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

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。

• 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|Newton–Raphson

Armed with the first two derivatives, one can easily implement a NewtonRaphson algorithm to obtain the ML estimates. Without the derivatives written out analytically, one could still implement a Newton-Raphson algorithm by programming numeric derivatives (calculated using difference equations).
After optimization is achieved, one must estimate a suitable variance matrix for $\boldsymbol{\beta}$. An obvious and suitable choice is based on the estimated observed Hessian matrix. This is the most common default choice in software implementations because the observed Hessian matrix is a component of the estimation algorithm. As such, it is already calculated and available. We discuss in section $3.6$ that there are other choices for estimated variance matrices.
Thus, the Newton-Raphson algorithm provides

1. an algorithm for estimating the coefficients for all single-parameter exponential family GLM members and
2. estimated standard errors of estimated coefficients: square roots of the diagonal elements of the inverse of the estimated observed negative Hessian matrix.
Our illustration of the Newton-Raphson algorithm could be extended in several ways. The presentation did not show the estimation of the scale parameter, $\phi$. Other implementations could include the scale parameter in the derivatives and cross derivatives to obtain ML estimates.

## 统计代写|广义线性模型代写generalized linear model代考|Starting values for Newton-Raphson

To implement an algorithm for obtaining estimates of $\boldsymbol{\beta}$, we must have an initial guess for the parameters. There is no global mechanism for good starting values, but there is a reasonable solution for obtaining starting values when there is a constant in the model.
If the model includes a constant, then a common practice is to find the estimates for a constant-only model. For ML, this is a part of the model of interest, and knowing the likelihood for a constant-only model then allows a likelihood-ratio test for the parameters of the model of interest.
Often, the ML estimate for the constant-only model may be found analytically. For example, in chapter 12 we introduce the Poisson model. That model has a log likelihood given by
$$\mathcal{L}=\sum_{i=1}^{n}\left{y_{i}\left(x_{i} \boldsymbol{\beta}\right)-\exp \left(x_{i} \boldsymbol{\beta}\right)-\ln \Gamma\left(y_{i}+1\right)\right}$$
If we assume that there is only a constant term in the model, then the log likelihood may be written
$$\mathcal{L}=\sum_{i=1}^{n}\left{y_{i} \beta_{0}-\exp \left(\beta_{0}\right)-\ln \Gamma\left(y_{i}+1\right)\right}$$
The ML estimate of $\beta_{0}$ is found by setting the derivative
$$\frac{\partial \mathcal{L}}{\partial \beta_{0}}=\sum_{i=1}^{n}\left{y_{i}-\exp \left(\beta_{0}\right)\right}$$

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

1. 一种用于估计所有单参数指数族 GLM 成员的系数的算法和
2. 估计系数的估计标准误差：估计观察到的负 Hessian 矩阵的逆对角元素的平方根。
我们对 Newton-Raphson 算法的说明可以通过多种方式进行扩展。演示文稿没有显示尺度参数的估计，φ. 其他实现可以在导数和交叉导数中包括尺度参数以获得 ML 估计。

## 有限元方法代写

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。

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

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。

• 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|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.

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

This chapter covers the theory behind GLMs. We present the material in a general fashion, showing all the results in terms of the exponential family of distributions. We illustrate two computational approaches for obtaining the parameter estimates of interest and discuss the assumptions that each method inherits. Parts II through VI of this text will then illustrate the application of this general theory to specific members of the exponential family.
The goal of our presentation is a thorough understanding of the underpinnings of the GLM method. We also wish to highlight the assumptions and limitations that algorithms inherit from their associated framework.
Traditionally, GLMS are fit by applying Fisher scoring within the NewtonRaphson method applied to the entire single-parameter exponential family of distributions. After making simplifications (which we will detail), the estimation algorithm is then referred to as iteratively reweighted least squares (IRLS). Before the publication of this algorithm, models based on a member distribution of the exponential family were fit using distribution-specific Newton-Raphson algorithms.
GLM theory showed how these models could be unified and fit using one IRLS algorithm that does not require starting values for the coefficients $\widehat{\beta}$; rather, it substitutes easy-to-compute fitted values $\widehat{y}_{i}$. This is the beauty and attraction of GLM. Estimation and theoretical presentation are simplified by addressing the entire family of distributions. Results are valid regardless of the inclusion of Fisher scoring in the Newton-Raphson computations.

In what follows, we highlight the Newton-Raphson method for finding the zeros (roots) of a real-valued function. In the simplest case, we view this problem as changing the point of view from maximizing the log likelihood to that of determining the root of the derivative of the log likelihood. Because the values of interest are obtained by setting the derivative of the log likelihood to zero and solving, that equation is referred to as the estimating equation.

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

GLM 理论展示了如何使用一种不需要系数起始值的 IRLS 算法来统一和拟合这些模型b^; 相反，它替代了易于计算的拟合值是^一世. 这就是 GLM 的美丽和吸引力。通过解决整个分布族来简化估计和理论表示。无论在 Newton-Raphson 计算中是否包含 Fisher 评分，结果都是有效的。

## 有限元方法代写

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。

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

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。

• 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|Origins and motivation

We wrote this text for researchers who want to understand the scope and application of generalized linear models while being introduced to the underlying theory. For brevity’s sake, we use the acronym GLM to refer to the generalized linear model, but we acknowledge that GLM has been used elsewhere as an acronym for the general linear model. The latter usage, of course, refers to the area of statistical modeling based solely on the normal or Gaussian probability distribution.
We take GLm to be the generalization of the general, because that is precisely what GLMs are. They are the result of extending ordinary least-squares (OLS) regression, or the normal model, to a model that is appropriate for a variety of response distributions, specifically to those distributions that compose the single parameter exponential family of distributions. We examine exactly how this extension is accomplished. We also aim to provide the reader with a firm understanding of how GLMs are evaluated and when their use is appropriate. We even advance a bit beyond the traditional GLM and give the reader a look at how GLMs can be extended to model certain types of data that do not fit exactly within the GLM framework.

Nearly every text that addresses a statistical topic uses one or more statistical computing packages to calculate and display results. We use Stata exclusively, though we do refer occasionally to other software packages – especially when it is important to highlight differences.

## 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 exponentid 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.

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

GLM 传统上是在指数分布族的框架内制定的。在相关表示中，我们可以使用第3.3节中详述的评分过程（IRLS）推导出一个通用模型.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、伽马、逆高斯等。使用指数族的符号提供了一种指定连续、离散、比例、计数和二元结果模型的方法。

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|STAT3022

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。

• 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|Correspondence Analysis

The analysis of the hair-eye color data in the previous section revealed how hair and eye color are dependent. But this does not tell us how they are dependent. To study this, we can use a kind of residual analysis for contingency tables called correspondence analysis.

