## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Random Forests

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Random Forests

The experience with fitting tree models to random partitions of the data provides the inspiration for a method that builds on trees to form a forest. The random forest (RF) method, introduced by Breiman (2001a), uses bootstrap aggregating, known as bagging. For $b=1, \ldots, B$,

1. We draw a sample with replacement from $(X, Y)$ to generate $\left(X_{b}, Y_{b}\right)$.
2. We fit a regression tree to $\left(X_{b}, Y_{b}\right)$.
3. For the set of cases not drawn in bootstrap sample (this will be about one third), we compute the mean squared error of prediction by inputting these predictor cases and comparing the predicted value to the observed value.

The latter step means that we have a measure of prediction performance that avoids the overfitting problem by not using data that was used in the construction of the given tree.

The $B$ trees form the forest. Larger values of $B$ are better although incremental improvement in performance levels off at some point. We will show later how we can be confident we have a sufficiently large $B$. We grow the trees as far as we can without going below a minimum of five cases per node. The trees in the forest will typically be larger than the one we would select as a single tree. New predictions can be made feeding the new predictor value into each of the trees in the forest and averaging the predictions made.

It has been observed that, for some datasets, certain predictors are chosen very frequently, meaning that there are strong correlations among the trees in the forest. To reduce this effect, at each node, a subsample of predictors is selected from which to choose a split. This ensures that every predictor has an opportunity to contribute to the prediction. The default choice of the subsample size is $\sqrt{p}$ where $p$ is the number of predictors.

Let’s fit and examine the default forest. We use the randomForest package of Liaw and Wiener $(2002)$.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Classification Trees

Trees can be used for several different types of response data. For the regression tree, we computed the mean within each partition. This is just the null model for a regression. We can extend the tree method to other types of response by fitting an appropriate null model on each partition. For example, we can extend the idea to binomial, multinomial, Poisson and survival data by using a deviance, instead of the RSS, as a criterion.

Classification trees work similarly to regression trees except the residual sum of squares is no longer a suitable criterion for splitting the nodes. The splits should divide the observations within a node so that the class types within a split are mostly of one kind (or failing that, just a few kinds). We can measure the purity of the node with several possible measures. Let $n_{i k}$ be the number of observations of type $k$ within terminal node $i$ and $p_{i k}$ be the observed proportion of type $k$ within node $i$. Let $D_{i}$ be the measure for node $i$ so that the total measure is $\sum D_{i}$. There are several choices for $D_{i}$ :

1. Deviance:
$$D_{i}=-2 \sum_{k} n_{i k} \log p_{i k}$$
2. Entropy:
$$D_{i}=-\sum_{k} p_{i k} \log p_{i k}$$
3. Gini index:
$$D_{i}=1-\sum_{k} p_{i k}^{2}$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Random Forests

1. 我们从(X,和)生成(Xb,和b).
2. 我们拟合回归树(Xb,和b).
3. 对于未在 bootstrap 样本中绘制的案例集（这将是大约三分之一），我们通过输入这些预测变量案例并将预测值与观察值进行比较来计算预测的均方误差。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Classification Trees

1. 偏差：
D一世=−2∑到n一世到日志⁡p一世到
2. 熵：
D一世=−∑到p一世到日志⁡p一世到
3. 基尼指数：
D一世=1−∑到p一世到2

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Trees

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Regression Trees

1. Consider all partitions of the region of the predictors into two regions where the division is parallel to one of the axes. In other words, we partition a single predictor by choosing a point along the range of that predictor to make the split. It does
343
TREES
344
not matter exactly where we make the split between two adjacent points so there will be at most $(n-1) p$ partitions to consider.
2. For each partition, we take the mean of the response in that partition. We then compute:
$$R S S(\text { partition })=R S S\left(\text { part }{1}\right)+R S S\left(\text { part }{2}\right)$$
We then choose the partition that minimizes the residual sum of squares (RSS). We do need to consider many partitions, but the computations on each partition are simple, so that fit can be accomplished without excessive effort.
3. We now subpartition the partitions in a recursive manner. We only allow partitions within existing partitions and not across them. This means that the partitioning can be represented using a tree. There is no restriction preventing us from splitting the same variables consecutively.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Tree Pruning

