# 统计代写|广义线性模型代写generalized linear model代考|STA517

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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
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## 统计代写|广义线性模型代写generalized linear model代考|SUM OF SQUARES AND COVARIANCE MATRIX ALGORITHMS

In Section $4.1$ a finite model was presented for an experiment with $r$ replicate observations nested in $b t$ block treatment combinations. This experiment is now used to establish the sum of squares and covariance matrix algorithm rules for finite models.

Let the $b$ tr $\times 1$ random vector $\mathbf{Y}=\left(Y_{111}, \ldots, Y_{11 r}, \ldots, Y_{b t 1}, \ldots, Y_{b t r}\right)^{\prime}$. The covariance matrix $\Sigma=\operatorname{cov}(\mathbf{Y})$ for the finite model is given by
\begin{aligned} \Sigma=& \sigma_B^2\left[\mathbf{I}b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right] \ &+\sigma{B T}^2\left[\mathbf{I}b \otimes\left(\mathbf{I}_t-\frac{1}{t} \mathbf{J}_t\right) \otimes \mathbf{J}_r\right] \ &+\sigma{R(B T)}^2\left[\mathbf{I}_b \otimes \mathbf{I}_t \otimes \mathbf{I}_r\right] . \end{aligned}
The rules for constructing the matrix $\Sigma$ are given in the following paragraphs. The matrix $\Sigma$ is constructed in tabular form. The first rule describes the construction of the table, and the second rule describes the matrix terms that fill the table.
Rule $\Sigma 1$ List the variances of all random factors and interactions, one variance in each row. Construct column headings where the first column heading designates the main factor letters and the second heading designates the number of levels of the factor. Place brackets ([ ]), Kronecker product symbols $(\otimes)$, and plus signs $(+)$ in each row, as described in Example 4.3.1.

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

The covariance algorithm can be applied to complete, balanced finite models with any number of fixed and random main effects, interactions, or nested factors.
For infinite models, the same covariance matrix algorithm can be used, except that Rule $\Sigma 2.2$ is omitted. That is, for infinite models that do not contain restrictions on variables representing interactions of random and fixed factors, the covariance matrix is constructed following Rules $\Sigma 1, \Sigma 2, \Sigma 2$.1, and $\Sigma 2.3$. The next example illustrates the construction of covariance matrices in such models.
Example 4.3.2 Consider the experiment in Example 4.3.1, but now use an infinite model that does not admit restrictions. Using Rules $\Sigma 1, \Sigma 2, \Sigma 2.1$, and $\Sigma 2.3$, the covariance matrix is given by
$$\begin{array}{rlr} \Sigma= & \sigma_B^2 & {\left[\mathbf{I}b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{B T}^2 & {\left[\mathbf{I}b \otimes \mathbf{I}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{R(B T)}^2 & {\left[\mathbf{I}b \otimes \mathbf{I}_t \otimes \mathbf{I}_r\right] .} \end{array}$$ Although finite and infinite models are motivated in different ways and produce different covariance structures, algebraically the two covariance structures are simply reparameterizations of each other. To illustrate this point, consider the previous experiment with $b$ random blocks, $t$ fixed treatments, and $r$ random replicates per treatment. First, rewrite the covariance matrix for the finite model in the following equivalent form. $$\begin{array}{rlr} \Sigma= & \left(\sigma_B^2-\frac{1}{t} \sigma{B T}^2\right) & {\left[\mathbf{I}b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{B T}^2 & {\left[\mathbf{I}b \otimes \mathbf{I}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{R(B T)}^2 & {\left[\mathbf{I}b \otimes \mathbf{I}_t \otimes \mathbf{I}_r\right] .} \end{array}$$ Now to distinguish the parameters in the finite and infinite models, rename the variance parameters $\sigma_B^2, \sigma{B T}^2$, and $\sigma_{R(B T)}^2$ in the infinite model as $\sigma_{B^}^2, \sigma_{B T^}^2$, and $\sigma_{R(B T)}^2$ * , respectively. Then the covariance matrix for the infinite model becomes
$$\begin{array}{rlr} \Sigma= & \sigma_B^2 . & {\left[\mathbf{I}b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{B T^}^2 & {\left[\mathbf{I}b \otimes \mathbf{I}_t \otimes \mathbf{J}_r\right]} \ & +\sigma{R(B T)^}^2 & {\left[\mathbf{I}_b \otimes \mathbf{I}_t \otimes \mathbf{I}_r\right] .} \end{array}$$

# 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|平方和和协方差矩阵算法

$$\Sigma=\sigma_B^2\left[\mathbf{I} b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right] \quad+\sigma B T^2\left[\mathbf{I} b \otimes\left(\mathbf{I}_t-\frac{1}{t} \mathbf{J}_t\right) \otimes \mathbf{J}_r\right]+\sigma R(B T)^2\left[\mathbf{I}_b\right.$$

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

$\Sigma=\sigma_B^2 \quad\left[\mathbf{I} b \otimes \mathbf{J}t \otimes \mathbf{J}_r\right] \quad+\sigma B T^2 \quad\left[\mathbf{I} b \otimes \mathbf{I}_t \otimes \mathbf{J}_r\right] \quad+\sigma R(B T)^2 \quad\left[\mathbf{I} b \otimes \mathbf{I}_t \otimes\right.$ 屈管有限和无限模型以不同的方式激发并产生不同的协方差结构，但从代数上讲，这两个协 方差结构只是彼此的简单重新参数化。为了说明这一点，考虑前面的实验 $b$ 随机块， $t$ 固定治 疗，和 $r$ 每个处理随机重复。首先，用以下等价形式重写有限模型的协方差矩阵。 $\Sigma=\left(\sigma_B^2-\frac{1}{t} \sigma B T^2\right) \quad\left[\mathbf{I} b \otimes \mathbf{J}_t \otimes \mathbf{J}_r\right] \quad+\sigma B T^2 \quad\left[\mathbf{I} b \otimes \mathbf{I}_t \otimes \mathbf{J}_r\right]+\sigma R(B T)^2$ 现在要区分有限和无限模型中的参数，重命名方差参数 $\sigma_B^2, \sigma B T^2$ ，和 $\sigma{R(B T)}^2$ 在无限模型

## 有限元方法代写

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## 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。

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