Compute the Pearson residuals $r_{P}$ and write them in the matrix form $R_{i j}$, where $i=1, \ldots, r$ and $j=1, \ldots, c$, according to the structure of the data. Perform the singular value decomposition:
$$R_{r \times c}=U_{r \times w} D_{w \times w} V_{w \times c}^{T}$$
where $r$ is the number of rows, $c$ is the number of columns and $w=\min (r, c) . U$ and $V$ are called the right and left singular vectors, respectively. $D$ is a diagonal matrix with sorted elements $d_{i}$, called singular values. Another way of writing this is:
$$R_{i j}=\sum_{k=1}^{w} U_{i k} d_{k} V_{j k}$$
As with eigendecompositions, it is not uncommon for the first few singular values to be much larger than the rest. Suppose that the first two dominate so that:
$$R_{i j} \approx U_{i 1} d_{1} V_{j 1}+U_{i 2} d_{2} V_{j 2}$$

We usually absorb the $d$ s into $U$ and $V$ for plotting purposes so that we can assess the relative contribution of the components. Thus:
\begin{aligned} R_{i j} & \approx\left(U_{i 1} \sqrt{d_{1}}\right) \times\left(V_{j 1} \sqrt{d_{1}}\right)+\left(U_{i 2} \sqrt{d_{2}}\right) \times\left(V_{j 2} \sqrt{d_{2}}\right) \ & \equiv U_{i 1} V_{j 1}+U_{i 2} V_{j 2} \end{aligned}
where in the latter expression we have redefined the $U \mathrm{~s}$ and $V \mathrm{~s}$ to include the $\sqrt{d}$.

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

\begin{aligned}
&\text { In the typical two-way contingency tables, we display accumulated information } \
&\text { about two categorical measures on the same object. In matched pairs, we observe } \
&\text { one measure on two matched objects. } \
&\text { In Stuart (1955), data on the vision of a sample of women is presented. The left } \
&\text { and right eye performance is graded into four categories: } \
&\text { data (eyegrade) } \
&\text { (ct c- xtabs }(y \sim \text { right+left, eyegrade)) } \
&\text { right best second third worst } \
&\text { second } 234 \text { left } 1512 \quad 432 \quad 78 \
\end{aligned}

If we check for independence:
summary (et)
Call: xtabs (formula – y right + left, data – eyegrade)
Number of cases in table: 7477
Number of factors: 2
Test for independence of all factors:
Chisq – 8097, df – 9, p-value $=0$
We are not surprised to find strong evidence of dependence. Most people’s eyes are similar. A more interesting hypothesis for such matched pair data is symmetry. Is $p_{i j}=p_{j i}$ ? We can fit such a model by defining a factor where the levels represent the symmetric pairs for the off-diagonal elements. There is only one observation for each level down the diagonal:
(symfac <- factor (apply (eyegrade $[, 2: 3], 1$, function (x) paste (sort $(x)$,
$\rightarrow$ collapse=” ” “))))
[1] best-best best-second best-third best-worst
[5] best-second second-second second-third second-worst
[9] best-third second-third third-third third-worst
10 Levels: best-best best-second best-third … worst-worst
We now fit this model:
mods <- glm(y symfac, eyegrade, familympoisson)
c (deviance (mods), df . residual (mods))
[1] $19.2496 .000$
pchisq (deviance (mods), df . residual (mods), lower=F)
[1] $0.0037629$
Here, we see evidence of a lack of symmetry. It is worth checking the residuals:
round (xtabs (residuals (mods) right+left, eyegrade), 3)
round (xtabs (residuals (mods) righ left
We see that the residuals above the diagonal are mostly positive, while they are mostly negative below the diagonal. So there are generally more poor left, good right eye combinations than the reverse. Furthermore, we can compute the marginals:
margin table $(c t, 1)$
right
$\begin{array}{lrr}\text { best second third } & \text { worst } \ 1976 & 2256 & 2456\end{array}$

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

Some variables have a natural order. We can use the methods for nominal variables described earlier in this chapter, but more information can be extracted by taking advantage of the structure of the data. Sometimes we might identify a particular ordinal variable as the response. In such cases, the methods of Section $7.4$ can be used. However, sometimes we are interested in modeling the association between ordinal variables. Here the use of scores can be helpful.

Consider a two-way table where both variables are ordinal. We may assign scores $u_{i}$ and $v_{j}$ to the rows and columns such that $u_{1} \leq u_{2} \leq \cdots \leq u_{I}$ and $v_{1} \leq v_{2} \leq \cdots \leq v_{J}$. The assignment of scores requires some judgment. If you have no particular prefer-

ence, even spacing allows for the simplest interpretation. If you have an interval scale, for example, $0-10$ years old, 10-20 years old, $20-40$ years old and so on, midpoints are often used. It is a good idea to check that the inference is robust to the assignment of scores by trying some reasonable alternative choices. If your qualitative conclusions are changed, this is an indication that you cannot make any strong finding.
Now fit the linear-by-linear association model:
$$\log E Y_{i j}=\log \mu_{i j}=\log n p_{i j}=\log n+\alpha_{i}+\beta_{j}+\gamma u_{i} v_{j}$$
So $\gamma=0$ means independence while $\gamma$ represents the amount of association and can be positive or negative. $\gamma$ is rather like an (unscaled) correlation coefficient. Consider underlying (latent) continuous variables which are discretized by the cutpoints $u_{i}$ and $v_{j}$. We can then identify $\gamma$ with the correlation coefficient of the latent variables.
Consider an example drawn from a subset of the 1996 American National Election Study (Rosenstone et al. (1997)). Using just the data on party affiliation and level of education, we can construct a two-way table:
data (nes96)
xtabs ( PID + educ, nes96)
\begin{tabular}{lrrrrrrrr}
\multicolumn{8}{c}{ educ } \
PID & MS & HSdrop HS Coll cCdeg & BAdeg MAdeg \
strDem & 5 & 19 & 59 & 38 & 17 & 40 & 22 \
weakDem & 4 & 10 & 49 & 36 & 17 & 41 & 23 \
indDem & 1 & 4 & 28 & 15 & 13 & 27 & 20 \
indind & 0 & 3 & 12 & 9 & 3 & 6 & 4 \
indRep & 2 & 7 & 23 & 16 & 8 & 22 & 16 \
weakRep & 0 & 5 & 35 & 40 & 15 & 38 & 17 \
strRep & 1 & 4 & 42 & 33 & 17 & 53 & 25
\end{tabular}
Both variables are ordinal in this example. We need to convert this to a dataframe with one count per line to enable model fitting.

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

Rr×C=在r×在D在×在在在×C吨

R一世j=∑ķ=1在在一世ķdķ在jķ

R一世j≈在一世1d1在j1+在一世2d2在j2

R一世j≈(在一世1d1)×(在j1d1)+(在一世2d2)×(在j2d2) ≡在一世1在j1+在一世2在j2

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

在典型的双向列联表中，我们显示累积信息   关于同一对象的两个分类度量。在配对中，我们观察到   对两个匹配的对象进行一次测量。   在 Stuart (1955) 中，提供了关于女性样本视力的数据。左边   右眼表现分为四类：   数据（眼级）   (ct c-xtabs (是∼ 右+左，眼级））   对 最好 第二 第三 最差   最好的 152026612466  第二 234 剩下 151243278  第三 1173621772205  最坏的 3682179492

summary (et)
Call: xtabs (formula – y right + left, data – eyegrade)

Chisq – 8097, df – 9、p值=0

(symfac <- factor (apply (eyegrade[,2:3],1, 函数 (x) 粘贴（排序(X),
→collapse=” ” “)))))
[1] 最佳-最佳-最佳-第二-最佳-第三–最差
[5] 最佳-第二-第二-第二-第三-第二-最差
[9] 最佳-第三-第二-第三-第三-第三第三最差
10 个级别：最好最好最好第二最好第三…最差

mods <- glm(y symfac, eyegrade, familympoisson)
c (deviance (mods), df .residual (mods ))
[1]19.2496.000
pchisq (deviance (mods), df .residual (mods), lower=F)
[1]0.0037629

round (xtabs(residuals (mods) right+left, eyegrade), 3)
round (xtabs(residuals (mods) right left

margin table(C吨,1)