One general problem with model selection is that measures of fit such as the RSS (or deviance) usually improve as the complexity of the model increases. The measures tend to give a misleadingly optimistic impression of how well the model will predict future observations. A generic method of obtaining a better estimate of predictive ability is cross-validation (CV). For a given tree, leave out one observation, recalculate the tree and use that tree to predict the left-out observation. Repeat for all observations. For regression, this criterion would be:
$$\sum_{j=1}^{n}\left(y_{j}-\hat{f}{(j)}\left(x{j}\right)\right)^{2}$$
where $\hat{f}{(j)}\left(x{j}\right)$ denotes the predicted value of the tree given the input $x_{j}$ when case $j$ is not used in the construction of the tree. For other types of trees, a different criterion would be used. For classification problems, it might be the deviance.
$\mathrm{CV}$ is a more realistic estimate of how the tree will perform in practice.
348
TREES
Leave-out-one cross-validation is computationally expensive so often $k$-fold crossvalidation is used. The data is randomly divided into $k$ roughly equal parts. We use $k-1$ parts to predict the cases in the remaining part. We repeat $k$ times, leaving out a different part each time. $k=10$ is a typical choice. As well as being much less expensive computationally than the full leave-out-one method, it may even work better. One drawback is that the partition is random so that repeating the method will give different numerical results.

However, there may be very many possible trees if we consider all subsets of a large tree; cross-validation would just be too expensive. We need a method to reduce the set of trees to be considered to just those that are worth considering. This is where cost-complexity pruning is useful. We define a cost-complexity function for trees:
$$C C(\text { Tree })=\sum_{\text {terminal nodes: } i} \operatorname{RSS}_{\mathrm{i}}+\lambda(\text { number of terminal nodes })$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Regression Trees

1. 考虑将预测变量区域的所有分区分成两个区域，其中分区平行于轴之一。换句话说，我们通过在预测器范围内选择一个点来分割单个预测器来进行分割。它确实
343
TREES
344
我们在两个相邻点之间进行分割的确切位置无关紧要，所以最多会有(n−1)p要考虑的分区。
2. 对于每个分区，我们取该分区中响应的平均值。然后我们计算：
R小号小号( 划分 )=R小号小号( 部分 1)+R小号小号( 部分 2)
3. 我们现在以递归方式对分区进行子分区。我们只允许现有分区内的分区，不允许跨它们。这意味着可以使用树来表示分区。没有限制阻止我们连续拆分相同的变量。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Tree Pruning

∑j=1n(和j−F^(j)(Xj))2

C五是对树在实践中的表现的更现实的估计。
348

CC( 树 )=∑终端节点： 一世RSS一世+λ( 终端节点数 )

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Generalized Additive Models

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Additive Modelsa

In generalized linear models:
$$\eta=X \beta \quad E Y=\mu \quad g(\mu)=\eta \quad \operatorname{Var}(Y) \propto V(\mu)$$
The approach is readily extended to additive models to form generalized additive models (GAM). We replace the linear predictor with
$$\eta=\beta_{0}+\sum_{j=1}^{p} f_{j}\left(X_{j}\right)$$
In the mgcv package, the $f_{j}$ are represented by splines. These splines have coefficients that are just more parameters that can be estimated using the likelihood approach.
The ozone data has a response with relatively small integer values. Furthermore, the diagnostic plot in Figure $15.5$ shows nonconstant variance. This suggests that a Poisson response might be suitable. We fit this using:

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Alternating Conditional Expectations

$$y=\alpha+\sum_{j=1}^{p} f_{j}\left(X_{j}\right)+\varepsilon$$
but in the transform-both-sides (TBS) model:
$$\theta(y)=\alpha+\sum_{j=1}^{p} f_{j}\left(X_{j}\right)+\varepsilon$$
For example, $y=e^{x_{1}+\sqrt{x_{2}}}$ cannot be modeled well by additive models, but can if we transform both sides: $\log y=x_{1}+\sqrt{x_{2}}$. This fits within the TBS model framework. A more complicated alternative approach would be nonlinear regression. One particular way of fitting TBS models is alternating conditional expectation (ACE) which is designed to minimize $\sum_{i}\left(\theta\left(y_{i}\right)-\sum f_{j}\left(x_{i j}\right)\right)^{2}$. Distractingly, this can be trivially minimized by setting $\theta=f_{j}=0$ for all $j$. To avoid this solution, we impose the restriction that the variance of $\theta(y)$ be one. The fitting proceeds using the following algorithm:

1. Initialize:
$$\theta(y)=\frac{y-\bar{y}}{S D(y)} \quad f_{j}=\hat{\beta}{j} x{j} \quad j=1, \ldots p$$
332
2. Cycle:
\begin{aligned} f_{j} &=S\left(x_{j}, \theta(y)-\sum_{i \neq j} f_{i}\left(x_{i}\right)\right) \ \theta &=S\left(y, \sum_{j} f_{j}\left(x_{j}\right)\right) \end{aligned}

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Alternating Conditional Expectations

