究估计量的可变性。收集子样本估计值并与全样本估计值进行比较，以评估变异性。由Quenouille(1949)介绍，Miller(1974)对该技术进行了极好的回顾和扩展。
夹心估计方差与折刀有关。渐近地，它等价于一步迭代的折刀估计，如Efron(1981)所示，方差的夹心估计等于无穷小的折刀估计。
计算方差的折刀估计有两种一般方法。一种方法是从全样本估计中计算个体估计的可变性。我们为这种方法提供了公式。一种不太保守的方法是从单个估计的平均值计算单个估计的可变性。您可以在其他来源中看到对该方法的引用。一般来说，我们更喜欢这里概述的方法，因为它更保守。

统计代写|广义线性模型代写generalized linear model代考|Goodness of fit

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|Goodness of fit

Posted on 2023年5月30日2023年5月30日 by statistics-lab_01, statistics-lab_01

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计代写|广义线性模型代写generalized linear model代考|Goodness of fit

In developing a model, we hope to generate fitted values $\widehat{\mu}$ that are close to the data $y$. For a dataset with $n$ observations, we may consider candidate models with one to $n$ parameters. The simplest model would include only one parameter. The best one-parameter model would result in $\widehat{\mu}_i=\mu$ (for all $i$ ). Although the model is parsimonious, it does not estimate the variability in the data. The saturated model (with $n$ parameters) would include one parameter for each observation and result in $\widehat{\mu}_i=y_i$. This model exactly reproduces the data but is uninformative because there is no summarization of the data.

We define a measure of fit for the model as twice the difference between the log likelihoods of the model of interest and the saturated model. Because this difference is a measure of the deviation of the model of interest from a perfectly fitting model, the measure is called the deviance. Our competing goals in modeling are to find the simplest model (fewest parameters) that has the smallest deviance (reproduces the data).
The deviance, $D$, is given by
$$
D=\sum_{i=1}^n 2\left[y_i\left{\theta\left(y_i\right)-\theta\left(\mu_i\right)\right}-b\left{\theta\left(y_i\right)\right}+b\left{\theta\left(\mu_i\right)\right}\right]
$$
where the equation is given in terms of the mean parameter $\mu$ instead of the canonical parameter $\theta$. In fitting a particular model, we seek the values of the parameters that minimize the deviance. Thus, optimization in the IRLS algorithm is achieved when the difference in deviance calculations between successive iterations is small (less than some chosen tolerance). The values of the parameters that minimize the deviance are the same as the values of the parameters that maximize the likelihood.

统计代写|广义线性模型代写generalized linear model代考|Estimated variance matrices

It is natural to ask how the Newton-Raphson (based on the observed Hessian) variance estimates compare with the usual (based on the expected Hessian) variance estimates obtained using the IRLS algorithm outlined in the preceding section. The matrix of second derivatives in the IRLS algorithm is equal to the first term in (3.31). As Newson (1999) points out, the calculation of the expected Hessian is simplified from that of the observed Hessian because we assume that $E(\mu-y)=0$ or, equivalently, the conditional mean of $y$ given $X$ is correct. As such, the IRLS algorithm assumes that the conditional mean is specified correctly. Both approaches result in parameter estimates that differ only because of numeric roundoff or because of differences in optimization criteria.

This distinction is especially important in the calculation of sandwich estimates of variance. The Hessian may be calculated as given above in (3.31) or may be calculated using the more restrictive (naïve) assumptions of the IRLS algorithm as
$$
E\left(\frac{\partial^2 \mathcal{L}}{\partial \beta_j \partial \beta_k}\right)=-\sum_{i=1}^n \frac{1}{a(\phi)} \frac{1}{v\left(\mu_i\right)}\left(\frac{\partial \mu}{\partial \eta}\right)i^2 x{j i} x_{k i}
$$
occurs because for the canonical link we can make the substitution that $\theta=\eta$ to zero because

\begin{aligned}
\left(\mu_i-y_i\right) & \left{\frac{1}{v\left(\mu_i\right)^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial v\left(\mu_i\right)}{\partial \mu}-\frac{1}{v\left(\mu_i\right)}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}_i \
& =\left(\mu_i-y_i\right)\left{\frac{1}{(\partial \mu / \partial \eta)_i^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\frac{1}{(\partial \mu / \partial \eta)_i}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}(3.52) \
& =\left(\mu_i-y_i\right)\left{\frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\left(\frac{\partial \eta}{\partial \mu}\right)_i\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right} \
& =\left(\mu_i-y_i\right)\left{\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i-\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i\right} \
& =0
\end{aligned}

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Goodness of fit

在开发模型时，我们希望生成与数据$y$接近的拟合值$\widehat{\mu}$。对于具有$n$观测值的数据集，我们可以考虑具有1到$n$参数的候选模型。最简单的模型将只包含一个参数。最好的单参数模型会得到$\widehat{\mu}_i=\mu$(对于所有的$i$)。虽然该模型是简洁的，但它不估计数据的可变性。饱和模型(具有$n$参数)将为每个观测和结果$\widehat{\mu}_i=y_i$包含一个参数。该模型准确地再现了数据，但没有提供信息，因为没有对数据进行汇总。

我们将模型的拟合度量定义为感兴趣模型的对数似然与饱和模型的对数似然之差的两倍。由于这种差异是对目标模型与完美拟合模型偏差的度量，因此这种度量称为偏差。我们在建模中的竞争目标是找到偏差最小(再现数据)的最简单模型(参数最少)。
偏差$D$由
$$
D=\sum_{i=1}^n 2\left[y_i\left{\theta\left(y_i\right)-\theta\left(\mu_i\right)\right}-b\left{\theta\left(y_i\right)\right}+b\left{\theta\left(\mu_i\right)\right}\right]
$$
其中方程是用平均参数$\mu$而不是规范参数$\theta$给出的。在拟合特定模型时，我们寻求使偏差最小的参数值。因此，当连续迭代之间的偏差计算差异很小(小于选定的容差)时，IRLS算法中的优化就实现了。使偏差最小化的参数值与使似然最大化的参数值相同。

统计代写|广义线性模型代写generalized linear model代考|Estimated variance matrices

很自然地要问牛顿-拉夫森(基于观察到的黑森)方差估计与使用前一节概述的IRLS算法获得的通常(基于期望的黑森)方差估计相比如何。IRLS算法中的二阶导数矩阵等于式(3.31)中的第一项。正如Newson(1999)所指出的那样，期望黑森的计算是从观测到的黑森的计算中简化出来的，因为我们假设$E(\mu-y)=0$，或者等价地，假设$y$给定$X$的条件平均值是正确的。因此，IRLS算法假设条件均值被正确指定。这两种方法都会导致参数估计的不同，这仅仅是因为数字舍入或优化标准的不同。

这种区别在计算夹心估计方差时尤为重要。Hessian可以按照上面(3.31)中给出的方法计算，也可以使用IRLS算法的更严格的假设(naïve)来计算
$$
E\left(\frac{\partial^2 \mathcal{L}}{\partial \beta_j \partial \beta_k}\right)=-\sum_{i=1}^n \frac{1}{a(\phi)} \frac{1}{v\left(\mu_i\right)}\left(\frac{\partial \mu}{\partial \eta}\right)i^2 x{j i} x_{k i}
$$
发生是因为对于规范链接我们可以将$\theta=\eta$替换为零，因为

\begin{aligned}
\left（\mu＿i-y＿i\right) ＆ \left{\frac{1}{v\left(\mu_i\right)^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial v\left(\mu_i\right)}{\partial \mu}-\frac{1}{v\left(\mu_i\right)}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}＿i \＆ =\left（\mu＿i-y＿i\right）\left{\frac{1}{(\partial \mu / \partial \eta)_i^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\frac{1}{(\partial \mu / \partial \eta)_i}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}(3.52) \＆ =\left（\mu＿i-y＿i\right）\left{\frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\left(\frac{\partial \eta}{\partial \mu}\right)_i\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right} \＆ =\left（\mu＿i-y＿i\right）\left{\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i-\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i\right} \＆ =0
\end{aligned}

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|Exponential family

Posted on 2023年5月30日2023年5月30日 by statistics-lab_01, statistics-lab_01

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计代写|广义线性模型代写generalized linear model代考|Exponential family

GLMS are traditionally formulated within the framework of the exponential family of distributions. In the associated representation, we can derive a general model that may be fit using the scoring process (IRLS) detailed in section 3.3 . Many people confuse the estimation method with the class of GLMs. This is a mistake because there are many estimation methods. Some software implementations allow specification of more diverse models than others. We will point this out throughout the text.
The exponential family is usually (there are other algebraically equivalent forms in the literature) written as
$$
f_y(y ; \theta, \phi)=\exp \left{\frac{y \theta-b(\theta)}{a(\phi)}+c(y, \phi)\right}
$$
where $\theta$ is the canonical (natural) parameter of location and $\phi$ is the parameter of scale. The location parameter (also known as the canonical link function) relates to the means, and the scalar parameter relates to the variances for members of the exponential family of distributions including Gaussian, gamma, inverse Gaussian, and others. Using the notation of the exponential family provides a means to specify models for continuous, discrete, proportional, count, and binary outcomes.