最好的第二第三  最坏的  197622562456

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

data (nes96)
xtabs ( PID + educ, nes96)

\begin{tabular}{lrrrrrrrr} \multicolumn{8}{c}{ educ} \ PID & MS & HSdrop HS Coll cCdeg & BAdeg MAdeg \ strDem & 5 & 19 & 59 & 38 & 17 & 40 & 22 \weakDem & 4 & 10 & 49 & 36 & 17 & 41 & 23 \ indDem & 1 & 4 & 28 & 15 & 13 & 27 & 20 \ indind & 0 & 3 & 12 & 9 & 3 & 6 & 4 \ indRep & 2 & 7 & 23 & 16 & 8 & 22 & 16 \weakRep & 0 & 5 & 35 & 40 & 15 & 38 & 17 \ strRep & 1 & 4 & 42 & 33 & 17 & 53 & 25 \end{tabular}\begin{tabular}{lrrrrrrrr} \multicolumn{8}{c}{ educ} \ PID & MS & HSdrop HS Coll cCdeg & BAdeg MAdeg \ strDem & 5 & 19 & 59 & 38 & 17 & 40 & 22 \weakDem & 4 & 10 & 49 & 36 & 17 & 41 & 23 \ indDem & 1 & 4 & 28 & 15 & 13 & 27 & 20 \ indind & 0 & 3 & 12 & 9 & 3 & 6 & 4 \ indRep & 2 & 7 & 23 & 16 & 8 & 22 & 16 \weakRep & 0 & 5 & 35 & 40 & 15 & 38 & 17 \ strRep & 1 & 4 & 42 & 33 & 17 & 53 & 25 \end{tabular}

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|STAT3015

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。

• 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|Negative Binomial

Given a series of independent trials, each with probability of success $p$, let $Z$ be the number of trials until the $k^{h t h}$ success. Then:
$$P(Z=z)=\left(\begin{array}{l} z-1 \ k-1 \end{array}\right) p^{k}(1-p)^{z-k} \quad z=k, k+1, \ldots$$
The negative binomial can arise naturally in several ways. Imagine a system that can withstand $k$ hits before failing. The probability of a hit in a given time period is $p$ and we count the number of time periods until failure. The negative binomial also arises from a generalization of the Poisson where the parameter $\lambda$ is gamma distributed. The negative binomial also comes up as a limiting distribution for urn schemes that can be used to model contagion.

We get a more convenient parameterization if we let $Y=Z-k$ and $p=(1+\alpha)^{-1}$ so that:
$$P(Y=y)=\left(\begin{array}{c} y+k-1 \ k-1 \end{array}\right) \frac{\alpha^{y}}{(1+\alpha)^{y+k}}, \quad y=0,1,2, \ldots$$
then $E Y=\mu=k \alpha$ and var $Y=k \alpha+k \alpha^{2}=\mu+\mu^{2} / k$
The log-likelihood is then:
$$\sum_{i=1}^{n}\left(y_{i} \log \frac{\alpha}{1+\alpha}-k \log (1+\alpha)+\sum_{j=0}^{y_{i}-1} \log (j+k)-\log \left(y_{i} !\right)\right)$$
The most convenient way to link the mean response $\mu$ to a linear combination of the predictors $X$ is:
$$\eta=x^{T} \beta=\log \frac{\alpha}{1+\alpha}=\log \frac{\mu}{\mu+k}$$
We can regard $k$ as fixed and determined by the application or as anditional parameter to be estimated. More on regression models for negative binomial responses may be found in Cameron and Trivedi (1998) and Lawless (1987).

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

Sometimes we see count response data where the number of zeroes appearing is significantly greater than the Poisson or negative binomial models would predict. Consider the number of arrests for criminal offenses incurred by individuals. A large number of people have never been arrested by the police while a smaller number have been detained on multiple occasions. Modifying the Poisson by adding a dispersion parameter does not adequately model this divergence from the standard count distributions.

We consider a sample of 915 biochemistry graduate students as analyzed by Long $(1990)$. The response is the number of articles produced during the last three years of the PhD. We are interested in how this is related to the gender, marital status, number of children, prestige of the department and productivity of the advisor of the student. The dataset may be found in the pscl package of Zeileis et al. (2008) which also provides the new model fitting functions needed in this section. We start by fitting a Poisson regression model:
$n=915 p-6$
Deviance $=1634.371$ Null Deviance $=1817.405$ (Difference $=183.034$ )
We can see that deviance is significantly larger than the degrees of freedom. Some experimentation reveals that this cannot be solved by using a richer linear predictor or by eliminating some outliers. We might consider a dispersed Poisson model or negative binomial but some thought suggests that there are good reasons why a student might produce no articles at all. We count and predict how many students produce between zero and seven articles. Very few students produce more than seven articles so we ignore these. The predprob function produces the predicted probabilities for each case. By summing these, we get the expected number for each article count.

## 统计代写|广义线性模型代写generalized linear model代考|Two-by-Two Tables

The data shown in Table $6.1$ were collected as part of a quality improvement study at a semiconductor factory. A sample of wafers was drawn and cross-classified according to whether a particle was found on the die that produced the wafer and whether the wafer was good or bad. More details on the study may be found in Hall (1994). The data might have arisen under several possible sampling schemes:

1. We observed the manufacturing process for a certain period of time and observed 450 wafers. The data were then cross-classified. We could use a Poisson model.
2. We decided to sample 450 wafers. The data were then cross-classified. We could use a multinomial model.
3. We selected 400 wafers without particles and 50 wafers with particles and then recorded the good or bad outcome. We could use a binomial model.
4. We selected 400 wafers without particles and 50 wafers with particles that also included, by design, 334 good wafers and 116 bad ones. We could use a hypergeometric model.

The first three sampling schemes are all plausible. The fourth scheme seems less likely in this example, but we include it for completeness. Such a scheme is more attractive when one level of each variable is relatively rare and we choose to oversample both levels to ensure some representation.

The main question of interest concerning these data is whether the presence of particles on the wafer affects the quality outcome. We shall see that all four sampling schemes lead to exactly the same conclusion. First, let’s set up the data in a convenient form for analysis:
$y<-\mathrm{c}(320,14,80,36)$ particle <- gl $(2,1,4$, labelsmc (“no”, “yes”) quality $<-\mathrm{g}(2,2$, labelsmc (“good”, “bad”)) (wafer <- data. frame (y, particle, quality)) y particle quality $\begin{array}{llll}1 & 320 & \text { no } & \text { good } \ 2 & 14 & \text { yes } & \text { good } \ 3 & 80 & \text { no } & \text { bad } \ 4 & 36 & \text { yes } & \text { bad }\end{array}$.