θ(和)=一种+∑j=1pFj(Xj)+e

1. 初始化：
θ(和)=和−和¯小号D(和)Fj=b^jXjj=1,…p
332
附加模型
2. 循环：
Fj=小号(Xj,θ(和)−∑一世≠jF一世(X一世)) θ=小号(和,∑jFj(Xj))

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Additive Models

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Modeling Ozone Concentration

In its basic form, the additive model will do poorly when strong interactions exist. In this case we might consider adding terms like $f_{i j}\left(x_{i} x_{j}\right)$ or even $f_{i j}\left(x_{i}, x_{j}\right)$ if there is sufficient data. Categorical variables can be easily accommodated within the model using the usual regression approach. For example:
$$y=\beta_{0}+\sum_{j=1}^{p} f_{j}\left(X_{j}\right)+Z \gamma+\varepsilon$$
where $Z$ is the design matrix for the variables that will not be modeled additively, where some may be quantitative and others qualitative. The $\gamma$ are the associated regression parameters. We can also have an interaction between a factor and a continuous predictor by fitting a different function for each level of that factor. For example, we might have $f_{\text {male }}$ and $f_{\text {female }}$.

There are several different ways of fitting additive models in $R$. The gam package originates from the work of Hastie and Tibshirani (1990). The mgcv package is part of the recommended suite that comes with the default installation of $R$ and is based on methods described in Wood $(2000)$. The gam package allows more choice in the smoothers used while the mgcv package has an automatic choice in the amount of smoothing as well as wider functionality. The gss package of Gu (2002) takes a spline-based approach.

The fitting algorithm depends on the package used. The backfitting algorithm is used in the gam package. It works as follows:

1. We initialize by setting $\beta_{0}=\bar{y}$ and $f_{j}(x)=\hat{\beta}_{j} x$ where $\hat{\beta}$ is some initial estimate, such as the least squares, for $j=1, \ldots p$.
2. We cycle $j=1, \ldots, p, 1, \ldots, p, 1, \ldots$
$$f_{j}=S\left(x_{j}, y-\beta_{0}-\sum_{i \neq j} f_{i}\left(X_{i}\right)\right)$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Additive Models Using mgcv

The intercept is the only parametric coefficient in this model because all the predictor terms have smooths. We can compute the equivalent degrees of freedom by an analogy to linear models. For linear smoothers, the relationship between the observed and fitted values may be written as $\hat{y}=P y$. The trace of $P$ then estimates the effective number of parameters. For example, in linear regression, the projection matrix is $X\left(X^{T} X\right)^{-1} X^{T}$ whose trace is equal to the rank of $X$ or the number of identifiable parameters. This notion can be used to obtain the degrees of freedom for additive models. The column marked Ref. df is a modified computation of the degrees of freedom which is more appropriate for use in test statistics.

Since we have sums of squares and degrees of freedom, we can compute $F$ statistics in the same way as linear models. However, the $F$-statistics quoted in the summary output have been modified to produce somewhat better statistical properties. The $p$-values are computed from these $F$-statistics and degrees of freedom although we cannot claim the null distributions are exactly $F$-distributed. Usually, they are good approximations. We see that the $R^{2}$, which in this case is called the “Deviance explained” is somewhat higher than in the $1 \mathrm{~m}$ fit.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Modeling Ozone Concentration

1. 我们通过设置初始化b0=和¯和Fj(X)=b^jX在哪里b^是一些初始估计，例如最小二乘，对于j=1,…p.
2. 我们骑自行车j=1,…,p,1,…,p,1,…
Fj=小号(Xj,和−b0−∑一世≠jF一世(X一世))

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Local Polynomials

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Confidence Bands

Examples of orthogonal bases are orthogonal polynomials and the Fourier basis. The disadvantage of both these families is that the basis functions are not compactly supported so that the fit of each basis function depends on the whole data. This means that these fits lack the desirable local fit properties that we have seen in previously discussed smoothing methods. Although Fourier methods are popular for some applications, particularly those involving periodic data, they are not typically used for general-purpose smoothing.

Cubic B-splines are compactly supported, but they are not orthogonal. Wavelets have the advantage that they are compactly supported and can be defined so as to possess the orthogonality property. They also possess the multiresolution property which allows them to fit the grosser features of the curve while focusing on the finer detail where necessary.

