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

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

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

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

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

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

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

Now plot the data:
$>$ library (lattice)
$>$ xyplot (income $\sim$ year I person, psid, type=” $1 “$,
subset=(person $<21$ ), strip=FALSE)
The first 20 subjects are shown in Figure 9.1. We see that some individuals have a slowly increasing income, typical of someone in steady employment in the same job. Other individuals have more erratic incomes. We can also show how the incomes vary by sex. Income is more naturally considered on a log-scale:
$$\text { xyplot }(\log (\text { income+100) year I sex, psid, type=” } 1 “)$$

## 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|STAT3030

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

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

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

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

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

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

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

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

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

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

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

We shall take as our response the math test score result from the final year and try to model this as a function of gender, social class and the Raven’s test score from the first year which might be taken as a measure of ability when entering the school. We subset the data to ignore the math scores from the first two years:
$>\operatorname{data}(j s p)$
$>j \operatorname{spr}<-j \operatorname{sp} \quad[j \operatorname{sp} \$ y e a r==2$, We start with two plots of the data. Due to the discreteness of the score results, it is helpful to jitter (add small random perturbations) the scores to avoid overprinting: plot (jitter (math) jitter (raven), data=jspr, xlab=”Raven score”,$\quad$ylab=”Math score”) boxplot (math social, data=jspr,xlab=”Social class”,ylab=”Math score”) In Figure 8.4, we can see the positive correlation between the Raven’s test score and the final math score. The maximum math score was 40 which reduces the variability at the upper end of the scale. We also see how the math scores tend to decline with social class. # 广义线性模型代考 ## 统计代写|广义线性模型代写generalized linear model代考|Crossed Effects 当效果没有嵌套时，据说​​它们是交叉的。在全因子设计中，效应完全交叉，因为一个因素的每个水平都与另一个因素的每个水平发生。然而，在其他一些设计中，交叉是不完整的。即使在所有四个组合中只出现两个因素的两个水平，这些因素也会交叉。不完全交叉的一个例子是拉丁方设计，其中有一个处理因子和两个区组因子。尽管并非所有因素组合都会发生，但区组因素并不嵌套。当至少发生一些交叉时，不能使用嵌套设计的方法。我们考虑一个拉丁方的例子。 在 Davies (1954) 报告的一项实验中，四种材料 A、B、C 和 D 被送入磨损试验机。反应是体重减轻0.1 米米在测试期间。该机器一次可以处理四个样品，过去的经验表明这四个样品的位置存在一些差异。还怀疑运行与运行之间存在一些差异。可以在 Faraway (2004) 中找到该数据集的固定效应分析。进行了四次运行。可以观察到设计的拉丁方结构： lmer 函数能够识别运行和位置效应交叉并适当地拟合模型。固定效应的 F 检验与相应的固定效应分析几乎相同。唯一的区别是固定效应分析使用的分母自由度为 6，而随机效应分析以估计的随机效应参数为条件，从而产生 12 个自由度。区别在这里并不重要。 随机效应的显着性可以使用参数引导方法进行测试。然而，由于该实验的设计已经限制了随机化以允许这些影响，因此没有动机进行这些测试，因为我们不会修改当前实验的分析。 固定效应分析在某种程度上更容易执行，但随机效应分析的优点是可以估计区组因子的变化，这在未来的研究中更有用。此实验的运行效果的固定效果估计仅对当前研究有用。 ## 统计代写|广义线性模型代写generalized linear model代考|Multilevel Models 多级模型是用于具有层次结构的数据模型的术语。该术语在社会科学中最常用。我们可以使用 我们已经开发的方法来拟合其中一些模型。 我们以初级学校项目的一些数据为例，这些数据是从伦敦市中心的小学（美国术语是小学）收 集的。Mortimore、Sammons、Stoll、Lewis 和 Ecob (1988) 对数据进行了详细描述， Goldstein (1995) 对其中一个子集进行了广泛分析。 数据中的变量是学校，学校内的班级（最多四个），性别，父亲的社会阶层$(\mathrm{I}=1 ; 二=2$; III 非手动$=3$; 三、说明书$=4 ; I \mathrm{I}=5 ； \mathrm{~V}=6$；长期失业$=7$; 目前末就业$=8$；父亲缺席$=9 ）$，第 一年的瑞文考试，学号，英语考试成绩，数学考试成绩和学年（第一，第二和第三年编码为 0,1 和 2) 。所以每个学生最多有 3 个小节。数据来自 http://www.ioe.ac.uk/multilevel/ 的多 级模型项目。 我们应将最后一年的数学考试成绩作为我们的回应，并尝试将其建模为性别、社会阶层和第一 年的 Raven 考试成绩的函数，这可能被视为入学时的能力衡量标准. 我们对数据进行子集化以 忽略前两年的数学成绩:$>\operatorname{data}(j s p)>j$spr$<-j$sp$\quad[j$sp$\$y e a r==2$,