In the exponential family presentation, we construe each of the $y_i$ observations as being defined in terms of the parameters $\theta$. Because the observations are independent, the joint density of the sample of observations $y_i$, given parameters $\theta$ and $\phi$, is defined by the product of the density over the individual observations (review section 2.2). Interested readers can review Barndorff-Nielsen (1976) for the theoretical justification that allows this factorization:
$$
f_{y_1, y_2, \ldots, y_n}\left(y_1, y_2, \ldots, y_n ; \theta, \phi\right)=\prod_{i=1}^n \exp \left{\frac{y_i \theta_i-b\left(\theta_i\right)}{a(\phi)}+c\left(y_i, \phi\right)\right}
$$

统计代写|广义线性模型代写generalized linear model代考|Example: Using an offset in a GLM

In subsequent chapters (especially chapter $3$ ), we illustrate the two main components of the specification of a GLM. The first component of a GLM specification is a function of the linear predictor, which substitutes for the location (mean) parameter of the exponential family. This function is called the link function because it links the expected value of the outcome to the linear predictor comprising the regression coefficients; we specify this function with the link ( ) option. The second component of a GLM specification is the variance as a scaled function of the mean. In Stata, this function is specified using the name of a particular member distribution of the exponential family; we specify this function with the family ( ) option. The example below highlights a log-link Poisson GLM.
For this example, it is important to note the treatment of the offset in the linear predictor. The particular choices for the link and variance functions are not relevant to the utility of the offset.

Below, we illustrate the use of an offset with Stata’s glm command. From an analysis presented in chapter 12 , consider the output of the following model:

We would like to test whether the coefficient on white is equal to -0.20 . We could use Stata’s test command to obtain a Wald test

test white=-.20
(1) [los] white $=-.2$
$$
\begin{aligned}
\operatorname{chi}(1) & = & 2.83 \
\text { Prob }>\operatorname{chi2} & = & 0.0924
\end{aligned}
$$
which indicates that -0.15 (coefficient on white) is not significantly different at a $5 \%$ level from -0.20 . However, we want to use a likelihood-ratio test, which is usually a more reliable test of parameter estimate significance. Stata provides a command that stores the likelihood from the unrestricted model (above) and then compares it with a restricted model. Having fit the unrestricted model, our attention now turns to fitting a model satisfying our specific set of constraints. Our constraint is that the coefficient on white be restricted to the constant value -0.20 .

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Exponential family

传统上，GLMS是在指数族分布的框架内制定的。在相关的表示中，我们可以推导出一个通用模型，该模型可以使用3.3节中详细介绍的评分过程(IRLS)进行拟合。许多人将估计方法与glm类混淆。这是一个错误，因为有许多估计方法。一些软件实现允许比其他实现更多样化的模型规范。我们将在整篇文章中指出这一点。
指数族通常(文献中还有其他代数等价形式)写成
$$
f_y(y ; \theta, \phi)=\exp \left{\frac{y \theta-b(\theta)}{a(\phi)}+c(y, \phi)\right}
$$
其中$\theta$为位置的规范(自然)参数，$\phi$为尺度参数。位置参数(也称为规范链接函数)与均值有关，标量参数与指数分布族成员的方差有关，包括高斯分布、伽马分布、逆高斯分布等。使用指数族的符号提供了一种方法来指定连续、离散、比例、计数和二进制结果的模型。

在指数族表示中，我们将每个$y_i$观测值解释为根据参数$\theta$定义的。由于观测值是独立的，观测样本的联合密度$y_i$(给定参数$\theta$和$\phi$)由密度对单个观测值的乘积定义(参见2.2节)。感兴趣的读者可以回顾一下Barndorff-Nielsen(1976)的理论依据:
$$
f_{y_1, y_2, \ldots, y_n}\left(y_1, y_2, \ldots, y_n ; \theta, \phi\right)=\prod_{i=1}^n \exp \left{\frac{y_i \theta_i-b\left(\theta_i\right)}{a(\phi)}+c\left(y_i, \phi\right)\right}
$$

统计代写|广义线性模型代写generalized linear model代考|Example: Using an offset in a GLM

在随后的章节中(特别是$3$章节)，我们将说明GLM规范的两个主要组成部分。GLM规范的第一个组成部分是线性预测器的函数，它替代了指数族的位置(平均)参数。这个函数被称为链接函数，因为它将结果的期望值与包含回归系数的线性预测器联系起来;我们用link()选项指定这个函数。GLM规范的第二个组成部分是作为均值的缩放函数的方差。在Stata中，该函数使用指数族的特定成员分布的名称来指定;我们使用family()选项指定这个函数。下面的示例突出显示了一个日志链接泊松GLM。
对于这个例子，注意线性预测器中偏移量的处理是很重要的。链接和方差函数的特定选择与偏移量的效用无关。

下面，我们用Stata的glm命令说明偏移量的使用。根据第12章的分析，考虑以下模型的输出:

我们想检验白色上的系数是否等于-0.20。我们可以使用Stata的test命令来获得Wald测试

检验白=- 0.20
(1) [los] white $=-.2$
$$
\begin{aligned}
\operatorname{chi}(1) & = & 2.83 \
\text { Prob }>\operatorname{chi2} & = & 0.0924
\end{aligned}
$$
这表明-0.15(白色系数)与-0.20在$5 \%$水平上没有显著差异。然而，我们希望使用似然比检验，这通常是参数估计显著性的更可靠的检验。Stata提供了一个命令来存储来自不受限制模型(如上)的可能性，然后将其与受限制模型进行比较。在拟合了无限制模型之后，我们的注意力现在转向拟合一个满足我们特定约束集的模型。我们的约束条件是白色的系数被限制在常数-0.20。

统计代写|广义线性模型代写generalized linear model代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|BIOS6940

Posted on 2023年2月11日2023年2月11日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|BIOS6940

统计代写|广义线性模型代写generalized linear model代考|Repeated Measures and Longitudinal Data

In repeated measures designs, there are several individuals and measurements are taken repeatedly on each individual. When these repeated measurements are taken over time, it is called a longitudinal study or, in some applications, a panel study. Typically various covariates concerning the individual are recorded and the interest centers on how the response depends on the covariates over time. Often it is reasonable to believe that the response of each individual has several components: a fixed effect, which is a function of the covariates; a random effect, which expresses the variation between individuals; and an error, which is due to measurement or unrecorded variables.

Suppose each individual has response $y_i$, a vector of length $n_i$ which is modeled conditionally on the random effects $\gamma i$ as:
$$
y_i \mid \gamma_i \sim N\left(X_i \boldsymbol{\beta}+Z_i \gamma_i, \sigma^2 \Lambda_i\right)
$$
Notice this is very similar to the model used in the previous chapter with the exception of allowing the errors to have a more general covariance ai. As before, we assume that the random effects $\gamma i \sim N\left(0, \sigma^2 D\right)$ so that:
$$
y_i \sim N\left(X_i \beta, \Sigma_i\right)
$$
where $\Sigma_i=\sigma^2\left(\Lambda_i+Z_i D Z_i^T\right)$.Now suppose we have $M$ individuals and we can assume the errors and random effects between individuals are uncorrelated, then we can combine the data as:
$$
y=\left[\begin{array}{l}
y_1 \
y_2 \
\cdots \
y_M
\end{array}\right] \quad X=\left[\begin{array}{c}
X_1 \
X_2 \
\cdots \
X_M
\end{array}\right] \quad \gamma=\left[\begin{array}{c}
\gamma_1 \
\gamma_2 \
\cdots \
\gamma_M
\end{array}\right]
$$
and $\tilde{D}=\operatorname{diag}(D, D, \ldots, D), Z=\operatorname{diag}\left(Z_1, \quad Z_2, \ldots, \quad Z_M\right), \quad \Sigma=\operatorname{diag}\left(\Sigma_1, \quad \Sigma_2, \ldots, \quad \Sigma_M\right)$, and $\Lambda=\operatorname{diag}\left(\Lambda_1, \Lambda_2, \ldots, \Lambda_M\right)$. Now we can write the model simply as
$$
y \sim N(X \beta, \Sigma) \quad \Sigma=\sigma^2\left(\Lambda+Z \tilde{D} Z^T\right)
$$
The log-likelihood for the data is then computed as above and estimation, testing, standard errors and confidence intervals all follow using standard likelihood theory as before. In fact, there is no strong distinction between the methodology used in this and the previous chapter.