We begin with the simplest type of wavelet: the Haar basis. The mother wavelet for the Haar family is defined on the interval $[0,1)$ as:
$$w(x)=\left{\begin{array}{rl} 1 & x \leq 1 / 2 \ -1 & x>1 / 2 \end{array}\right.$$
We generate the members of the family by dilating and translating this function. The next two members of the family are defined on $[0,1 / 2)$ and $[1 / 2,1)$ by rescaling the mother wavelet to these two intervals. The next four members are defined on the quarter intervals in the same way. We can index the family members by level $j$ and within the level by $k$ so that each function will be defined on the interval $\left[k / 2^{j},(k+1) / 2^{j}\right)$ and takes the form:
$$h_{n}(x)=2^{j / 2} w\left(2^{j} x-k\right)$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Wavelets

Instead of simply throwing away higher-order coefficients, we could zero out only the small coefficients. We choose the threshold using the default method:
wtd2 $<-$ threshold (wds)
fd2 <-wr (wtd2)
Now we plot the result as seen in the second panel of Figure 14.11.
plot $(\mathbf{y} \sim \mathbf{x}$, exa, col=gray $(0.75))$
lines (m $\sim \mathbf{x}$, exa)
lines (fd2 $\sim x$, exa, 1ty=5, lwdw2)
Instead of simply throwing away higher-order coefficients, we could zero out
only the small coefficients. We choose the threshold using the default method:
wtd2 <- threshold (wds)
fd2 <- wr (wtd2)
Now we plot the result as seen in the second panel of Figure 14 . 11 .
plot ( $\mathrm{x}$, exa, col=gray $(0.75)$ )
lines (m $\sim \mathrm{x}$, exa)
lines (fd2 $\mathbf{x}$, exa, 1 ty $=5, \quad 1 w d=2$ )
Again, we see a piecewise constant fit, but now the segments are of varying lengths.
Where the function is relatively flat, we do not need the detail from the higher-order
terms. Where the function is more variable, the finer detail is helpful.
We could view the thresholded coefficients as a compressed version of the orig-
inal data (or signal). Some information has been lost in the compression, but the
thresholding algorithm ensures that we tend to keep the detail we need, while throw-
ing away noisier elements.
Even so, the fit is not particularly good because the fit is piecewise constant. We
Again, we see a piecewise constant fit, but now the segments are of varying lengths.
Where the function is relatively flat, we do not need the detail from the higher-order
terms. Where the function is more variable, the finer detail is helpful.
We could view the thresholded coefficients as a compressed version of the original data (or signal). Some information has been lost in the compression, but the thresholding algorithm ensures that we tend to keep the detail we need, while throw= ing away noisier elements.

Even so, the fit is not particularly good because the fit is piecewise constant.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Confidence Bands

$$w(x)=\left{1X≤1/2 −1X>1/2\正确的。 在和G和n和r一种吨和吨H和米和米b和rs○F吨H和F一种米一世一世和b和d一世一世一种吨一世nG一种nd吨r一种ns一世一种吨一世nG吨H一世sF你nC吨一世○n.吨H和n和X吨吨在○米和米b和rs○F吨H和F一种米一世一世和一种r和d和F一世n和d○n[0,1/2)一种nd[1/2,1)b和r和sC一种一世一世nG吨H和米○吨H和r在一种v和一世和吨吨○吨H和s和吨在○一世n吨和rv一种一世s.吨H和n和X吨F○你r米和米b和rs一种r和d和F一世n和d○n吨H和q你一种r吨和r一世n吨和rv一种一世s一世n吨H和s一种米和在一种和.在和C一种n一世nd和X吨H和F一种米一世一世和米和米b和rsb和一世和v和一世j一种nd在一世吨H一世n吨H和一世和v和一世b和到s○吨H一种吨和一种CHF你nC吨一世○n在一世一世一世b和d和F一世n和d○n吨H和一世n吨和rv一种一世[到/2j,(到+1)/2j)一种nd吨一种到和s吨H和F○r米: h_{n}(x)=2^{j / 2} w\left(2^{j} xk\right)$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Wavelets

wtd2<−threshold (wds)
fd2 <-wr (wtd2)

wtd2 <- threshold (wds)
fd2 <- wr (wtd2)

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Nonparametric Regression

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Kernel Estimators

In its simplest form, this is just a moving average estimator. More generally, our estimate of $f$, called $\hat{f}{\lambda}(x)$, is: $\hat{f}{\lambda}(x)=\frac{1}{n \lambda} \sum_{j=1}^{n} K\left(\frac{x-x_{j}}{\lambda}\right) Y_{j}=\frac{1}{n} \sum_{j=1}^{n} w_{j} Y_{j} \quad$ where $\quad w_{j}=K\left(\frac{x-x_{j}}{\lambda}\right) / \lambda$
$K$ is a kernel where $\int K=1$. The moving average kernel is rectangular, but smoother kernels can give better results. $\lambda$ is called the bandwidth, window width or smoothing parameter. It controls the smoothness of the fitted curve.