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

∑一世=1n(是一世日志⁡一个1+一个−ķ日志⁡(1+一个)+∑j=0是一世−1日志⁡(j+ķ)−日志⁡(是一世!))

n=915p−6

## 统计代写|广义线性模型代写generalized linear model代考|Two-by-Two Tables

1. 我们观察了一段时间的制造过程，观察了450个晶圆。然后对数据进行交叉分类。我们可以使用泊松模型。
2. 我们决定对 450 个晶圆进行采样。然后对数据进行交叉分类。我们可以使用多项式模型。
3. 我们选择了 400 个没有颗粒的晶圆和 50 个有颗粒的晶圆，然后记录了结果的好坏。我们可以使用二项式模型。
4. 我们选择了 400 个没有颗粒的晶圆和 50 个有颗粒的晶圆，按照设计，还包括 334 个好晶圆和 116 个坏晶圆。我们可以使用超几何模型。

## 有限元方法代写

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。

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

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。

• 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|Poisson Regression

If $Y$ is Poisson with mean $\mu>0$, then:
$$P(Y=y)=\frac{e^{-\mu} \mu^{y}}{y !}, \quad y=0,1,2, \ldots$$
Three examples of the Poisson density are depicted in Figure 5.1. In the left panel, we see a distribution that gives highest probability to $y=0$ and falls rapidly as $y$ increases. In the center panel, we see a skew distribution with longer tail on the right. Even for a not so large $\mu=5$, we see the distribution become more normally shaped. This becomes more pronounced as $\mu$ increases.
barplot (dpois $(0: 5,0.5)$, xlab=” $y$ “, ylab=”Probability”, names=0:5, main=”
$\hookrightarrow$ mean $\left.=0.5^{\prime \prime}\right)$
barplot (dpois $(0: 10,2), x 1 a b=” y ” y$ labm”Probability”, names= $0: 10$, main $=$ “
$\rightarrow$ mean $\left.=2^{\prime \prime}\right)$
barplot (dpois $(0: 15,5)$, xlab=” ” $”, y l a b=”$ Probability”, names $0: 15$, main ” “
$\rightarrow$ mean $\left.=5^{\prime \prime}\right)$
The expectation and variance of a Poisson are the same: $E Y=\operatorname{var} Y=\mu$. The Poisson distribution arises naturally in several ways:

1. If the count is some number out of some possible total, then the response would be more appropriately modeled as a binomial. However, for small success probabilities and large totals, the Poisson is a good approximation and can be used. For example, in modeling the incidence of rare forms of cancer, the number of people affected is a small proportion of the population in a given geographical area. Specifically, if $\mu=n p$ while $n \rightarrow \infty$, then $B(n, p)$ is well approximated by Pois $(\mu)$. Also, for small $p$, note that $\operatorname{logit}(p) \approx \log p$, so that the use of the Poisson with a log link is comparable to the binomial with a logit link. Where $n$ varies between cases, a rate model can be used as described in Section 5.3.

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

We can modify the standard Poisson model to allow for more variation in the response. But before we do that, we must check whether the large size of deviance might be related to some other cause.

In the Galápagos example, we check the residuals to see if the large deviance can be explained by an outlier:
halfnorm (residuals (modp))
The half-normal plot of the (absolute value of the) residuals shown in Figure $5.3$ shows no outliers. It could be that the structural form of the model needs some improvement, but some experimentation with different forms for the predictors will reveal that there is little scope for improvement. Furthermore, the proportion of deviance explained by this model, $1-717 / 3510=0.796$, is about the same as in the linear model above.

For a Poisson distribution, the mean is equal to the variance. Let’s investigate this relationship for this model. It is difficult to estimate the variance for a given value of the mean, but $(y-\hat{\mu})^{2}$ does serve as a crude approximation. We plot this estimated variance against the mean, as seen in the second panel of Figure 5.3:
plot ( $\log ($ fitted (modp) ), $\log (($ gala\$Species-fitted (modp) ) 2$), \quad x l a b=\hookrightarrow$expression (hat (mu)), ylab=expression$\left.\left((y-h a t(m u))^{\wedge} 2\right)\right)$abline$(0,1)$We see that the variance is proportional to, but larger than, the mean. When the variance assumption of the Poisson regression model is broken but the link function and choice of predictors are correct, the estimates of$\beta$are consistent, but the standard er- rors will be wrong. We cannot determine which predictors are statistically significant in the above model using the output we have. The Poisson distribution has only one parameter and so is not very flexible for empirical fitting purposes. We can generalize by allowing ourselves a dispersion parameter. Over- or underdispersion can occur in various ways in Poisson models. For example, suppose the Poisson response$Y$has rate$\lambda$which is itself a random variable. The tendency to fail for a machine may vary from unit to unit even though they are the same model. We can model this by letting$\lambda$be gamma distributed with$E \lambda=\mu$and var$\lambda=\mu / \phi$. Now$Y$is negative binomial with mean$E Y=\mu$. The mean is the same as the Poisson, but the variance var$Y=\mu(1+\phi) / \phi$which is not equal to$\mu$. In this case, overdispersion would occur and could be modeled using a negative binomial model as demonstrated in Section 5.4. If we know the specific mechanism, as in the above example, we could model the response as a negative binomial or other more flexible distribution. If the mechanism is not known, we can introduce a dispersion parameter$\phi$such that var$Y=\phi E Y=\phi \mu$.$\phi=1$is the regular Poisson regression case, while$\phi>1$is overdispersion and$\phi<1$is underdispersion. The dispersion parameter may be estimated using: $$\hat{\phi}=\frac{X^{2}}{n-p}=\frac{\sum_{i}\left(y_{i}-\hat{\mu}{i}\right)^{2} / \hat{\mu}{i}}{n-p}$$ ## 统计代写|广义线性模型代写generalized linear model代考|Rate Models The number of events observed may depend on a size variable that determines the number of opportunities for the events to occur. For example, if we record the number of burglaries reported in different cities, the observed number will depend on the number of households in these cities. In other cases, the size variable may be time. For example, if we record the number of customers served by a sales worker, we must take account of the differing amounts of time worked. Sometimes, it is possible to analyze such data using a binomial response model. For the burglary example above, we might model the number of burglaries out of the number of households. However, if the proportion is small, the Poisson approxima- tion to the binomial is effective. Furthermore, in some examples, the total number of potential cases may not be known exactly. The modeling of rare diseases illustrates this issue as we may know the number of cases but not have precise population data. Sometimes, the binomial model simply cannot be used. In the burglary example, some households may be robbed more than once. In the customer service example, the size variable is not a count. An alternative approach is to model the ratio. However, there are often difficulties with normality and unequal variance when taking this approach, particularly if the counts are small. In Purott and Reeder (1976), some data is presented from an experiment conducted to determine the effect of gamma radiation on the numbers of chromosomal abnormalities (ca) observed. The number (cells), in hundreds of cells exposed in each run, differs. The dose amount (doseamt) and the rate (doserate) at which the dose is applied are the predictors of interest. We may format the data for observation like this: data (dicentric, package=”faraway”) round (xtabs (ca/cells doseamt+doserate, dicentric),2) ## 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|Poisson Regression 如果是是泊松的均值μ>0， 然后： 磷(是=是)=和−μμ是是!,是=0,1,2,… 图 5.1 描述了泊松密度的三个示例。在左侧面板中，我们看到一个分布，它给出的概率最高是=0并迅速下降是增加。在中心面板中，我们看到右侧有较长尾部的偏斜分布。即使对于一个不是那么大的μ=5，我们看到分布变得更正常。这变得更加明显μ增加。 条形图（dpois(0:5,0.5), xlab =”是“, ylab=”概率”, 名称=0:5, main=” 意思是=0.5′′) 条形图（dpois(0:10,2),X1一个b=”是”是实验室“概率”，名称=0:10， 主要的= “ →意思是=2′′) 条形图（dpois(0:15,5), xlab =” ””,是l一个b=”概率”，名称0:15， 主要的 ” ” →意思是=5′′) 泊松的期望和方差是相同的：和是=曾是⁡是=μ. 泊松分布以多种方式自然产生： 1. 如果计数是某个可能总数中的某个数字，则响应将更适合建模为二项式。但是，对于较小的成功概率和较大的总数，泊松是一个很好的近似值，可以使用。例如，在模拟罕见癌症的发病率时，受影响的人数只是特定地理区域内人口的一小部分。具体来说，如果μ=np尽管n→∞， 然后乙(n,p)由 Pois 很好地逼近(μ). 另外，对于小p， 注意罗吉特⁡(p)≈日志⁡p，因此使用对数链接的泊松与使用对数链接的二项式相当。在哪里n不同情况下的不同，可以使用第 5.3 节中描述的费率模型。 ## 统计代写|广义线性模型代写generalized linear model代考|Dispersed Poisson Model 我们可以修改标准泊松模型以允许响应的更多变化。但在我们这样做之前，我们必须检查较大的偏差是否与其他原因有关。 在加拉帕戈斯的例子中，我们检查残差，看看是否可以用异常值来解释大偏差： halfnorm (residuals (modp)) 残差（ 的绝对值）的半正态图如图所示5.3显示没有异常值。可能是模型的结构形式需要一些改进，但是对预测变量的不同形式进行一些实验会发现改进的余地很小。此外，该模型解释的偏差比例，1−717/3510=0.796, 与上述线性模型中的大致相同。 对于泊松分布，均值等于方差。让我们研究这个模型的这种关系。对于给定的均值，很难估计方差，但是(是−μ^)2确实可以作为粗略的近似值。 我们将这个估计的方差与平均值作图，如图 5.3 的第二个面板所示：日志⁡(安装（modp）），日志⁡((晚会$物种拟合 (modp) ) 2),Xl一个b=

