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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

## 统计代写|广义线性模型代写generalized linear model代考|ANCOVA-type models

So far, the baseline data $y_{i j 0}$ was used as one value of the response variable. In this section, we shall introduce some ANCOVA-type models adjusting for the baseline data $y_{i j 0}$. To compare the ANOVA model, we shall consider the following two ANCOVA-type models:
\begin{aligned} \text { Model A: } y_{k i j} &=\mu+\alpha_k+\beta_j+\gamma_{k j}+\epsilon_{k i j}(k=0,1, \ldots, T) \ \text { Model B: } y_{k i j} &=\mu+\theta y_{k i 0}+\alpha_k^{\prime}+\beta_j^{\prime}+\gamma_{k j}^{\prime}+\epsilon_{k i j}^{\prime}(k=1,2, \ldots, T)(3.34) \ \text { Model C: } y_{k i j} &=\mu+\theta y_{k i 0}+\alpha_i^{\prime}+\beta_j^{\prime}+\phi_j\left(y_{k i 0} \times \text { Time }j\right)+\gamma{k j}^{\prime}+\epsilon_{k i j}^{\prime} \ \epsilon_{k i}^{\prime} &=(k=1,2, \ldots, T) \end{aligned}
where
Model A denotes the ANOVA model, Model B denotes an ANCOVA-type model with the baseline effects $\theta$ constant over time, and Model C denotes an ANCOVA-type model with the baseline effects $\theta+\phi_j$ which varies over time.

## 统计代写|广义线性模型代写generalized linear model代考|Shift to mixed-effects repeated measures models

To understand the situation, let us consider the relationship between a pair of data points, the baseline data $y_{k i 0}$ and the data $y_{k i j}$ measured at time $j(>0)$ for the same subject $i$ of the treatment group $k$ in the ANOVA model (3.3). For simplicity, consider here the comparison of two treatment groups $(G=2)$ where $k=1$ denotes the control group and $k=2$ denotes the new treatment group.

In the ANOVA model, as was illustrated with the Rat Data in Section $3.5$, you can choose the best model for the covariance structure $\boldsymbol{\Sigma}k$ (3.4) from many candidates. However, with this approach, you may not be able to understand the reason why the selected covariance model has arisen. So, to understand the covariance structure, let us decompose the error term $\epsilon{k i j}$ into two independent components, one relating to the inter-subject variability and the other relating to the residual error term $\epsilon_{k i j}$. For example, we can consider the following decompositions:
\begin{aligned} y_{k i 0} &=\mu+\alpha_k+\beta_0+\gamma_{k 0}+\epsilon_{k i 0} \ &=\mu+\alpha_k+0+0+\left(b_{0 k i}+\epsilon_{k i 0}\right) \ y_{k i j} &=\mu+\alpha_k+\beta_j+\gamma_{k j}+\epsilon_{k i j} \ &=\mu+\alpha_k+\beta_j+\gamma_{k j}+\left(b_{0 k i}+b_{1 k i}+\epsilon_{k i j}\right) \end{aligned}
where $b_{0 k i}$ denotes the random intercept, which may reflect inter-subject variability due to possibly many unobserved prognostic factors in the baseline period, and $b_{1 k i}$ denotes the random slope, which may reflect inter-subject variability of the response to the treatment and assumed to be constant here regardless of the measurement time $j$. It should be noted that the random slope introduced here does not mean the slope on the time or a linear time trend. Furthermore, these two random variables are assumed to have the bivariate normal distribution:
$$\boldsymbol{b}{k i}=\left(b{0 k i}, b_{1 k i}\right)^t \sim N(0, \Phi),$$
where
$$\Phi=\left(\begin{array}{cc} \sigma_{B 0}^2 & \rho_B \sigma_{B 0} \sigma_{B 1} \ \rho_B \sigma_{B 0} \sigma_{B 1} & \sigma_{B 1}^2 \end{array}\right) .$$

# 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|ANCOVA-type models

Model A: $y_{k i j}=\mu+\alpha_k+\beta_j+\gamma_{k j}+\epsilon_{k i j}(k=0,1, \ldots, T)$ Model B: $y_{k i j} \quad=\mu+\theta y_{k i 0}+\alpha_k^{\prime}+\beta_j^{\prime}+\gamma_{k j}^{\prime}+\epsilon_{k i j}^{\prime}(k=1,2, \ldots, T)(3.34)$ Model C: $y_{k i j}$

## 统计代写|广义线性模型代写generalized linear model代考|Shift to mixed-effects repeated measures models

$$y_{k i 0}=\mu+\alpha_k+\beta_0+\gamma_{k 0}+\epsilon_{k i 0} \quad=\mu+\alpha_k+0+0+\left(b_{0 k i}+\epsilon_{k i 0}\right) y_{k i j}=\mu+\alpha_k+\beta_j+\gamma_{k j}+\epsilon_{k i j} \quad=\mu+\alpha_k+\beta_j+\gamma_{k j}+\left(b_{0 k i}+b_{1 k i}+\epsilon_{k i j}\right)$$

$$\boldsymbol{b} k i=\left(b 0 k i, b_{1 k i}\right)^t \sim N(0, \Phi)$$

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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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