If the $x$ s are spaced very unevenly, then this estimator can give poor results. This problem is somewhat ameliorated by the Nadaraya-Watson estimator:
$$f_{\lambda}(x)=\frac{\sum_{j=1}^{n} w_{j} Y_{j}}{\sum_{j=1}^{n} w_{j}}$$
We see that this estimator simply modifies the moving average estimator so that it is a true weighted average where the weights for each $y$ will sum to one.

It is worth understanding the basic asymptotics of kernel estimators. The optimal choice of $\lambda$ gives:
$$\operatorname{MSE}(x)=E\left(f(x)-\hat{f}_{\lambda}(x)\right)^{2}=O\left(n^{-4 / 5}\right)$$
MSE stands for mean squared error and we see that this decreases at a rate proportional to $n^{-4 / 5}$ with the sample size. Compare this to the typical parametric estimator where $\operatorname{MSE}(x)=O\left(n^{-1}\right)$, provided that the parametric model is correct. So the kernel estimator is less efficient. Indeed, the relative difference between the MSEs becomes substantial as the sample size increases. However, if the parametric model is incorrect, the MSE will be $O(1)$ and the fit will not improve past a certain point even with unlimited data. The advantage of the nonparametic approach is the protection against model specification error. Without assuming much stronger restrictions on $f$, nonparametric estimators cannot do better than $O\left(n^{-4 / 5}\right)$.

The implementation of a kernel estimator requires two choices: the kernel and the smoothing parameter. For the choice of kernel, smoothness and compactness are desirable. We prefer smoothness to ensure that the resulting estimator is smooth, so for example, the uniform kernel will give stepped-looking fit that we may wish to avoid. We also prefer a compact kernel because this ensures that only data, local to the point at which $f$ is estimated, is used in the fit. This means that the Gaussian kernel is less desirable, because although it is light in the tails, it is not zero, meaning that the contribution of every point to the fit must be computed. The optimal choice under some standard assumptions is the Epanechnikov kernel:
$$K(x)= \begin{cases}\frac{3}{4}\left(1-x^{2}\right) & |x|<1 \ 0 & \text { otherwise }\end{cases}$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Splines

Smoothing Splines: The model is $y_{i}=f\left(x_{i}\right)+\varepsilon_{i}$, so in the spirit of least squares, we might choose $\hat{f}$ to minimize the MSE: $\frac{1}{n} \sum\left(y_{i}-f\left(x_{i}\right)\right)^{2}$. The solution is $\hat{f}\left(x_{i}\right)=y_{i}$ This is a “join the dots” regression that is almost certainly too rough. Instead, suppose we choose $\hat{f}$ to minimize a modified least squares criterion:
$$\frac{1}{n} \sum\left(Y_{i}-f\left(x_{i}\right)\right)^{2}+\lambda \int\left[f^{\prime \prime}(x)\right]^{2} d x$$
where $\lambda>0$ is the smoothing parameter and $\int\left[f^{\prime \prime}(x)\right]^{2} d x$ is a roughness penalty. When $f$ is rough, the penalty is large, but when $f$ is smooth, the penalty is small. Thus the two parts of the criterion balance fit against smoothness. This is the smoothing spline fit.
SPLINES
303
For this choice of roughness penalty, the solution is of a particular form: $\hat{f}$ is a cubic spline. This means that $\hat{f}$ is a piecewise cubic polynomial in each interval $\left(x_{i}, x_{i+1}\right)$ (assuming that the $x_{i}$ s are unique and sorted). It has the property that $\hat{f}, \hat{f}^{\prime}$ and $\hat{f}^{\prime \prime}$ are continuous. Given that we know the form of the solution, the estimation is reduced to the parametric problem of estimating the coefficients of the polynomials. This can be done in a numerically efficient way.

Several variations on the basic theme are possible. Other choices of roughness penalty can be considered, where penalties on higher-order derivatives lead to fits with more continuous derivatives. We can also use weights by inserting them in the sum of squares part of the criterion. This feature is useful when smoothing splines are means to an end for some larger procedure that requires weighting. A robust version can be developed by modifying the sum of squares criterion to:
$$\sum \rho\left(y_{i}-f\left(x_{i}\right)\right)+\lambda \int\left[f^{\prime \prime}(x)\right]^{2} d x$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Kernel Estimators

Fλ(X)=∑j=1n在j和j∑j=1n在j

MSE⁡(X)=和(F(X)−F^λ(X))2=○(n−4/5)
MSE 代表均方误差，我们看到它以与n−4/5与样本量。将此与典型的参数估计器进行比较，其中MSE⁡(X)=○(n−1)，前提是参数模型是正确的。因此内核估计器的效率较低。事实上，随着样本量的增加，MSE 之间的相对差异变得很大。但是，如果参数模型不正确，则 MSE 将○(1)即使有无限的数据，拟合度也不会提高到某个点。非参数方法的优点是防止模型规范错误。没有假设更严格的限制F, 非参数估计器不能比○(n−4/5).