统计代写|广义线性模型代写generalized linear model代考|Longitudinal Data

The Panel Study of Income Dynamics (PSID), begun in 1968, is a longitudinal study of a representative sample of U.S. individuals described in Hill (1992). The study is conducted at the Survey Research Center, Institute for Social Research, University of Michigan, and is still continuing. There are currently 8700 households in the study and many variables are measured. We chose to analyze a random subset of this data, consisting of 85 heads of household who were aged 25-39 in 1968 and had complete data for at least 11 of the years between 1968 and 1990. The variables included were annual income, gender, years of education and age in 1968:

Now plot the data:
$>$ library (lattice)
$>$ xyplot (income $\sim$ year I person, psid, type=” $1 “$,
subset=(person $<21$ ), strip=FALSE)
The first 20 subjects are shown in Figure 9.1. We see that some individuals have a slowly increasing income, typical of someone in steady employment in the same job. Other individuals have more erratic incomes. We can also show how the incomes vary by sex. Income is more naturally considered on a log-scale:
$$

\text { xyplot }(\log (\text { income+100) year I sex, psid, type=” } 1 “)
$$
See Figure 9.2. We added $\$ 100$ to the income of each subject to remove the effect of some subjects having very low incomes for short periods of time. These cases distorted the plots without the adjustment. We see that men’s incomes are generally higher and less variable while women’s incomes are more variable, but are perhaps increasing more quickly. We could fit a line to each subject starting with the first.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Repeated Measures and Longitudinal Data

在重复测量设计中，有几个人并且对每个人重复进行测量。当随着时间的推移进行这些重复测量时，它被称为纵向研究，或者在某些应用中称为面板研究。通常会记录与个体有关的各种协变量，并且关注的焦点是响应随时间的变化如何依赖于协变量。通常有理由相信每个人的反应都有几个组成部分：固定效应，它是协变量的函数；随机效应，表示个体之间的差异；和一个错误，这是由于测量或末记录的变量造成的。
假设每个人都有反应 $y_i$ ，长度向量 $n_i$ 这是根据随机效应有条件地建模的 $\gamma i$ 作为:
$$
y_i \mid \gamma_i \sim N\left(X_i \beta+Z_i \gamma_i, \sigma^2 \Lambda_i\right)
$$
请注意，这与上一章中使用的模型非常相似，只是允许误差具有更一般的协方差 $a i_{\text {。和以前一 }}$ 样，我们假设随机效应 $\gamma i \sim N\left(0, \sigma^2 D\right)$ 以便:
$$
y_i \sim N\left(X_i \beta, \Sigma_i\right)
$$
在哪里 $\Sigma_i=\sigma^2\left(\Lambda_i+Z_i D Z_i^T\right)$.现在假设我们有 $M$ 个体，我们可以假设个体之间的误差和随机效应是不相关的，那么我们可以将数据组合为:
$$
y=\left[\begin{array}{llll}
y_1 & y_2 & \cdots & y_M
\end{array}\right] \quad X=\left[\begin{array}{llll}
X_1 & X_2 & \cdots & X_M
\end{array}\right] \quad \gamma=\left[\begin{array}{llll}
\gamma_1 & \gamma_2 & \cdots & \gamma_M
\end{array}\right]
$$
和
$$
\tilde{D}=\operatorname{diag}(D, D, \ldots, D), Z=\operatorname{diag}\left(Z_1, \quad Z_2, \ldots, \quad Z_M\right), \quad \Sigma=\operatorname{diag}\left(\Sigma_1, \quad \Sigma_2, \ldots,\right.
$$
，和 $\Lambda=\operatorname{diag}\left(\Lambda_1, \Lambda_2, \ldots, \Lambda_M\right)$. 现在我们可以简单地将模型写成
$$
y \sim N(X \beta, \Sigma) \quad \Sigma=\sigma^2\left(\Lambda+Z \tilde{D} Z^T\right)
$$
然后如上所述计算数据的对数似然，然后像以前一样使用标准似然理论进行估计、检验、标准误差和置信区间。事实上，本章所用的方法与上一章并无明显区别。

统计代写|广义线性模型代写generalized linear model代考|Longitudinal Data

收入动态面板研究 (PSID) 始于 1968 年，是对 Hill (1992) 中描述的美国个人代表性样本的纵向研究。该研究在密歇根大学社会研究所调查研究中心进行，目前仍在继续。目前有 8700 户家庭参与研究，并测量了许多变量。我们选择分析该数据的随机子集，该子集由 1968 年 25-39 岁的 85 位户主组成，并且拥有 1968 年至 1990 年之间至少 11 年的完整数据。包括的变量是年收入、性别、受教育年限和 1968 年年龄:
现在绘制数据:
$>$ 图书馆 (格子)
$>$ xyplot (收入年份 I person, psid, type=”1″,
子集 $=($ 人 $<21)$, strip $=F A L S E)$
前20个受试者如图9.1所示。我们看到一些人的收入增长缓慢，典型的是从事同一工作的稳定就业的人。其他人的收入更不稳定。我们还可以显示收入如何因性别而异。在对数尺度上更自然地考虑收入:
$\$ \$$
Itext ${$ xyplot $}(\log ($ (text ${$ income+100) year I sex, psid, type=” $} 1$ “) $\$ \$$
见图9.2。我们添加了 $\$ 100$ 每个受试者的收入，以消除一些短期收入非常低的受试者的影响。这些案例在没有调整的情况下扭曲了情节。我们看到，男性的收入普遍较高且波动较小，而女性的收入波动较大，但可能增长得更快。我们可以从第一个开始为每个主题配一条线。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|STAT3030

Posted on 2023年2月11日2023年2月11日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|STAT3030

统计代写|广义线性模型代写generalized linear model代考|Crossed Effects

Effects are said to be crossed when they are not nested. In full factorial designs, effects are completely crossed because every level of one factor occurs with every level of another factor. However, in some other designs, crossing is less-than-complete. Even if just two levels of two factors occur in all four combinations, the factors are crossed. An example of less than complete crossing is a latin square design, where there is one treatment factor and two blocking factors. Although not all combinations of factors occur, the blocking factors are not nested. When at least some crossing occurs, methods for nested designs cannot be used. We consider a latin square example.

In an experiment reported by Davies (1954), four materials, A, B, C and D, were fed into a wear-testing machine. The response is the loss of weight in $0.1 \mathrm{~mm}$ over the testing period. The machine could process four samples at a time and past experience indicated that there were some differences due to the position of these four samples. Also some differences were suspected from run to run. A fixed effects analysis of this dataset may be found in Faraway (2004). Four runs were made. The latin square structure of the design may be observed:

The lmer function is able to recognize that the run and position effects are crossed and fits the model appropriately. The F-test for the fixed effects is almost the same as the corresponding fixed effects analysis. The only difference is that the fixed effects analysis uses a denominator degrees of freedom of six while the random effects analysis is made conditional on the estimated random effects parameters which results in 12 degrees of freedom. The difference is not crucial here.

The significance of the random effects could be tested using the parametric bootstrap method. However, since the design of this experiment has already restricted the randomization to allow for these effects, there is no motivation to make these tests since we will not modify the analysis of this current experiment.

The fixed effects analysis was somewhat easier to execute, but the random effects analysis has the advantage of producing estimates of the variation in the blocking factors which will be more useful in future studies. Fixed effects estimates of the run effect for this experiment are only useful for the current study.

统计代写|广义线性模型代写generalized linear model代考|Multilevel Models

Multilevel models is a term used for models for data with hierarchical structure. The term is most commonly used in the social sciences. We can use the methodology we have already developed to fit some of these models.

We take as our example some data from the Junior School Project collected from primary (U.S. term is elementary) schools in inner London. The data is described in detail in Mortimore, Sammons, Stoll, Lewis, and Ecob (1988) and a subset is analyzed extensively in Goldstein (1995).

The variables in the data are the school, the class within the school (up to four), gender, social class of the father $(\mathrm{I}=1$; II $=2$; III nonmanual $=3$; III manual $=4$; IV=5; V=6; Long-term unemployed $=7$; Not currently employed=8; Father absent=9), raven’s test in year 1, student id number, english test score, mathematics test score and school year (coded 0,1 , and 2 for years one, two and three). So there are up to three measures per student. The data was obtained from the Multilevel Models project at http://www.ioe.ac.uk/multilevel/.