plot (jitter (math) jitter (raven), data=jspr, $x l a b=$ “Raven

ylab=”Math score”)
boxplot (math social, data=jspr,xlab=”Social
class”,ylab=”Math score”)

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

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

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

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

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

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

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

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

# 广义线性模型代考

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

$$y_{i j k}=\mu+i_i+v_j+(\mathrm{iv}) i j+f_k+(\mathrm{v} f) j k+\varepsilon_{i j k}$$
$\mu, i_i, v_j,(i v) i j$ 是固定效应，其余是随机的，有方差 $\sigma_f^2, \sigma v f^2$ 和 $\sigma_{\varepsilon}^2$ 请注意，我们没有 $(\text { if })_{i k}$ 这个模型中的术语。不可能估计这种影响，因为给定的田地只使用一种濩溉方式；这些 因素没有交叉。

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

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

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

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

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

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

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

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

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

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

# 广义线性模型代考

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

Bliss (1935) 分析了一些关于在不同杀虫剂浓度水平下死亡的昆蝼量的数据。我们适合所有 三个链㢺功能:

$>$ 绘图 $(x$, 绑定 $(p p / p l,(1-p p) /(1-$
pl)), type=”1″, $x l a b=$ 剂量”, $1 \mathrm{ab}=$ “比率”)
$>$ matplot $(x$, cbind $(\mathrm{pc} / \mathrm{pl},(1-\mathrm{pc}) /(1-$
pl)), type=”1″, 1 lab=”Dose”,ylab=”Ratio”)

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

$$X^2=\sum_{i=1}^n \frac{\left(O_i-E_i\right)^2}{E_i}$$

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

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

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

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

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

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

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

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

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

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

# 广义线性模型代考

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

$$\frac{p}{1-p}=o \quad p=\frac{o}{1+o}$$

$$\log (\text { oods })=\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2$$

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

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

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

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

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

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

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

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

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

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

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

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

# 广义线性模型代考

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

1986 年 1 月，挑战者号航天飞机在发射后不久就爆炸了。对坠机原因展开了调查，并将注意 力集中在火箭助推器中的橡胶 $O$ 形密封圈上。在较低的温度下，橡胶变得更脆并且是一种效 果较差的密封剂。发射时的温度是 $31^{\circ} \mathrm{F}$. 是否可以预测 $\mathrm{O}$ 形圈的失效? 在现有数据的 23 次航 天飞机任务中，一些 $O$ 形环上记录了由于吹过和侵蚀造成的损坏证据。每架航天飞机都有两 个助推器，每个助推器都有三个 $O$ 形圈。对于每个任务，我们知道有多少 0 -六分之一的环显 示了一些损坏和发射温度。这是问题的简化一一有关详细信息，请参阅 Dalal、Fowlkes 和 Hoadley (1989)。

$>$ 图书馆 (遥远)

$>$ 情节 (伤害 $6 \sim$ 温度, orings, $x$ lim $=c(25,85)$ ， 优越的 $=$ $c(0,1)$,
$x l a b=$ “Temperature”, ylab=”Prob of damage”)

\begin{aligned} & >\operatorname{lmod}<-1 \operatorname{lm}(\text { damage } / 6 \sim \text { temp, orings) } \\ & >\text { abline }(\operatorname{lmod}) \end{aligned}

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

$$P\left(Y_i=y_i\right)=\left(n_i y_i\right) p_i^{y_i}\left(1-p_i\right)^{n_i-y_i}$$

$$\eta_i=\beta_0+\beta_1 x_{i 1}+\ldots+\beta_q x_{i q}$$

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

## 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|STAT3030

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

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

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

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

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

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

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

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

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

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

# 广义线性模型代考

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

$$\mathrm{E}(\hat{\boldsymbol{\beta}})=\boldsymbol{\beta} .$$

$$\operatorname{var}(\hat{\boldsymbol{\beta}})=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2$$

$$\hat{\boldsymbol{\beta}} \sim N_p\left(\boldsymbol{\beta},\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \sigma^2\right)$$