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Splines

1n∑(和一世−F(X一世))2+λ∫[F′′(X)]2dX

SPLINES
303

∑ρ(和一世−F(X一世))+λ∫[F′′(X)]2dX

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Count Response

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|the STAN fit to the epilepsy data

Both were not treated $($ treat $=0)$. The expind indicates the baseline phase by 0 and the treatment phase by 1. The length of these time phases is recorded in timeadj. We have created three new convenience variables: period, denoting the 2- or 8 week periods, drug recording the type of treatment in nonnumeric form and phase indicating the phase of the experiment.

We now compute the mean number of seizures per week broken down by the treatment and baseline vs. experimental period. The dplyr package is useful for these types of group summaries:
library (dplyr)
epilepsy 와>읨
group by (drug, phase) 학하의
summarise (rate-mean (seizures/timeadj)) t के ?
xtabs (formula=rate phase $+$ drug)
We see that the rate of seizures in the treatment group actually increases during the period in which the drug was taken. The rate of seizures also increases even more in the placebo group. Perhaps some other factor is causing the rate of seizures to increase during the treatment period and the drug is actually having a beneficial effect. Now we make some plots to show the difference between the treatment and the control. The first plot shows the difference between the two groups during the experimental period only:

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Generalized Estimating Equations

The advantage of the quasi-likelihood approach as described in Section $9.4$ compared to GLMs was that we did not need to specify the distribution of the response. We only needed to give the link function and the variance. We can adapt this approach for repeated measures and/or longitudinal studies. Let $Y_{i}$ be a vector of random variables representing the responses on a given individual or cluster and let $E Y_{i}=\mu_{i}$ which is then linked to the linear predictor using $g\left(\mu_{i}\right)=x_{i}^{T} \beta$, where $g$ is a link function appropriate to the response type and $x_{i}$ is the predictor vector.
As with the quasi-likelihood, we also need to specify a variance function $a()$ :
$$\operatorname{var} Y_{i}=\phi a\left(\mu_{i}\right)$$
Certain choices of $a()$ will be sensible depending on the type of response. The $\phi$ is a scale parameter which may be set to one if not needed.

In addition, we must also specify how the responses within an individual or cluster are correlated with each other. We set a working correlation matrix $R_{i}(\alpha)$ depending on a parameter $\alpha$ which we will estimate. This results in a working covariance matrix for $Y_{i}$ :
$$V_{i}=\phi A_{i}^{1 / 2} R_{i}(\alpha) A_{i}^{1 / 2}$$
where $A_{i}$ is a diagonal matrix formed from $a\left(\mu_{i}\right)$.
Given estimates of $\phi$ and $\alpha$, we can estimate $\beta$ by setting the (multivariate) score function to zero and solving:
$$\sum_{i}\left(\frac{\partial \mu_{i}}{\partial \beta}\right)^{T} V_{i}^{-1}\left(Y_{i}-\mu_{i}\right)=0$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|the STAN fit to the epilepsy data

library (dplyr)
epilepsy 와>읨
group by (drug, phase) 학하의
summarise (rate-mean (seizures/timeadj)) t के ?
xtabs（公式=速率阶段+药物）

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Generalized Estimating Equations

∑一世(∂μ一世∂b)吨五一世−1(和一世−μ一世)=0

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Mixed Effect Models

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Generalized Linear Mixed Models

Generalized linear mixed models (GLMM) combine the ideas of generalized linear models with the random effects modeling ideas of the previous two chapters. The response is a random variable, $Y_{i}$, taking observed values, $y_{i}$, for $i=1, \ldots, n$, and follows an exponential family distribution as defined in Chapter 8 :
$$f\left(y_{i} \mid \theta_{i}, \phi\right)=\exp \left[\frac{y_{i} \theta_{i}-b\left(\theta_{i}\right)}{a(\phi)}+c(y, \phi)\right]$$
Let $E Y_{i}=\mu_{i}$ and let this be connected to the linear predictor $\eta_{i}$ using the link function $g$ by $\eta_{i}=g\left(\mu_{i}\right)$. Suppose for simplicity that we use the canonical link for $g$ so that we may make the direct connection that $\theta_{i}=\mu_{i}$.