We shall take as our response the math test score result from the final year and try to model this as a function of gender, social class and the Raven’s test score from the first year which might be taken as a measure of ability when entering the school. We subset the data to ignore the math scores from the first two years:
$>\operatorname{data}(j s p)$
$>j \operatorname{spr}<-j \operatorname{sp} \quad[j \operatorname{sp} \$ y e a r==2$,
We start with two plots of the data. Due to the discreteness of the score results, it is helpful to jitter (add small random perturbations) the scores to avoid overprinting:

plot (jitter (math) jitter (raven), data=jspr, xlab=”Raven
score”,
$\quad$ ylab=”Math score”)
boxplot (math social, data=jspr,xlab=”Social
class”,ylab=”Math score”)
In Figure 8.4, we can see the positive correlation between the Raven’s test score and the final math score. The maximum math score was 40 which reduces the variability at the upper end of the scale. We also see how the math scores tend to decline with social class.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Crossed Effects

当效果没有嵌套时，据说它们是交叉的。在全因子设计中，效应完全交叉，因为一个因素的每个水平都与另一个因素的每个水平发生。然而，在其他一些设计中，交叉是不完整的。即使在所有四个组合中只出现两个因素的两个水平，这些因素也会交叉。不完全交叉的一个例子是拉丁方设计，其中有一个处理因子和两个区组因子。尽管并非所有因素组合都会发生，但区组因素并不嵌套。当至少发生一些交叉时，不能使用嵌套设计的方法。我们考虑一个拉丁方的例子。

在 Davies (1954) 报告的一项实验中，四种材料 A、B、C 和 D 被送入磨损试验机。反应是体重减轻0.1 米米在测试期间。该机器一次可以处理四个样品，过去的经验表明这四个样品的位置存在一些差异。还怀疑运行与运行之间存在一些差异。可以在 Faraway (2004) 中找到该数据集的固定效应分析。进行了四次运行。可以观察到设计的拉丁方结构：

lmer 函数能够识别运行和位置效应交叉并适当地拟合模型。固定效应的 F 检验与相应的固定效应分析几乎相同。唯一的区别是固定效应分析使用的分母自由度为 6，而随机效应分析以估计的随机效应参数为条件，从而产生 12 个自由度。区别在这里并不重要。

随机效应的显着性可以使用参数引导方法进行测试。然而，由于该实验的设计已经限制了随机化以允许这些影响，因此没有动机进行这些测试，因为我们不会修改当前实验的分析。

固定效应分析在某种程度上更容易执行，但随机效应分析的优点是可以估计区组因子的变化，这在未来的研究中更有用。此实验的运行效果的固定效果估计仅对当前研究有用。

统计代写|广义线性模型代写generalized linear model代考|Multilevel Models

多级模型是用于具有层次结构的数据模型的术语。该术语在社会科学中最常用。我们可以使用我们已经开发的方法来拟合其中一些模型。
我们以初级学校项目的一些数据为例，这些数据是从伦敦市中心的小学（美国术语是小学）收集的。Mortimore、Sammons、Stoll、Lewis 和 Ecob (1988) 对数据进行了详细描述， Goldstein (1995) 对其中一个子集进行了广泛分析。
数据中的变量是学校，学校内的班级（最多四个），性别，父亲的社会阶层 $(\mathrm{I}=1 ; 二=2$; III 非手动 $=3$; 三、说明书 $=4 ; I \mathrm{I}=5 ； \mathrm{~V}=6$ ；长期失业 $=7$; 目前末就业 $=8$ ；父亲缺席 $=9 ）$ ，第一年的瑞文考试，学号，英语考试成绩，数学考试成绩和学年（第一，第二和第三年编码为 0,1 和 2) 。所以每个学生最多有 3 个小节。数据来自 http://www.ioe.ac.uk/multilevel/ 的多级模型项目。
我们应将最后一年的数学考试成绩作为我们的回应，并尝试将其建模为性别、社会阶层和第一年的 Raven 考试成绩的函数，这可能被视为入学时的能力衡量标准. 我们对数据进行子集化以忽略前两年的数学成绩:
$>\operatorname{data}(j s p)$
$>j$ spr $<-j$ sp $\quad[j$ sp $\$ y e a r==2$,
我们从两个数据图开始。由于分数结果的离散性，抖动（添加小的随机扰动) 分数有助于避免㨕印:
plot (jitter (math) jitter (raven), data=jspr, $x l a b=$ “Raven
分数”,
ylab=”Math score”)
boxplot (math social, data=jspr,xlab=”Social
class”,ylab=”Math score”)
在图8.4中，我们可以看到Raven的考试成绩和最终的数学成绩呈正相关关系. 最高数学分数为 40，这减少了量表上端的可变性。我们还看到数学成绩如何随着社会阶层的增加而下降。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|MAST30025

Posted on 2023年2月11日2023年2月11日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|MAST30025

统计代写|广义线性模型代写generalized linear model代考|Split Plots

Split plot designs originated in agriculture, but occur frequently in other settings. As the name implies, main plots are split into several subplots. The main plot is treated with a level of one factor while the levels of some other factor are allowed to vary with the subplots. The design arises as a result of restrictions on a full randomization. For example, a field may be divided into four subplots. It may be possible to plant different varieties in the subplots, but only one type of irrigation may be used for the whole field. Note the distinction between split plots and blocks. Blocks are features of the experimental units which we have the option to take advantage of in the experimental design. Split plots impose restrictions on what assignments of factors are possible. They impose requirements on the design that prevent a complete randomization. Split plots often arise in nonagricultural settings when one factor is easy to change while another factor takes much more time to change. If the experimenter must do all runs for each level of the hard-to-change factor consecutively, a split-plot design results with the hardto-change factor representing the whole plot factor.

Consider the following example. In an agricultural field trial, the objective was to determine the effects of two crop varieties and four different irrigation methods. Eight fields were available, but only one type of irrigation may be applied to each field. The fields may be divided into two parts with a different variety planted in each half. The whole plot factor is the method of irrigation, which should be randomly assigned to the fields. Within each field, the variety is randomly assigned. Here is a summary of the data:

The irrigation and variety are fixed effects, but the field is clearly a random effect. We must also consider the interaction between field and variety, which is necessarily also a random effect because one of the two components is random. The fullest model that we might consider is:
$$
y_{i j k}=\mu+i_i+v_j+(\mathrm{iv}){i j}+f_k+(\mathrm{v} f){j k}+\varepsilon_{i j k}
$$
$\mu, i_i, v_j,(i v){i j}$ are fixed effects, the rest are random having variances $\sigma_f^2, \sigma{v f}^2$ and $\sigma_{\varepsilon}^2 \cdot$ Note that we have no $(i f)_{i k}$ term in this model. It would not be possible to estimate such an effect since only one type of irrigation is used on a given field; the factors are not crossed.

统计代写|广义线性模型代写generalized linear model代考|Nested Effects

When the levels of one factor vary only within the levels of another factor, that factor is said to be nested. For example, when measuring the performance of workers at several different job locations, if the workers only work at one location, the workers are nested within the locations. If the workers work at more than one location, then the workers are crossed with locations.

Here is an example to illustrate nesting. Consistency between laboratory tests is important and yet the results may depend on who did the test and where the test was performed. In an experiment to test levels of consistency, a large jar of dried egg powder was divided up into a number of samples. Because the powder was homogenized, the fat content of the samples is the same, but this fact is withheld from the laboratories. Four samples were sent to each of six laboratories. Two of the samples were labeled as $\mathrm{G}$ and two as $\mathrm{H}$, although in fact they were identical. The laboratories were instructed to give two samples to two different technicians. The technicians were then instructed to divide their samples into two parts and measure the fat content of each. So each laboratory reported eight measures, each technician four measures, that is, two replicated measures on each of two samples. The data comes from Bliss (1967): Although the technicians have been labeled “one” and “two,” they are two different people in each lab. Thus the technician factor is nested within laboratories. Furthermore, even though the samples are labeled”H” and “G,” these are not the same samples across the technicians and the laboratories. Hence we have samples nested within technicians. Technicians and samples should be treated as random effects since we may consider these as randomly sampled. If the labs were specifically selected, then they should be taken a fixed effects. If, however, they were randomly selected from those available, then they should be treated as random effects. If the purpose of the study is come to some conclusion about consistency across laboratories, the latter approach is advisable.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Split Plots