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

$$\log L\left(\sigma^2\right)=-\frac{n}{2} \log \left(2 \pi \sigma^2\right)-\frac{1}{2} \operatorname{RSS}(\hat{\boldsymbol{\beta}}) / \sigma^2 .$$

$$\hat{\sigma^2}=\operatorname{RSS}(\hat{\boldsymbol{\beta}}) / n .$$

## 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|STA517

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

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

Let us now turn our attention to the systematic part of the model. Suppose that we have data on $p$ predictors $x_1, \ldots, x_p$ which take values $x_{i 1}, \ldots, x_{i p}$ for the $i$-th unit. We will assume that the expected response depends on these predictors. Specifically, we will assume that $\mu_i$ is as linear function of the predictors
$$\mu_i=\beta_1 x_{i 1}+\beta_2 x_{i 2}+\ldots+\beta_p x_{i p}$$
for some unknown coefficients $\beta_1, \beta_2, \ldots, \beta_p$. The coefficients $\beta_j$ are called regression coefficients and we will devote considerable attention to their interpretation.

This equation may be written more compactly using matrix notation as
$$\mu_i=\mathbf{x}_i^{\prime} \boldsymbol{\beta},$$
where $\mathbf{x}_i^{\prime}$ is a row vector with the values of the $p$ predictors for the $i$-th unit and $\boldsymbol{\beta}$ is a column vector containing the $p$ regression coefficients. Even more compactly, we may form a column vector $\boldsymbol{\mu}$ with all the expected responses and then write
$$\boldsymbol{\mu}=\mathbf{X} \boldsymbol{\beta},$$
where $\mathbf{X}$ is an $n \times p$ matrix containing the values of the $p$ predictors for the $n$ units. The matrix $\mathbf{X}$ is usually called the model or design matrix. Matrix notation is not only more compact but, once you get used to it, it is also easier to read than formulas with lots of subscripts.

The expression $\mathbf{X} \boldsymbol{\beta}$ is called the linear predictor, and includes many special cases of interest. Later in this chapter we will show how it includes simple and multiple linear regression models, analysis of variance models and analysis of covariance models.

The simplest possible linear model assumes that every unit has the same expected value, so that $\mu_i=\mu$ for all $i$. This model is often called the null model, because it postulates no systematic differences between the units. The null model can be obtained as a special case of Equation $2.3$ by setting $p=1$ and $x_i=1$ for all $i$. In terms of our example, this model would expect fertility to decline by the same amount in all countries, and would attribute all observed differences between countries to random variation.

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

The likelihood principle instructs us to pick the values of the parameters that maximize the likelihood, or equivalently, the logarithm of the likelihood function. If the observations are independent, then the likelihood function is a product of normal densities of the form given in Equation 2.1. Taking logarithms we obtain the normal log-likelihood
$$\log L\left(\boldsymbol{\beta}, \sigma^2\right)=-\frac{n}{2} \log \left(2 \pi \sigma^2\right)-\frac{1}{2} \sum\left(y_i-\mu_i\right)^2 / \sigma^2,$$
where $\mu_i=\mathbf{x}_i^{\prime} \boldsymbol{\beta}$. The most important thing to notice about this expression is that maximizing the log-likelihood with respect to the linear parameters $\boldsymbol{\beta}$ for a fixed value of $\sigma^2$ is exactly equivalent to minimizing the sum of squared differences between observed and expected values, or residual sum of squares
$$\operatorname{RSS}(\boldsymbol{\beta})=\sum\left(y_i-\mu_i\right)^2=(\mathbf{y}-\mathbf{X} \boldsymbol{\beta})^{\prime}(\mathbf{y}-\mathbf{X} \boldsymbol{\beta}) .$$
In other words, we need to pick values of $\boldsymbol{\beta}$ that make the fitted values $\mu_i=\mathbf{x}_i^{\prime} \boldsymbol{\beta}$ as close as possible to the observed values $y_i$.

Taking derivatives of the residual sum of squares with respect to $\boldsymbol{\beta}$ and setting the derivative equal to zero leads to the so-called normal equations for the maximum-likelihood estimator $\hat{\boldsymbol{\beta}}$
$$\mathbf{X}^{\prime} \mathbf{X} \hat{\boldsymbol{\beta}}=\mathbf{X}^{\prime} \mathbf{y} \text {. }$$
If the model matrix $\mathbf{X}$ is of full column rank, so that no column is an exact linear combination of the others, then the matrix of cross-products $\mathbf{X}^{\prime} \mathbf{X}$ is of full rank and can be inverted to solve the normal equations. This gives an explicit formula for the ordinary least squares (OLS) or maximum likelihood estimator of the linear parameters.