Now let the random effects, $\gamma$, have distribution $h(\gamma \mid V)$ for parameters $V$. The fixed effects are $\beta$. Conditional on the random effects, $\gamma$,
$$\theta_{i}=x_{i}^{T} \beta+z_{i}^{T} \gamma$$
where $x_{i}$ and $z_{i}$ are the corresponding rows from the design matrices, $X$ and $Z$, for the respective fixed and random effects. Now the likelihood may be written as:
$$L(\beta, \phi, V \mid y)=\prod_{i=1}^{n} \int f\left(y_{i} \mid \beta, \phi, \gamma\right) h(\gamma \mid V) d \gamma$$
Typically the random effects are assumed normal: $\gamma \sim N(0, D)$. However, unless $f$ is also normal, the integral remains in the likelihood, which becomes difficult to compute, particularly if the random effects structure is complicated.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Inference

A variety of approaches are available for estimating and performing inference for these models. All have strengths and weaknesses so it is not possible to recommend a single method to use in all circumstances. We present an overview of the theory behind these approaches before demonstrating the implementation on two examples. Later in the chapter, we discuss a related method called generalized estimating equations (GEE).

Penalized Quasi-Likelihood (PQL): In Section 8.2, we described a method by
275
276
MIXED EFFECT MODELS FOR NONNORMAL RESPONSES
which GLMs can be fit using only LMs with weights. The idea is to produce a linearized version of the response which we called the adjusted dependent variable (sometimes called the pseudo or working response) defined as
$$\tilde{y}^{i}=\hat{\eta}^{i}+\left.\left(y-\hat{\mu}^{i}\right) \frac{d \eta}{d \mu}\right|_{\eta^{i}}$$

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Generalized Linear Mixed Models

F(和一世∣θ一世,φ)=经验⁡[和一世θ一世−b(θ一世)一种(φ)+C(和,φ)]

θ一世=X一世吨b+和一世吨C

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Inference

275
276个

，仅使用带权重的 LM 可以拟合 GLM。这个想法是产生响应的线性化版本，我们将其称为调整后的因变量（有时称为伪响应或工作响应），定义为

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Discussion

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Exercises

1. The denim dataset concerns the amount of waste in material cutting for a jeans manufacturer due to five suppliers. See another question on this dataset in Chapter 10 .
(a) Plot the data and comment.
(b) Fit the one-way ANOVA model using INLA using the default prior. Comment on the fit.
(c) Refit the model but with more informative priors. Make a density plot of the error and supplier SD posterior densities.
(d) Calculate summaries of the posteriors from the model fit.
(e) Report $95 \%$ credible intervals for the SDs using the summary output. Compute the posterior modes for the error and supplier SDs and compare these to the posterior means.
(f) Remove the two outliers from the data and repeat the analysis. Comment on any interesting differences.
2. Use the denim dataset again for this question but conduct the analysis using STAN.
(a) Fit the one-way ANOVA model using STAN with the default prior. Produce diagnostic plots for the three parameters: the mean and standard deviations of the supplier and error effects.
(b) Report the posterior mean, $95 \%$ credible intervals and effective sample size for the three parameters.
(c) Make a plot of the posterior densities of the supplier and error effects. Estimate the probability that the supplier SD is bigger than the error SD.
(d) Plot the posterior distributions of the five suppliers. Which supplier tends to produce the least waste and which the most? What is the probability that the best supplier is better than the worst supplier?
(e) A plot of the data reveals two obvious outliers. Repeat the analysis without these two points and report on any interesting differences with the full data.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|maximum

The maximum likelihood analysis of linear mixed models, demonstrated in Chapters 10 and 11 , has several advantages. The models can be specified and fit with a single $R$ command. The statistical hypothesis testing paradigm is widely accepted and may be required for the communication of some scientific research. The calculation of the $p$-values can be difficult, but is possible, even if simulation methods, such as the bootstrap, are required. Even so, problems may arise in fitting these models, particularly to larger datasets. Some types of valid questions cannot be answered in this mode of analysis.

The Bayesian approach offers a quite different way of analyzing this class of models. It offers several advantages in that we can use prior information to improve the inference and we can answer various relevant questions about the application in natural ways. There are some drawbacks. The models are more difficult to specify and require more programming knowledge, particularly when using STAN. The fitting process may fail in ways which are difficult to diagnose and rectify. The specification of reliable, so-called noninformative priors does not seem possible as failures producing unreasonable results are not uncommon. This requires us to think carefully about the specification of these priors. To the Bayesian, this is expected, but to others, this introduces an additional element of subjectivity which makes reaching convincing conclusions more difficult.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|Exercises