裂区设计起源于农业，但在其他环境中也经常出现。顾名思义，主要情节被分成几个次要情节。主要地块用一个因素的水平处理，而其他一些因素的水平允许随子地块变化。该设计是由于对完全随机化的限制而产生的。例如，一个田地可以被分成四个子地块。可以在子地块中种植不同的品种，但整个田地只能使用一种灌溉方式。注意裂区和块之间的区别。块是实验单元的特征，我们可以选择在实验设计中利用这些特征。裂区对可能的因子分配施加了限制。他们对防止完全随机化的设计提出要求。当一个因素很容易改变而另一个因素需要更多时间才能改变时，裂区通常出现在非农业环境中。如果实验者必须连续地对难以更改的因子的每个水平进行所有试验，则裂区设计会产生一个裂区设计，其中难以更改的因子代表整区因子。
考虑以下示例。在农业田间试验中，目标是确定两种作物品种和四种不同灌溉方法的影响。有八块田地，但每块田地只能采用一种淮溉方式。这些田地可以分成两部分，每半部分种植不同的品种。整区因子是灌溉方式，应随机分配到田间。在每个字段中，品种是随机分配的。以下是数据樀要:
灌溉和品种是固定效应，但田地显然是随机效应。我们还必须考虑领域和多样性之间的相互作用，这也必然是一种随机效应，因为这两个成分之一是随机的。我们可能考虑的最完整的模型是:
$$
y_{i j k}=\mu+i_i+v_j+(\mathrm{iv}) i j+f_k+(\mathrm{v} f) j k+\varepsilon_{i j k}
$$
$\mu, i_i, v_j,(i v) i j$ 是固定效应，其余是随机的，有方差 $\sigma_f^2, \sigma v f^2$ 和 $\sigma_{\varepsilon}^2$ 请注意，我们没有 $(\text { if })_{i k}$ 这个模型中的术语。不可能估计这种影响，因为给定的田地只使用一种濩溉方式；这些因素没有交叉。

统计代写|广义线性模型代写generalized linear model代考|Nested Effects

当一个因素的水平仅在另一个因素的水平内变化时，该因素被称为嵌套。例如，在衡量多个不同工作地点的员工的绩效时，如果员工只在一个地点工作，则这些员工会嵌套在这些地点内。如果工人在不止一个地点工作，那么这些工人会跨地点工作。

下面是一个例子来说明嵌套。实验室测试之间的一致性很重要，但结果可能取决于谁进行了测试以及在何处进行测试。在测试一致性水平的实验中，将一大罐干蛋粉分成许多样品。由于粉末经过均质化处理，因此样品的脂肪含量相同，但实验室隐瞒了这一事实。四个样本被送到六个实验室中的每一个。其中两个样本被标记为G和两个作为H，尽管实际上它们是相同的。指示实验室将两个样本提供给两名不同的技术人员。然后指示技术人员将他们的样品分成两部分并测量每部分的脂肪含量。因此，每个实验室报告了八项措施，每位技术人员报告了四项措施，即对两个样品中的每一个样品进行了两次重复测量。数据来自 Bliss (1967)：虽然技术人员被标记为“一个”和“两个”，但他们在每个实验室中都是两个不同的人。因此，技术因素嵌套在实验室中。此外，即使样本被标记为“H”和“G”，但这些样本在技术人员和实验室中并不是相同的。因此，我们将样本嵌套在技术人员中。技术人员和样本应被视为随机效应，因为我们可以将它们视为随机抽样。如果专门选择实验室，则应采用固定效果。但是，如果它们是从可用的那些中随机选择的，那么它们应该被视为随机效应。如果研究的目的是得出关于实验室间一致性的结论，则后一种方法是可取的。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|STATS3001

Posted on 2023年2月10日2023年2月10日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|STATS3001

统计代写|广义线性模型代写generalized linear model代考|Choice of Link Function

We must choose a link function to specify a binomial regression model. It is usually not possible to make this choice based on the data alone. For regions of moderate $p$, that is not close to zero or one, the link functions we have proposed are quite similar and so a very large amount of data would be necessary to distinguish between them. Larger differences are apparent in the tails, but for very small $p$, one needs a very large amount of data to obtain just a few successes, making it expensive to distinguish between link functions in this region. So usually, the choice of link function is made based on assumptions derived from physical knowledge or simple convenience. We now look at some of the advantages and disadvantages of the three proposed link functions and what motivates the choice.

Bliss (1935) analyzed some data on the numbers of insects dying at different levels of insecticide concentration. We fit all three link functions:

The lines in the left panel of Figure $2.3$ do not seem very different, but look at the relative differences:
$>$ matplot $(x$, cbind $(p p / p l,(1-p p) /(1-$
pl)), type=”1″, $x l a b=$ Dose”, $1 \mathrm{ab}=$ “Ratio”)
$>$ matplot (x, cbind (pc/pl, (1-pc) /(1-
pl)), type=”1″, 1 lab=”Dose”,ylab=”Ratio”)
as they appear in the second and third panels of Figure 2.3. We see that the probit and logit differ substantially in the tails. The same phenomenon is observed for the complementary log-log. This is problematic since the former plot indicates it would be difficult to distinguish between the two using the data we have. This is an issue in trials of potential carcinogens and other substances that must be tested for possible harmful effects on humans. Some substances are highly poisonous in that their effects become immediately obvious at doses that might normally be experienced in the environment. It is not difficult to detect such substances. However, there are other substances whose harmful effects only become apparent at large dosages where the observed probabilities are sufficiently larger than zero to become estimable without immense sample sizes. In order to estimate the probability of a harmful effect at a low dose, it would be necessary to select an appropriate link function and yet the data for high dosages will be of little help in doing this. As Paracelsus (1493-1541) said, “All substances are poisons; there is none which is not a poison. The right dose differentiates a poison.”

A good example of this problem is asbestos. Information regarding the harmful effects of asbestos derives from historical studies of workers in industries exposed to very high levels of asbestos dust. However, we would like to know the risk to individuals exposed to low levels of asbestos dust such as those found in old buildings. It is virtually impossible to accurately determine this risk. We cannot accurately measure exposure or outcome. This is not to argue that nothing should be done, but that decisions should be made in recognition of the uncertainties.

统计代写|广义线性模型代写generalized linear model代考|Goodness of Fit

The deviance is one measure of how well the model fits the data, but there are alternatives. The Pearson’s $X^2$ statistic takes the general form:
$$
X^2=\sum_{i=1}^n \frac{\left(O_i-E_i\right)^2}{E_i}
$$
where $O_i$ is the observed counts and $E_i$ are the expected counts for case $i$. For a binomial response, we count the number of successes for which $\theta_i=y_i$ while $E_i=n_i \hat{p}i$ and failures for which $O_i=n_i-y_i$ and $E_i=n_i\left(1-\hat{p}_i\right){\text {which results in: }}$
$$
X^2=\sum_{i=1}^n \frac{\left(y_i-n_i \hat{p}i\right)^2}{n_i \hat{p}_i\left(1-\hat{p}_i\right)} $$ If we define Pearson residuals as: $$ r_i^P=\left(y_i-n_i \hat{p}_i\right) / \sqrt{\operatorname{var} \hat{y}_i} $$ which can be viewed as a type of standardized residual, then $X^2=\sum{i=1}^n\left(r_i^P\right)^2$.So the Pearson’s $X^2$ is analogous to the residual sum of squares used in normal linear models.
The Pearson $X^2$ will typically be close in size to the deviance and can be used in the same manner. Alternative versions of the hypothesis tests described above might use the $X^2$ in place of the deviance with the same approximate null distributions.

However, some care is necessary because the model is fit to minimize the deviance and not the Pearson’s $X^2$. This means that it is possible, although unlikely, that the $X^2$ could increase as a predictor is added to the model. $X^2$ can be computed like this:

The proportion of variance explained or $R^2$ is a popular measure of fit for normal linear models. We might consider applying the same concept to binomial regression models by using the proportion of deviance explained. However, a better statistic is due to Naglekerke (1991):
$$
R^2=\frac{1-\left(\hat{L}0 / \hat{L}\right)^{2 / n}}{1-\hat{L}_o^{2 / n}}=\frac{1-\exp \left(\left(D-D{\text {null }}\right) / n\right)}{1-\exp \left(-D_{\text {null }} / n\right)}
$$

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Choice of Link Function

我们必须选择一个链接函数来指定二项式回归模型。通常不可能仅根据数据做出这种选择。对于中度地区 $p$ ，即不接近于零或一，我们提出的链接函数非常相似，因此需要大量数据来区分它们。较大的差异在尾部很明显，但对于非常小的 $p$ ，需要大量数据才能获得少数成功，因此区分该区域中的链㢺功能非常昂贵。所以通常，链㢺函数的选择是基于从物理知识或简单的便利性得出的假设。我们现在看一下所提出的三个链接函数的一些优点和缺点，以及选择的动机。