rors 将是错误的。我们无法使用我们拥有的输出确定哪些预测变量在上述模型中具有统计显着性。

φ^=X2n−p=∑一世(是一世−μ^一世)2/μ^一世n−p

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

data (dicentric, package=”faraway”)
round (xtabs (ca/cells doseamt​​+doserate, dicentric),2)

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|MAST90084

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。

• 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|Prospective and Retrospective Sampling

Consider the data shown in Table $4.1$ from a study on infant respiratory disease which shows the proportions of children developing bronchitis or pneumonia in their first year of life by type of feeding and sex, which may be found in Payne (1987):

\begin{tabular}{llll}
& Bottle Only & Some Breast with Supplement & Breast Only \
\hline Boys & $77 / 458$ & $19 / 147$ & $47 / 494$ \
Girls & $48 / 384$ & $16 / 127$ & $31 / 464$
\end{tabular}
Table $4.1$ Incidence of respiratory disease in infants to the age of 1 year.
We can recover the layout above with the proportions as follows:
data (babyfood, package=” faraway”)
xtabs (disease/ (disease + nondisease) $\sim$ sex + food, babyfood)
food
sex $\quad$ Bottle Breast Suppl
G1rl $0.125000 .066810 \quad 0.12598$
In prospective sampling, the predictors are fixed and then the outcome is observed. This is also called a cohort study. In the infant respiratory disease example shown in Table 4.1, 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.

In retrospective sampling, the outcome is fixed and then the predictors are observed. This is also called a case-control study. 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 diseasefree infants and record their information. The method for obtaining the samples is important – we require that the probability of inclusion in the study is independent of the predictor values.

## 统计代写|广义线性模型代写generalized linear model代考|Prediction and Effective Doses

Sometimes we wish to predict the outcome for given values of the covariates. For binomial data this will mean estimating the probability of success. Given covariates $x_{0}$, the predicted response on the link scale is $\hat{\eta}=x_{0} \hat{\beta}$ with variance given by $x_{0}^{T}\left(X^{T} W X\right)^{-1} x_{0}$. Approximate confidence intervals may be obtained using a normal approximation. To get an answer in the probability scale, it will be necessary to transform back using the inverse of the link function. We predict the response for the insect data:
data (bliss, packagem” faraway”)
$1 \mathrm{mod}<-$ glm(cbind (dead, alive) conc, familymbinomial, data=bliss)
lmodsum <- summary (lmod)
We show how to predict the response at a dose of $2.5$ :
$x 0<-c(1,2.5)$
eta0 $<-\operatorname{sum}(x 0 * \operatorname{coe}(1 \mathrm{mod}))$
$1 \log i t(\mathrm{eta0})$
[1) $0.64129$
A $64 \%$ predicted chance of death at this dose – now compute a $95 \%$ confidence interval (CI) for this probability. First, extract the variance matrix of the coefficients:
(cm \&- lmodsum\$cov. unscaled) (Intercept)$\begin{array}{rr}\text { (Intercept) } & \text { conc } \ \text { conc } & -0.065823\end{array}$se <- sqrt$(t(x 0)$왛은$\mathrm{cm}$화화$x 0)$so the CI on the probability scale is: ilogit (c (eta0$-1.96 *$se, eta0$1.96 * \mathrm{se})$) [1)$0.534300 .73585$A more direct way of obtaining the same result is: predict (lmod, newdata data. frame (conc=2.5), se=$T$) [1]$0.58095$\$se.fit
[1] $0.2263$
1logit (c (0.58095-1.960.2263,0.58095+1.960.2263))
[1] $0.534300 .73585$
Note that in contrast to the linear regression situation, there is no distinction possible between confidence intervals for a future observation and those for the mean response. Now we try predicting the response probability at the low dose of $-5$ :
$x 0<-c(1,-5)$
se $<-\operatorname{sqrt}(t(x 0)$ 왛의 $\mathrm{cm} \mathrm{~ ㅇ}$
eta0 <- sum $(x 0 * 1 \mathrm{mod}$ scoef $)$
ilogit (c (eta0 -1.96*se, eta0 $0+1.96 * s e)$ )
[1) $2.3577 \mathrm{e}-053.6429 \mathrm{e}-03$

## 统计代写|广义线性模型代写generalized linear model代考|Matched Case-Control Studies

In a case-control study, we try to determine the effect of certain risk factors on the outcome. We understand that there are other confounding variables that may affect the outcome. One approach to dealing with these is to measure or record them, include them in the logistic regression model as appropriate and thereby control for

their effect. But this method requires that we model these confounding variables with the correct functional form. This may be difficult. Also, making an appropriate adjustment is problematic when the distribution of the confounding variables is quite different in the cases and controls. So we might consider an alternative where the confounding variables are explicitly adjusted for in the design.