1. 牛仔布数据集涉及一家牛仔裤制造商因五家供应商而在材料切割中产生的浪费量。请参阅第 10 章中有关此数据集的另一个问题。
(a) 绘制数据和评论。
(b) 使用默认先验使用 INLA 拟合单向 ANOVA 模型。评论合身。
(c) 重新拟合模型，但具有更多信息的先验。绘制误差和供应商 SD 后验密度的密度图。
(d) 根据模型拟合计算后验的总结。
(e) 报告95%使用汇总输出的 SD 的可信区间。计算误差和供应商 SD 的后验模式，并将其与后验均值进行比较。
(f) 从数据中删除两个异常值并重复分析。评论任何有趣的差异。
2. 再次使用牛仔布数据集解决这个问题，但使用 STAN 进行分析。
(a) 使用 STAN 与默认先验拟合单向 ANOVA 模型。为三个参数生成诊断图：供应商的平均值和标准偏差以及误差效应。
(b) 报告后验平均值，95%三个参数的可信区间和有效样本量。
(c) 绘制供应商后验密度和误差效应的图。估计供应商 SD 大于误差 SD 的概率。
(d) 绘制五个供应商的后验分布。哪个供应商倾向于产生最少的浪费，哪个最多？最好的供应商优于最差的供应商的概率是多少？
(e) 数据图显示了两个明显的异常值。在没有这两点的情况下重复分析，并报告与完整数据的任何有趣差异。

## 广义线性模型代考

statistics-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。

## 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。

## 统计代写| 广义线性模型project代写Generalized Linear Model代考| Bayesian Mixed Effect Models

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。

• 极大似然 Maximum likelihood
• 贝叶斯方法 Bayesian methods
• 线性回归 Linear regression
• 多项式Lo​​gistic回归 Multinomial regression
• 采样理论 sampling theory

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|STAN

One-Way ANOVA: Let’s see how we can use STAN to fit a Bayesian model to the pulp data that we have already explored with $1 \mathrm{me} 4$ in Chapter 10. See Figure 10.1 for a plot of the data. The model has a single factor at $a$ levels:
$$y_{i j}=\mu+\alpha_{i}+\varepsilon_{i j} \quad i=1, \ldots, a \quad j=1, \ldots, n_{i}$$
where the $\alpha$ s and $\varepsilon$ s are independently distributed $N\left(0, \sigma_{\alpha}^{2}\right)$ and $N\left(0, \sigma_{\varepsilon}^{2}\right)$, respectively. There is a single fixed effect parameter $\mu$ and two random effect parameters $\sigma_{\alpha}^{2}$ and $\sigma_{\varepsilon}^{2}$. We must specify prior distributions for these three parameters.

Here is the STAN code we have used to fit our model. It could be used for any one-way ANOVA data. Let’s suppose we have $N$ observations in total with $J$ groups with a response and predictor named just so. You don’t need to understand the STAN code to follow the output so you can skip to the discussion of the output unless you are interested in writing your own STAN programs. You should copy this code into a file called oneway.stan and save it into the working directory for your $R$ session.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|INLA

INLA stands for integrated nested Laplace approximation and was introduced by Rue et al. (2009). A Laplace approximation is a method for computing integrals of the form $\int \exp f(x) d x$. It requires only the maximum of $f$ and the second derivative of $f(x)$ at that point. It can be surprisingly accurate given how little information is required. The INLA method builds on this idea and can be used for a wide class known as Gaussian Markov random field models. This class includes all the models considered in the previous two chapters. Because the method requires no simulation, it is much faster than MCMC-based approaches.

INL.A is an R package that provides an interface to the INLA method. Visit http://WwW.r-inla.org for installation instructions as the package is not available from CRAN.

One-Way ANOVA: Let’s use INLA to fit a model to the pulp data that we have
INLA
267
already explored with lme4 in Chapter 10 and with STAN in Section 12.1. See Figure $10.1$ for a plot of the data and Section $12.1$ for a specification of the model.
We load the library and data before fitting the model.

## 统计代写| 广义线性模型project代写Generalized Linear Model代考|INLA

INLA 代表集成嵌套拉普拉斯近似，由 Rue 等人引入。（2009 年）。拉普拉斯近似是一种计算形式积分的方法∫经验⁡F(X)dX. 它只需要最大F和二阶导数F(X)在那时候。考虑到只需要很少的信息，它可能会非常准确。INLA 方法建立在这一思想之上，可用于称为高斯马尔可夫随机场模型的广泛类别。此类包括前两章中考虑的所有模型。因为该方法不需要仿真，所以它比基于 MCMC 的方法快得多。

INL.A 是一个为 INLA 方法提供接口的 R 包。访问 http://WwW.r-inla.org 获取安装说明，因为 CRAN 不提供该软件包。

INLA
267的纸浆数据。

## 广义线性模型代考

statistics-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。

## 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。