Bliss (1935) 分析了一些关于在不同杀虫剂浓度水平下死亡的昆蝼量的数据。我们适合所有三个链㢺功能:
图左面板中的线条 $2.3$ 看起来差别不大，但是看看相对的区别:
$>$ 绘图 $(x$, 绑定 $(p p / p l,(1-p p) /(1-$
pl)), type=”1″, $x l a b=$ 剂量”, $1 \mathrm{ab}=$ “比率”)
$>$ matplot $(x$, cbind $(\mathrm{pc} / \mathrm{pl},(1-\mathrm{pc}) /(1-$
pl)), type=”1″, 1 lab=”Dose”,ylab=”Ratio”)
它们出现在图 $2.3$ 的第二和第三图中。我们看到 probit 和 logit 在尾部有很大不同。互补对数对数也观察到相同的现象。这是有问题的，因为前一个图表明很难使用我们拥有的数据来区分两者。这是潜在致癌物和其他必须测试对人体可能有害影响的物质试验中的一个问题。有些物质具有剧毒，因为它们的影响在正常情况下可能在环境中经历的剂量下立即显现出来。检则此类物质并不困难。然而，还有其他一些物质，其有害影响只有在大剂量时才会显现，在这种情况下，观察到的概率远大于零，无需大量样本即可估计。为了估计低剂量有害影响的可能性，有必要选择一个合适的链接函数，但高剂量的数据对此帮助不大。正如 Paracelsus (14931541) 所兑，“所有物质都是毒药; 无一不是毒。正确的剂量可以区分毒药。”
这个问题的一个很好的例子是石棉。有关石棉有害影响的信息来自对暴露于高浓度石棉粉尘的行业工人的历史研究。但是，我们想知道暴露于低浓度石棉粉尘（例如在旧建筑物中发现的石棉粉尘）的个人所面临的风险。准确确定这种风险几乎是不可能的。我们无法准确衡量风险或结果。这并不是说什么都不应该做，而是应该在认识到不确定性的情兄下做出决定。

统计代写|广义线性模型代写generalized linear model代考|Goodness of Fit

偏差是模型与数据拟合程度的一种衡量标准，但还有其他选择。皮尔逊的 $X^2$ 统计采用一般形式:
$$
X^2=\sum_{i=1}^n \frac{\left(O_i-E_i\right)^2}{E_i}
$$
在哪里 $O_i$ 是观察到的计数和 $E_i$ 是案例的预期计数 $i$. 对于二项式响应，我们计算成功的次数 $\theta_i=y_i$ 尽管 $E_i=n_i \hat{p} i$ 和失败的原因 $O_i=n_i-y_i$ 和 $E_i=n_i\left(1-\hat{p}i\right)$ which results in: $$ X^2=\sum{i=1}^n \frac{\left(y_i-n_i \hat{p} i\right)^2}{n_i \hat{p}i\left(1-\hat{p}_i\right)} $$ 如果我们将 Pearson 残差定义为: $$ r_i^P=\left(y_i-n_i \hat{p}_i\right) / \sqrt{\operatorname{var} \hat{y}_i} $$ 可以看作是一种标准化残差，那么 $X^2=\sum i=1^n\left(r_i^P\right)^2$. 所以皮尔逊的 $X^2$ 类似于正态线性模型中使用的残差平方和。皮尔逊 $X^2$ 通常在大小上接近偏差，并且可以以相同的方式使用。上述假设检验的替代版本可能使用 $X^2$ 用相同的近似零分布代替偏差。但是，有些注意是必要的，因为该模型适用于最小化偏差而不是 Pearson 的 $X^2$. 这意味着尽管不太可能，但有可能 $X^2$ 可能会随着预测变量添加到模型中而增加。 $X^2$ 可以这样计算: 解释的方差比例或 $R^2$ 是正态线性模型的一种流行的拟合度量。我们可能会考虑通过使用解释的偏差比例将相同的概念应用于二项式回归模型。然而，更好的统计数据来自 Naglekerke (1991): $$ R^2=\frac{1-(\hat{L} 0 / \hat{L})^{2 / n}}{1-\hat{L}_o^{2 / n}}=\frac{1-\exp ((D-D \text { null }) / n)}{1-\exp \left(-D{\text {null }} / n\right)}
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|STAT7608

Posted on 2023年2月10日2023年2月10日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|STAT7608

统计代写|广义线性模型代写generalized linear model代考|Interpreting Odds

Odds are sometimes a better scale than probability to represent chance. They arose as a way to express the payoffs for bets. An evens bet means that the winner gets paid an equal amount to that staked. A $3-1$ against bet would pay $\$ 3$ for every $\$ 1$ bet while a $3-1$ on bet would pay only $\$ 1$ for every $\$ 3$ bet. If these bets are fair in the sense that a bettor would break even in the long-run average, then we can make a correspondence to probability. Let $p$ be the probability and $o$ be the odds, where we represent $3-1$ against as $1 / 3$ and $3-1$ on as 3 , then the following relationships hold:
$$
\frac{p}{1-p}=o \quad p=\frac{o}{1+o}
$$
One mathematical advantage of odds is that they are unbounded above which makes them more convenient for some modeling purposes.

Odds also form the basis of a subjective assessment of probability. Some probabilities are determined from considerations of symmetry or long-term frequencies, but such information is often unavailable. Individuals may determine their subjective probability for events by considering what odds they would be prepared to offer on the outcome. Under this theory, other potential persons would be allowed to place bets for or against the event occurring. Thus the individual would be forced to make an honest assessment of probability to avoid financial loss.
If we have two covariates $x_1$ and $x_2$, then the logistic regression model is:
$$
\log (o \mathrm{ods})=\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2
$$

Now $\beta_1$ can be interpreted as follows: a unit increase in $x_1$ with $x_2$ held fixed increases the log-odds of success by $\beta_1$ or increases the odds of success by a factor of exp $\beta_1$. Of course, the usual interpretational difficulties regarding causation apply as in standard regression. No such simple interpretation exists for other links such as the probit.

An alternative notion to odds-ratio is relative risk. Suppose the probability of “success” in the presence of some condition is $p_1$ and $p_2$ in its absence. The relative risk is $P_1 / P_2$. For rare outcomes, the relative risk and the o dds ratio will be very similar, but for larger probabilities, there may be substantial differences. There is some debate over which is the more intuitive way of expressing the effect of some condition.

统计代写|广义线性模型代写generalized linear model代考|Prospective and Retrospective Sampling

In prospective sampling, the predictors are fixed and then the outcome is observed. In other words, in the infant respiratory disease example shown in Table 2.1, we would select a sample of newborn girls and boys whose parents had chosen a particular method of feeding and then monitor them for their first year. This is also called a cohort study.
In retrospective sampling, the outcome is fixed and then the predictors are observed. Typically, we would find infants coming to a doctor with a respiratory disease in the first year and then record their sex and method of feeding. We would also obtain a sample of respiratory disease-free infants and record their information. How these samples are obtained is important-we require that the probability of inclusion in the study is independent of the predictor values. This is also called a case-control study.

Since the question of interest is how the predictors affect the response, prospective sampling seems to be required. Let’s focus on just boys who are breast or bottle fed. The data we need is:

Given the infant is breast fed, the log-odds of having a respiratory disease are $\log 47 / 447=-2.25$
Given the infant is bottle fed, the log-odds of having a respiratory disease are log $77 / 381=-1.60$
The difference between these two log-odds, $\Delta=-1.60–2.25=0.65$, represents the increased risk of respiratory disease incurred by bottle feeding relative to breast feeding. This is the log-odds ratio.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Interpreting Odds

赔率有时比概率更能代表机会。它们的出现是作为一种表达投注收益的方式。均等投注意味着获胜者将获得与下注金额相等的报酬。 $A 3-1$ 反对赌注会付出代价 $\$ 3$ 每一个 $\$ 1$ 下注 $3-1$ 打赌只会支付 $\$ 1$ 每一个 $\$ 3$ 赌注。如果这些投注在投注者长期平均收支平衡的意义上是公平的，那么我们可以与概率对应。让 $p$ 是概率和 $o$ 成为赔率，我们代表的地方 $3-1$ 反对作为 $1 / 3$ 和 $3-1$ 作为 3 ，则以下关系成立:
$$
\frac{p}{1-p}=o \quad p=\frac{o}{1+o}
$$
赔率的一个数学优势是它们不受限制，这使得它们更便于某些建模目的。
赔率也是概率主观评估的基础。一些概率是根据对称性或长期频率的考虑来确定的，但此类信息通常无法获得。个人可以通过考虑他们愿意为结果提供多少赔率来确定他们对事件的主观概率。根据这一理论，其他潜在的人将被允许为或反对正在发生的事件下注。因此，个人将被迫对概率做出诚实的评估，以避免经济损失。如果我们有两个协变量 $x_1$ 和 $x_2$ ，则逻辑回归模型为:
$$
\log (\text { oods })=\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2
$$
现在 $\beta_1$ 可以解释如下: 单位增加 $x_1$ 和 $x_2$ 保持固定增加了成功的对数几率 $\beta_1$ 或将成功几率增加 exp 倍 $\beta_1$. 当然，关于因果关系的常见解释困难适用于标准回归。其他链接 (例如 probit) 不存在这种简单的解释。
比值比的另一种概念是相对风险。假设在某些条件下“成功”的概率是 $p_1$ 和 $p_2$ 在没有它的情况下。相对风险是 $P_1 / P_2$. 对于罕见的结果，相对风险和优势比将非常相似，但对于更大的概率，可能会有很大差异。关于哪种是表达某些条件的影响的更直观的方式存在一些争论。