In a matched case-control study, we match each case (diseased person, defective object, success, etc.) with one or more controls that have the same or similar values of some set of potential confounding variables. For example, if we have a 56-year-old, Hispanic male case, we try to match him with some number of controls who are also 56-year-old Hispanic males. This group would be called a matched set. Obviously, the more confounding variables one specifies, the more difficult it will be to make the matches. Loosening the matching requirements, for example, accepting controls who are 50-60 years old, might be necessary. Matching also gives us the possibility of adjusting for confounders that are difficult to measure. For example, suppose we suspect an environmental effect on the outcome. However, it is difficult to measure exposure, particularly when we may not know which substances are relevant. We could match subjects based on their place of residence or work. This would go some way to adjusting for the environmental effects.

Matched case-control studies also have some disadvantages apart from the difficulties of forming the matched sets. One loses the possibility of discovering the effects of the variables used to determine the matches. For example, if we match on sex, we will not be able to investigate a sex effect. Furthermore, the data will likely be far from a random sample of the population of interest. So although relative effects may be found, it may be difficult to generalize to the population.

Sometimes, cases are rare but controls are readily available. A $1: M$ design has $M$ controls for each case. $M$ is typically small and can even vary in size from matched set to matched set due to difficulties in finding matching controls and missing values. Each additional control yields a diminished return in terms of increased efficiency in estimating risk factors – it is usually not worth exceeding $M=5$.

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

\begin{tabular}{llll} & 瓶装 & 一些含补充剂的乳房 & 仅乳房 \ \hline 男孩 & $77 / 458$ & $19 / 147$ & $47 / 494$ \ 女孩 & $48 / 384$ & $16 / 127$ & $31 / 464$ \end{表格}\begin{tabular}{llll} & 瓶装 & 一些含补充剂的乳房 & 仅乳房 \ \hline 男孩 & $77 / 458$ & $19 / 147$ & $47 / 494$ \ 女孩 & $48 / 384$ & $16 / 127$ & $31 / 464$ \end{表格}

data (babyfood, package=”faraway”)
xtabs (disease/ (disease + nondisease)∼性+食物，婴儿食品）

## 统计代写|广义线性模型代写generalized linear model代考|Prediction and Effective Doses

1米○d<−glm(cbind (dead, alive) conc, familymbinomial, data=bliss)
lmodsum <- summary (lmod)

X0<−C(1,2.5)

1日志⁡一世吨(和吨一个0)
[1) 0.64129

(cm \&- lmodsum $cov. unscaled) (Intercept) （截距） 浓 浓 −0.065823 se <- sqrt(吨(X0)哇C米华华X0) 所以概率尺度上的CI为： ilogit (c (eta0−1.96∗硒, eta01.96∗s和) ) [1) 0.534300.73585 获得相同结果的更直接的方法是： predict (lmod, newdata data.frame (conc=2.5), se=吨 ) [1] 0.58095$ se.fit
[1]0.2263
1logit (c (0.58095-1.960.2263,0.58095+1.960.2263))
[1]0.534300.73585

X0<−C(1,−5)

eta0 <- 总和(X0∗1米○d斯科夫)
ilogit (c (eta0 -1.96*se, eta00+1.96∗s和) )
[1) 2.3577和−053.6429和−03

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|STAT8111

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。

• 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|Beta Regression

Beta regression is useful for responses that are bounded in $(0,1)$ such as proportions. It could also be used for variables that are bounded in some other finite interval simply by rescaling to $(0,1)$. A Beta-distributed random variable $Y$ has density:
$$f(y \mid a, b)=\frac{\Gamma(a+b)}{\Gamma(a) \Gamma(b)} y^{a-1}(1-y)^{b-1}$$
for parameters $a, b$ and Gamma function $\Gamma()$. It is more convenient to transform the parameters so $\mu=a /(a+b)$ and $\phi=a+b$ so that $E Y=\mu$ and $\operatorname{var} Y=\mu(1-\mu) /(1+$ $\emptyset)$. We can then link the linear predictor $\eta$ using $\eta=g(\mu)$ using a link function $g$ where any of the choices used for the binomial model would be suitable.

An implementation of the Beta regression model can be found in the macv package of Wood (2006). We can apply this to the mammalsleep also used in the previous section.

The default choice of link is the logit function. The estimated value of $\phi$ is $8.927$. A comparison of the fitted values of this model and the quasi-binomial model fitted earlier reveals no substantial difference. The advantage of the Beta-based model is the full distributional model which would allow the construction of full predictive distributions rather than just a point estimate and standard error.

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

Suppose that students answer questions on a test and that a specific student has an aptitude $T$. A particular question might have difficulty $d$ and the student will get the answer correct only if $T>d$. Now if we consider $d$ fixed and $T$ as a random variable with density $f$ and distribution function $F$, then the probability that the student will get the answer wrong is:
$$p=P(T \leq d)=F(d)$$
$T$ is called a latent variable. Suppose that the distribution of $T$ is logistic:
$$F(y)=\frac{\exp (y-\mu) / \sigma}{1+\exp (y-\mu) / \sigma}$$
$\mathrm{SO}$
$$\operatorname{logit}(p)=-\mu / \sigma+d / \sigma$$
If we set $\beta_{0}=-\mu / \sigma$ and $\beta_{1}=1 / \sigma$, we now have a logistic regression model. We can illustrate this in the following example where we set $d=1$ and let $T$ have mean $-1$ and $\sigma=1$ :
$x<-\operatorname{seq}(-6,4,0.1)$
$y<-d \log _{\text {is }}(x$, location $=-1)$
plot (x,y, type=”1″, ylab=”density”, $x l a b=” t “)$
i1 $<-(x<1)$
polygon (c $(x[11], 1,-6), c(y[11], 0,0)$, col=’ gray’)
The plot in Figure $4.1$ shows a logistically distributed latent variable. We can see that this distribution is apparently very similar to the normal distribution. The shaded area represents the probability of getting an answer wrong. As the mean aptitude of this student is somewhat less than the difficulty of the question, this probability is substantially greater than one half.

This idea also arises in a bioassay where we might treat an animal, plant or person with some concentration of a treatment and observe the outcome. For example, suppose we are interested in the concentration of insecticide to be used in exterminating a pest. Insects will have varying tolerances for the toxin and will survive if their tolerance is greater than the dose. In this context, the term tolerance distribution for $T$ is used. Applications in several other areas exist where we observe only a binary outcome but believe this to be generated by some continuous but unobserved variable.

Until now we have used logit link function to connect the probability and the linear predictor. But other choices of link function are reasonable. We need a function that bounds the probability between zero and one. We also expect the link function to be monotone. It is conceivable that the success probability may go up and down as the linear predictor increases but this circumstance is best modeled by adding nonlinear components to the linear predictors such as quadratic terms rather than modifying the link function. The latent variable formulation suggests some other possibilities for the link function. Here are some choices which are implemented in the glm () function:

1. Probit: $\eta=\Phi^{-1}(p)$ where $\Phi$ is the normal cumulative distribution function. This arises from a normally distributed latent variable.
2. Complementary $\log -\log : \eta=\log (-\log (1-p))$. A Gumbel-distributed latent variable will lead to this.
3. Cauchit: $\eta=\tan ^{-1}(\pi(p-1 / 2))$ which is motivated by a Cauchy-distributed latent variable.

We can illustrate the choices using some data from Bliss (1935) on the numbers of insects dying at different levels of insecticide concentration. We fit all four link functions:

These are not very different, but now look at a wider range from $[-4,8]$. We apply the predict function to each of the four models forming a matrix of predicted values. We label the columns and add the information about the dose. The tidyr package is useful for reformatting data from a wide format of multiple measured values per row to a long format where there is only one response value per row. This is accomplished using the gather () function. This format, where each row is an observation and each column is a variable, is the most convenient form for many $R$ analyses. Finally, the ggplot 2 package is useful for completing and well-labeled plot.

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

Beta 回归对于有界的响应很有用(0,1)比如比例。它也可以用于限制在其他有限区间内的变量，只需重新缩放到(0,1). 一个 Beta 分布的随机变量是有密度：

F(是∣一个,b)=Γ(一个+b)Γ(一个)Γ(b)是一个−1(1−是)b−1

Beta 回归模型的实现可以在 Wood (2006) 的 macv 包中找到。我们可以将其应用于上一节中使用的哺乳动物睡眠。

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

p=磷(吨≤d)=F(d)

F(是)=经验⁡(是−μ)/σ1+经验⁡(是−μ)/σ

X<−序列⁡(−6,4,0.1)

i1<−(X<1)

1. 概率：这=披−1(p)在哪里披是正态累积分布函数。这是由一个正态分布的潜变量引起的。
2. 补充日志−日志:这=日志⁡(−日志⁡(1−p)). 一个 Gumbel 分布的潜在变量将导致这一点。
3. 考希特：这=棕褐色−1⁡(圆周率(p−1/2))这是由柯西分布的潜在变量驱动的。

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|OLET5608

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。

• 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|Pearson’s χ 2 Statistic

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 count and $E_{i}$ is the expected count for case $i$. For a binomial response, we count the number of successes for which $O_{i}=y_{i}$ while $E_{i}=n_{i} \hat{p}{i}$ and failures for which $O{i}=n_{i}-y_{i}$ and $E_{i}=n_{i}\left(1-\hat{p}{i}\right)$, 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:
[1] $28.067$
Compare this to:
deviance (lmod)
[1] $16.912$
In this case there is more than the typical small difference between $X^{2}$ and the deviance. However, a test for model fit:
1 -pchisq $(28.067,21)$
[1] $0.13826$
results in a moderate sized $p$-value which would not reject this model which agrees with decision based on the deviance statistic.

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

If the binomial model specification is correct, we expect that the residual deviance will be approximately distributed $\chi^{2}$ with the appropriate degrees of freedom. Sometimes, we observe a deviance that is much larger than would be expected if the model were correct. We must then determine which aspect of the model specification is incorrect.

The most common explanation is that we have the wrong structural form for the model. We have not included the right predictors or we have not transformed or combined them in the correct way. We have a number of ways of determining the importance of potential additional predictors and diagnostics for determining better transformations – see Section 8.4. Suppose, however, that we are able to exclude this explanation. This is difficult to achieve, but when we have only one or two predictors, it is feasible to explore the model space quite thoroughly and be sure that there is not a plausible superior model formula.

Another common explanation for a large deviance is the presence of a small

number of outliers. Fortunately, these are easily checked using diagnostic methods. When larger numbers of points are identified as outliers, they become unexceptional, and we might more reasonably conclude that there is something amiss with the error distribution.

Sparse data can also lead to large deviances. In the extreme case of a binary response, the deviance is not even approximately $\chi^{2}$. In situations where the group sizes are simply small, the approximation is poor. Because we cannot judge the fit using the deviance, we shall exclude this case from further consideration in this section.
Having excluded these other possibilities, we might explain a large deviance by deficiencies in the random part of the model. A binomial distribution for $Y$ arises when the probability of success $p$ is independent and identical for each trial within the group. If the group size is $m$, then var $Y=m p(1-p)$ if the binomial assumptions are correct. However, if the assumptions are broken, the variance may be greater. This is overdispersion. In rarer cases, the variance is less and underdispersion results.

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

In the previous section, we have demonstrated ways to model data where the supposedly binomial response is more variable than should be expected. A quasi-binomial model is another way to allow for extra-binomial variation. We will explain the method in greater generality than immediately necessary because the idea can be used across a wider range of response types.

The idea is to specify only how the mean and variance of the response are connected to the linear predictor. The method of weighted least squares, as used for standard linear models, would be a simple example of this. An examination of the fitting of the binomial model reveals that this only requires the mean and variance information and does not use any additional information about the binomial distribution. Hence, we can obtain the parameter estimates $\hat{\beta}$ and standard errors without making the full binomial assumption.

The problem arises when we attempt to do inference. To construct a confidence interval or perform an hypothesis test, we need some distributional assumptions. Previously we have used the deviance, but for this we need a likelihood and to compute a likelihood we need a distribution. Now we need a suitable substitute for a likelihood that can be computed without assuming a distribution.

Let $Y_{i}$ have mean $\mu_{i}$ and variance $\phi V\left(\mu_{i}\right)$. We assume that $Y_{i}$ are independent. We

define a score, $U_{i}$ :
$$U_{i}=\frac{Y_{i}-\mu_{i}}{\phi V\left(\mu_{i}\right)}$$
Now:
$$\begin{gathered} E U_{i}=0 \ \operatorname{var} U_{i}=\frac{1}{\phi V\left(\mu_{i}\right)} \ -E \frac{\partial U_{i}}{\partial \mu_{i}}=-E \frac{-\phi V\left(\mu_{i}\right)-\left(Y_{i}-\mu_{i}\right) \phi V^{\prime}\left(\mu_{i}\right)}{\left[\phi V\left(\mu_{i}\right)\right]^{2}}=\frac{1}{\phi V\left(\mu_{i}\right)} \end{gathered}$$
These properties are shared by the derivative of the log-likelihood, $l^{\prime}$. This suggests that we can use $U$ in place of $l^{\prime}$. So we define:
$$Q_{i}=\int_{y_{i}}^{\mu_{i}} \frac{y_{i}-t}{\phi V(t)} d t$$
The intent is that $Q$ should behave like the log-likelihood. We then define the log quasi-likelihood for all $n$ observations as:
$$Q=\sum_{i=1}^{n} Q_{i}$$

## 统计代写|广义线性模型代写generalized linear model代考|Pearson’s χ 2 Statistic

X2=∑一世=1n(○一世−和一世)2和一世

X2=∑一世=1n(是一世−n一世p^一世)2n一世p^一世(1−p^一世)

r一世磷=(是一世−n一世p^一世)/曾是⁡是^一世

[1]28.067

[1]进行比较16.912

1 -pchisq(28.067,21)
[1] 0.13826

## 有限元方法代写

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。

## 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|广义线性模型代写generalized linear model代考|STA441H5

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。

• 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|Estimation Problems

Estimation of the logistic regression model using the Fisher scoring algorithm, described in Section 8.2, is usually fast. However, difficulties can sometimes arise. When convergence fails, it is sometimes due to a problem exhibited by the following dataset. We take a subset of the famous Fisher Iris data to consider only two of the three species of Iris and use only two of the potential predictors:
ibrary (dplyr)
irisr <- filter(iris, Species ! “virginica”) to ? select (Sepal. Width,
$\rightarrow$ Sepal. Length, Species)
We plot the data using a different shape of plotting symbol for the two species:
(p <- ggplot(irisr, aes (x=Sepa1. Width, y=Sepal. Length, shape=Species))
$\hookrightarrow$ tgeom point ())
We now fit a logistic regression model to see if the species can be predicted from the two sepal dimensions.