统计代写|广义线性模型代写generalized linear model代考|Prospective and Retrospective Sampling

在前瞻性抽样中，预恻变量是固定的，然后观察结果。换句话说，在表 $2.1$ 所示的婴儿呼吸系统疾病示例中，我们将选译父母选择特定喂养方法的新生儿女孩和男孩样本，然后在第一年监测他们。这也称为队列研究。
在回顾性抽样中，结果是固定的，然后观察预财因子。通常，我们会发现婴儿在第一年因呼吸系统疾病去看医生，然后记录他们的性别和喂养方式。我们还将获得无呼吸道疾病婴儿的样本并记录他们的信息。如何获得这些样本很重要一一我们要求纳入研究的概率与预则值无关。这也称为病例对岹研究。
由于感兴趣的问题是预测变量如何影响响应，因此似乎需要前瞻性抽样。让我们只关注母乳喂养或奶瓶喂养的男孩。我们需要的数据是:

鉴于婴儿是母乳喂养，患呼吸系统疾病的对数几率是 $\log 47 / 447=-2.25$
鉴于婴儿是奶瓶喂养，患呼吸系统疾病的对数几率是对数 $77 / 381=-1.60$ 这两个对数赔率之间的差异， $\Delta=-1.60-2.25=0.65$, 表示相对于母乳喂养，奶瓶喂养引起呼吸道疾病的风险增加。这是对数优势比。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|MAST30025

Posted on 2023年2月10日2023年2月10日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|Challenger Disaster Example

In January 1986, the space shuttle Challenger exploded shortly after launch. An investigation was launched into the cause of the crash and attention focused on the rubber O-ring seals in the rocket boosters. At lower temperatures, rubber becomes more brittle and is a less effective sealant. At the time of the launch, the temperature was $31^{\circ} \mathrm{F}$. Could the failure of the O-rings have been predicted? In the 23 previous shuttle missions for which data exists, some evidence of damage due to blow by and erosion was recorded on some O-rings. Each shuttle had two boosters, each with three O-rings. For each mission, we know the number of $\mathrm{O}$-rings out of six showing some damage and the launch temperature. This is a simplification of the problem-see Dalal, Fowlkes, and Hoadley (1989) for more details.

Let’s start our analysis with R. For help in obtaining R and installing the necessary add-on packages and datasets, please see Appendix B. First we load the data. To do this, you will first need to load the faraway package using the library command as seen in here. You will need to do this in every session that you run examples from this book. If you forget, you will receive a warning message about the data not being found. We then plot the proportion of damaged O-rings against temperature in Figure 2.1:
$>$ library (faraway)
$>$ data (orings)
$>$ plot (damage/ $6 \sim$ temp, orings, $x l i m=c(25,85)$, ylim $=$
$c(0,1)$,
$\quad x l a b=$ “Temperature”, ylab=”Prob of damage”)
We are interested in how the probability of failure in a given O-ring is related to the launch temperature and predicting that probability when the temperature is $31^{\circ} \mathrm{F}$. A naive approach, based on linear models, simply fits a line to this data:
$$
\begin{aligned}
& >\text { lmod }<-1 \mathrm{~lm} \text { (damage } / 6 \sim \text { temp, orings) } \\ & >\text { abline (lmod) }
\end{aligned}
$$
The fit is shown in Figure 2.1. There are several problems with this approach. Most obviously from the plot, it can predict probabilities greater than one or less than zero. One might suggest truncating predictions outside the range to zero or one as appropriate, but it does not seem eredible that these probabilities would be exactly zero or one, in this particular example or many others.

统计代写|广义线性模型代写generalized linear model代考|Binomial Regression Model

Suppose the response variable $Y_i$ for $i=1, \ldots, n_i$ is binomially distributed $B\left(n_i, p_i\right)$ so that:
$$
P\left(Y_i=y_i\right)=\left(\begin{array}{c}
n_i \
y_i
\end{array}\right) p_i^{y_i}\left(1-p_i\right)^{n_i-y_i}
$$
We further assume that the $Y_i$ are independent. The individual trials that compose the response $Y_i$ are all subject to the same $q$ predictors $\left(x_{i 1}, \ldots, x_{i q}\right)$. The group of trials is known as a covariate class. We need a model that describes the relationship of $x_1, \ldots, x_q$ to $p$. Following the linear model approach, we construct a linear predictor:
$$
\eta_i=\beta_0+\beta_1 x_{i 1}+\ldots+\beta_q x_{i q}
$$

Since the linear predictor can accommodate quantitative and qualitative predictors with the use of dummy variables and also allows for transformations and combinations of the original predictors, it is very flexible and yet retains interpretability. This notion that we can express the effect of the predictors on the response solely through the linear predictor is important. The idea can be extended to models for other types of response and is one of the defining features of the wider class of generalized linear models (GLMs) discussed in Chapter 6.

We have already seen above that setting $\eta_i=p_i$ is not appropriate because we require $0 \leq p_i \leq 1$. Instead we shall use a link function $g$ such that $\eta i=g\left(p_i\right)$. For this application, we shall need $g$ to be monotone and be such that $0 \leq \mathrm{g}^{-1}(\eta) \leq 1$ for any $\eta$. There are three common choices:

Logit: $\eta=\log (p /(1-p))$.
Probit: $\eta=\Phi^{-1}(p)$ where $\Phi^{-1}$ is the inverse normal cumulative distribution function.
Complementary $\log -\log : \eta=\log (-\log (1-p))$.
The idea of the link function is also one of the central ideas of generalized linear models. It is used to link the linear predictor to the mean of the response in the wider class of models.

We will compare these three choices of link function later, but first we estimate the parameters of the model. We shall use the method of maximum likelihood; see Appendix A for a brief introduction to this method. The log-likelihood is given by:
$$
l(\beta)=\sum_{i=1}^n\left[y_i \eta_i-n_i \log \left(1+e_i^\eta\right)+\log \left(\begin{array}{l}
n_i \
y_i
\end{array}\right)\right]
$$
We can maximize this to obtain the maximum likelihood estimates $\hat{\beta}$ and use the standard theory to obtain approximate standard errors. An algorithm to perform the maximization will be discussed in Chapter 6 .

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Challenger Disaster Example

1986 年 1 月，挑战者号航天飞机在发射后不久就爆炸了。对坠机原因展开了调查，并将注意力集中在火箭助推器中的橡胶 $O$ 形密封圈上。在较低的温度下，橡胶变得更脆并且是一种效果较差的密封剂。发射时的温度是 $31^{\circ} \mathrm{F}$. 是否可以预测 $\mathrm{O}$ 形圈的失效? 在现有数据的 23 次航天飞机任务中，一些 $O$ 形环上记录了由于吹过和侵蚀造成的损坏证据。每架航天飞机都有两个助推器，每个助推器都有三个 $O$ 形圈。对于每个任务，我们知道有多少 0 -六分之一的环显示了一些损坏和发射温度。这是问题的简化一一有关详细信息，请参阅 Dalal、Fowlkes 和 Hoadley (1989)。
让我们从 R 开始分析。有关获取 R和安装必要的附加包和数据集的帮助，请参阅附录 $B$ 。首先我们加载数据。为此，您首先需要使用此处所示的库命令加载 faraway 包。您将需要在运行本书示例的每个会话中执行此操作。如果您忘记了，您将收到有关末找到数据的警告消息。然后，我们在图 $2.1$ 中绘制损坏的 O 形圈与温度的比例:
$>$ 图书馆 (遥远)

数据 (orings)
$>$ 情节 (伤害 $6 \sim$ 温度, orings, $x$ lim $=c(25,85)$ ，优越的 $=$ $c(0,1)$,
$x l a b=$ “Temperature”, ylab=”Prob of damage”)
我们感兴趣的是给定 $O$ 形环的失效概率与发射温度的关系，并预测当温度为 $31^{\circ} \mathrm{F}$.一种基于线生模型的朴素方法只是为该数据拟合一条线:
$$
\begin{aligned}
& >\operatorname{lmod}<-1 \operatorname{lm}(\text { damage } / 6 \sim \text { temp, orings) } \\ & >\text { abline }(\operatorname{lmod})
\end{aligned}
$$
拟合如图 $2.1$ 所示。这种方法有几个问题。从图中最明显的是，它可以预测大于一或小于零的概率。有人可能会建议适当地将范围外的预测截断为零或一，但在这个特定示例或许多其他示例中，这些概率恰好为零或一似乎并不可信。

统计代写|广义线性模型代写generalized linear model代考|Binomial Regression Model

假设响应变量 $Y_i$ 为了 $i=1, \ldots, n_i$ 是二项分布的 $B\left(n_i, p_i\right)$ 以便:
$$
P\left(Y_i=y_i\right)=\left(n_i y_i\right) p_i^{y_i}\left(1-p_i\right)^{n_i-y_i}
$$
我们进一步假设 $Y_i$ 是独立的。构成响应的个别试验 $Y_i$ 都受到相同的 $q$ 预测器 $\left(x_{i 1}, \ldots, x_{i q}\right)$. 这组试验称为协变量类。我们需要一个描述关系的模型 $x_1, \ldots, x_q$ 到 $p$. 按照线性模型方法，我们构建了一个线性预测器:
$$
\eta_i=\beta_0+\beta_1 x_{i 1}+\ldots+\beta_q x_{i q}
$$
由于线生预测器可以通过使用虚拟变量来容纳定量和定性预测器，并且还允许原始预测器的转换和组合，因此它非常灵活并保留了可解释性。我们可以仅通过线性预恻变量来表达预则变量对响应的影响这一概念很重要。这个想法可以扩展到其他类型吅应的模型，并且是第 6 章中讨论的更广泛的广义线性模型 (GLM) 类别的定义特征之一。
我们已经在上面看到了那个设置 $\eta_i=p_i$ 不合适，因为我们需要 $0 \leq p_i \leq 1$. 相反，我们将使用链接功能 $g$ 这样 $\eta i=g\left(p_i\right)$. 对于这个应用程序，我们需要 $g$ 是单调的，并且是这样的 $0 \leq \mathrm{g}^{-1}(\eta) \leq 1$ 对于任何 $\eta$. 常见的选择有以下三种:

登录: $\eta=\log (p /(1-p))$.
概率: $\eta=\Phi^{-1}(p)$ 在哪里 $\Phi^{-1}$ 是逆正态累积分布函数。
补充 $\log -\log : \eta=\log (-\log (1-p))$.
链㢺函数的思想也是广义线性模型的核心思想之一。它用于将线生预测变量链㢺到更广泛的模型类别中的响应均值。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|广义线性模型代写generalized linear model代考|STAT3030

Posted on 2022年12月19日2022年12月19日 by statistics-lab

如果你也在怎样代写广义线性模型generalized linear model这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的广义线性模型generalized linear model及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|广义线性模型代写generalized linear model代考|Properties of the Estimator

The least squares estimator $\hat{\boldsymbol{\beta}}$ of Equation $2.7$ has several interesting properties. If the model is correct, in the (weak) sense that the expected value of the response $Y_i$ given the predictors $\mathbf{x}_i$ is indeed $\mathbf{x}_i^{\prime} \boldsymbol{\beta}$, then the OLS estimator is unbiased, its expected value equals the true parameter value:
$$
\mathrm{E}(\hat{\boldsymbol{\beta}})=\boldsymbol{\beta} .
$$
It can also be shown that if the observations are uncorrelated and have constant variance $\sigma^2$, then the variance-covariance matrix of the OLS estimator is
$$
\operatorname{var}(\hat{\boldsymbol{\beta}})=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2 .
$$
This result follows immediately from the fact that $\hat{\boldsymbol{\beta}}$ is a linear function of the data $\mathbf{y}$ (see Equation 2.7), and the assumption that the variance-covariance matrix of the data is $\operatorname{var}(\mathbf{Y})=\sigma^2 \mathbf{I}$, where $\mathbf{I}$ is the identity matrix.

A further property of the estimator is that it has minimum variance among all unbiased estimators that are linear functions of the data, i.e.

it is the best linear unbiased estimator (BLUE). Since no other unbiased estimator can have lower variance for a fixed sample size, we say that OLS estimators are fully efficient.

Finally, it can be shown that the sampling distribution of the OLS estimator $\hat{\boldsymbol{\beta}}$ in large samples is approximately multivariate normal with the mean and variance given above, i.e.
$$
\hat{\boldsymbol{\beta}} \sim N_p\left(\boldsymbol{\beta},\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2\right)
$$

统计代写|广义线性模型代写generalized linear model代考|Estimation of 2

Substituting the OLS estimator of $\boldsymbol{\beta}$ into the log-likelihood in Equation $2.5$ gives a profile likelihood for $\sigma^2$
$$
\log L\left(\sigma^2\right)=-\frac{n}{2} \log \left(2 \pi \sigma^2\right)-\frac{1}{2} \operatorname{RSS}(\hat{\boldsymbol{\beta}}) / \sigma^2 .
$$
Differentiating this expression with respect to $\sigma^2$ (not $\sigma$ ) and setting the derivative to zero leads to the maximum likelihood estimator
$$
\hat{\sigma^2}=\operatorname{RSS}(\hat{\boldsymbol{\beta}}) / n .
$$
This estimator happens to be brased, but the bias is easily corrected dividing by $n-p$ instead of $n$. The situation is exactly analogous to the use of $n-1$ instead of $n$ when estimating a variance. In fact, the estimator of $\sigma^2$ for the null model is the sample variance, since $\hat{\beta}=\bar{y}$ and the residual sum of squares is $\operatorname{RSS}=\sum\left(y_i-\bar{y}\right)^2$.

Under the assumption of normality, the ratio RSS $/ \sigma^2$ of the residual sum of squares to the true parameter value has a chi-squared distribution with $n-p$ degrees of freedom and is independent of the estimator of the linear parameters. You might be interested to know that using the chi-squared distribution as a likelihood to estimate $\sigma^2$ (instead of the normal likelihood to estimate both $\boldsymbol{\beta}$ and $\sigma^2$ ) leads to the unbiased estimator.

For the sample data the RSS for the null model is $2650.2$ on 19 d.f. and therefore $\hat{\sigma}=11.81$, the sample standard deviation.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Properties of the Estimator

最小二乘估计量 $\hat{\beta}$ 方程式 $2.7$ 有几个有趣的属性。如果模型是正确的，在 (弱) 意义上，响应的期望值 $Y_i$ 给定预测变量 $\mathbf{x}_i$ 确实是 $\mathbf{x}_i^{\prime} \boldsymbol{\beta}$ ，则 OLS 估计量是无偏的，其期望值等于真实参数值:
$$
\mathrm{E}(\hat{\boldsymbol{\beta}})=\boldsymbol{\beta} .
$$
还可以证明，如果观测值不相关且方差恒定 $\sigma^2$ ，则OLS估计量的方差-协方差矩阵为
$$
\operatorname{var}(\hat{\boldsymbol{\beta}})=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2
$$
这个结果直接从以下事实得出 $\hat{\boldsymbol{\beta}}$ 是数据的线性函数 $\mathbf{y}$ （参见公式 2.7），并假设数据的方差-协方差矩阵为 $\operatorname{var}(\mathbf{Y})=\sigma^2 \mathbf{I}$ ，在哪里 $\mathbf{I}$ 是单位矩阵。
估计器的另一个属性是它在所有作为数据线性函数的无偏估计器中具有最小方差，即
它是最好的线性无偏估计器（蓝色）。由于没有其他无偏估计量可以针对固定样本量具有更低的方差，因此我们说 OLS 估计量是完全有效的。
最后可以证明OLS估计量的抽样分布 $\hat{\beta}$ 在大样本中近似于多元正态分布，具有上面给出的均值和方差，即
$$
\hat{\boldsymbol{\beta}} \sim N_p\left(\boldsymbol{\beta},\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2\right)
$$

统计代写|广义线性模型代写generalized linear model代考|Estimation of 2

代入 OLS 估计量 $\beta$ 进入等式中的对数似然 $2.5$ 给出概况可能性 $\sigma^2$
$$
\log L\left(\sigma^2\right)=-\frac{n}{2} \log \left(2 \pi \sigma^2\right)-\frac{1}{2} \operatorname{RSS}(\hat{\boldsymbol{\beta}}) / \sigma^2 .
$$
对这个表达式进行微分 $\sigma^2$ (不是 $\sigma$ ) 并将导数设置为零导致最大似然估计
$$
\hat{\sigma^2}=\operatorname{RSS}(\hat{\boldsymbol{\beta}}) / n .
$$
这个估计量恰好是 brased，但偏差很容易通过除以 $n-p$ 代替 $n$. 这种情况完全类似于使用 $n-1$ 代替 $n$ 估计方差时。事实上，估计量 $\sigma^2$ 对于空模型是样本方差，因为 $\hat{\beta}=\bar{y}$ 残差平方和为 $\mathrm{RSS}=\sum\left(y_i-\bar{y}\right)^2$.
在正态性假设下，比值 RSS $/ \sigma^2$ 残差平方和与真实参数值的关系服从卡方分布 $n-p$ 自由度并且独立于线性参数的估计量。您可能有兴趣知道使用卡方分布作为估计的可能性 $\sigma^2$ (而不是估计两者的正常可能性 $\boldsymbol{\beta}$ 和 $\sigma^2$ ) 导致无偏估计。
对于示例数据，空模型的 RSS 是 $2650.2$ 在 $19 \mathrm{df}$ 上，因此 $\hat{\sigma}=11.81$ ，样本标准偏差。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写