$n-100 p-3$ Deviance $-0.000$ Null Deviance $-138.629$ (Difference $-138.629$ ) Notice that the residual deviance is zero indicating a perfect fit and yet none of the predictors are significant due to the high standard errors. A look at the data reveals the reason for this. We see that the two groups are linearly separable so that a perfect fit is possible. We suffer from an embarrassment of riches in this example – we can fit the data perfectly. Unfortunately, this results in unstable estimates of the parameters and their standard errors and would (probably falsely) suggest that perfect predictions can be made. An alternative fitting approach might be considered in such cases called exact logistic regression. See Cox (1970) or Mehta and Patel (1995). Implementations can be found in the elrm and logistix packages in R.

## 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 $i=1, \ldots, n$ is binomially distributed $B\left(m_{i}, p_{i}\right)$ so that:
$$P\left(Y_{i}=y_{i}\right)=\left(\begin{array}{c} m_{i} \ y_{i} \end{array}\right) p_{i}^{y_{i}}\left(1-p_{i}\right)^{m_{i}-y_{i}}$$
We further assume that the $Y_{i}$ are independent. The individual outcomes or 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. For example, we might record whether customers of a particular type make a purchase or not. Conventionally, one outcome is labeled a success (say, making purchase in this example) and the other outcome is labeled as a failure. No emotional meaning should be attached to success and failure in this context. For example, success might be the label given to a patient death with survival being called a failure. Because we need to have multiple trials for each covariate class, data for binomial regression models is more likely to result from designed experiments with a few predictors at chosen values rather than observational data which is likely to be more sparse.
As in the binary case, we construct a linear predictor:
$$\eta_{i}=\beta_{0}+\beta_{1} x_{i 1}+\cdots+\beta_{q} x_{i q}$$
We can use a logistic link function $\eta_{i}=\log \left(p_{i} /\left(1-p_{i}\right)\right)$. The log-likelihood is then given by:
$$l(\beta)=\sum_{i=1}^{n}\left[y_{i} \eta_{i}-m_{i} \log \left(1+e_{i}^{\eta}\right)+\log \left(\begin{array}{c} m_{i} \ y_{i} \end{array}\right)\right]$$
Let’s work through an example to see how the analysis differs from the binary response case.

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 et al. (1989) for more details.

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

We use the same likelihood-based methods as in Section $2.3$ to derive the binomial deviance:
$$D=2 \sum_{i=1}^{n}\left{y_{i} \log y_{i} / \hat{y}{i}+\left(m{i}-y_{i}\right) \log \left(m_{i}-y_{i}\right) /\left(m_{i}-\hat{y}{i}\right)\right}$$ where $\hat{y}{i}$ are the fitted values from the model.
Provided that $Y$ is truly binomial and that the $m_{i}$ are relatively large, the deviance is approximately $\chi^{2}$ distributed with $n-q-1$ degrees of freedom if the model is correct. Thus we can use the deviance to test whether the model is an adequate fit. For the logit model of the Challenger data, we may compute:
pchisq (deviance (1mod), df . residual (1mod), lower FALSE)
[1] $0.71641$
Since this $p$-value is well in excess of $0.05$, we conclude that this model fits sufficiently well. Of course, this does not mean that this model is correct or that a simpler model might not also fit adequately. Even so, for the null model:
pchisq $(38.9,22$, lower FALSE)
[1] $0.014489$
We see that the fit is inadequate, so we cannot ascribe the response to simple variation not dependent on any predictor. Note that a $\chi_{d}^{2}$ variable has mean $d$ and standard deviation $\sqrt{2 d}$ so that it is often possible to quickly judge whether a deviance is large or small without explicitly computing the $p$-value. If the deviance is far in excess of the degrees of freedom, the null hypothesis can be rejected.

The $\chi^{2}$ distribution is only an approximation that becomes more accurate as the $m_{i}$ increase. The approximation is very poor for small $m_{i}$ and fails entirely in binary cases where $m_{i}=1$. Although it is not possible to say exactly how large $m_{i}$ should be for an adequate approximation, $m_{i} \geq 5 \forall i$ has often been suggested. Permutation or bootstrap methods might be considered as an alternative.

We can also use the deviance to compare two models, with smaller model $S$ representing a subspace (usually a subset) of a larger model $L$. The likelihood ratio test statistic becomes $D_{S}-D_{L}$. This test statistic is asymptotically distributed $\chi_{l-s}^{2}$, assuming that the smaller model is correct and the distributional assumptions hold. We can use this to test the significance of temperature by computing the difference in the deviances between the model with and without temperature. The model without temperature is just the null model and the difference in degrees of freedom or parameters is one:
pchisq (38.9-16.9,1, lower=FALSE)
[1] $2.7265 \mathrm{e}-06$

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

ibrary (dplyr)
irisr <- filter(iris, Species ! “virginica”) to ? 选择（萼片。宽度，
→萼片。长度，物种）

（p <- ggplot(irisr, aes (x=Sepa1. Width, y=Sepal.Length, shape=Species)）
tgeom point ())

n−100p−3偏差−0.000零偏差−138.629（区别−138.629) 请注意，残差为零表示完美拟合，但由于高标准误差，所有预测变量均不显着。看一下数据就可以发现其中的原因。我们看到这两组是线性可分的，因此可以完美拟合。在这个例子中，我们遭受了财富的尴尬——我们可以完美地拟合数据。不幸的是，这会导致参数及其标准误差的估计不稳定，并且会（可能错误地）表明可以做出完美的预测。在这种情况下，可以考虑另一种拟合方法，称为精确逻辑回归。参见 Cox (1970) 或 Mehta 和 Patel (1995)。可以在 R 的 elrm 和 logistix 包中找到实现。

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

l(b)=∑一世=1n[是一世这一世−米一世日志⁡(1+和一世这)+日志⁡(米一世 是一世)]

1986 年 1 月，挑战者号航天飞机在发射后不久爆炸。对坠机原因进行了调查，并将注意力集中在火箭助推器中的橡胶 O 形密封圈上。在较低温度下，橡胶变得更脆，并且是一种不太有效的密封剂。发射时气温为31∘F. O 形圈的故障是否可以预测？在有数据的之前的 23 次航天飞机任务中，一些 O 形环上记录了一些因吹漏和腐蚀而损坏的证据。每个航天飞机有两个助推器，每个助推器有三个 O 形环。对于每个任务，我们知道○- 六环显示一些损坏和发射温度。这是对问题的简化，请参见 Dalal 等人。(1989) 了解更多详情。

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

D=2 \sum_{i=1}^{n}\left{y_{i} \log y_{i} / \hat{y}{i}+\left(m{i}-y_{i}\右) \log \left(m_{i}-y_{i}\right) /\left(m_{i}-\hat{y}{i}\right)\right}D=2 \sum_{i=1}^{n}\left{y_{i} \log y_{i} / \hat{y}{i}+\left(m{i}-y_{i}\右) \log \left(m_{i}-y_{i}\right) /\left(m_{i}-\hat{y}{i}\right)\right}在哪里是^一世是模型的拟合值。

pchisq (deviance (1mod), df .residual (1mod), lower FALSE)
[1]0.71641

pchisq(38.9,22, 下 FALSE)
[1]0.014489

pchisq (38.9-16.9,1, lower=FALSE)
[1]2.7265和−06

## 有限元方法代写

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。

## 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。