# 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|The Systematic Structure

$$\mu_i=\beta_1 x_{i 1}+\beta_2 x_{i 2}+\ldots+\beta_p x_{i p}$$

$$\mu_i=\mathbf{x}_i^{\prime} \boldsymbol{\beta},$$

$$\boldsymbol{\mu}=\mathbf{X} \boldsymbol{\beta},$$

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

$$\log L\left(\boldsymbol{\beta}, \sigma^2\right)=-\frac{n}{2} \log \left(2 \pi \sigma^2\right)-\frac{1}{2} \sum\left(y_i-\mu_i\right)^2 / \sigma^2,$$

$$\operatorname{RSS}(\boldsymbol{\beta})=\sum\left(y_i-\mu_i\right)^2=(\mathbf{y}-\mathbf{X} \boldsymbol{\beta})^{\prime}(\mathbf{y}-\mathbf{X} \boldsymbol{\beta}) .$$

$$\mathbf{X}^{\prime} \mathbf{X} \hat{\boldsymbol{\beta}}=\mathbf{X}^{\prime} \mathbf{y}$$

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

## 统计代写|广义线性模型代写generalized linear model代考|The Program Effort Data

We will illustrate the use of linear models for continuous data using a small dataset extracted from Mauldin and Berelson (1978) and reproduced in Table 2.1. The data include an index of social setting, an index of family planning effort, and the percent decline in the crude birth rate (CBR) – the number of births per thousand population-between 1965 and 1975, for 20 countries in Latin America and the Caribbean.

The index of social setting combines seven social indicators, namely literacy, school enrollment, life expectancy, infant mortality, percent of males aged 15-64 in the non-agricultural labor force, gross national product per capita and percent of population living in urban areas. Higher scores represent higher socio-economic levels.

The index of family planning effort combines 15 different program indicators, including such aspects as the existence of an official family planning policy, the availability of contraceptive methods, and the structure of the family planning program. An index of 0 denotes the absence of a program, 1-9 indicates weak programs, 10-19 represents moderate efforts and 20 or more denotes fairly strong programs.

Figure $2.1$ shows scatterplots for all pairs of variables. Note that CBR decline is positively associated with both social setting and family planning effort. Note also that countries with higher socio-economic levels tend to have stronger family planning programs.

In our analysis of these data we will treat the percent decline in the CBR as a continuous response and the indices of social setting and family planning effort as predictors. In a first approach to the data we will treat the predictors as continuous covariates with linear effects. Later we will group them into categories and treat them as discrete factors.

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

The first issue we must deal with is that the response will vary even among units with identical values of the covariates. To model this fact we will treat each response $y_i$ as a realization of a random variable $Y_i$. Conceptually, we view the observed response as only one out of many possible outcomes that we could have observed under identical circumstances, and we describe the possible values in terms of a probability distribution.

For the models in this chapter we will assume that the random variable $Y_i$ has a normal distribution with mean $\mu_i$ and variance $\sigma^2$, in symbols:
$$Y_i \sim N\left(\mu_i, \sigma^2\right) .$$
The mean $\mu_i$ represents the expected outcome, and the variance $\sigma^2$ measures the extent to which an actual observation may deviate from expectation.
Note that the expected value may vary from unit to unit, but the variance is the same for all. In terms of our example, we may expect a larger fertility decline in Cuba than in Haiti, but we don’t anticipate that our expectation will be closer to the truth for one country than for the other.

The normal or Gaussian distribution (after the mathematician Karl Gauss) has probability density function
$$f\left(y_i\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left{-\frac{1}{2} \frac{\left(y_i-\mu_i\right)^2}{\sigma^2}\right} .$$

The standard density with mean zero and standard deviation one is shown in Figure 2.2.

Most of the probability mass in the normal distribution (in fact, 99.7\%) lies within three standard deviations of the mean. In terms of our example, we would be very surprised if fertility in a country declined $3 \sigma$ more than expected. Of course, we don’t know yet what to expect, nor what $\sigma$ is.

# 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|The Random Structure

f\left(y_i\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left{-\frac{1}{2} \frac{\left(y_i-\ mu_i\right)^2}{\sigma^2}\right} 。f\left(y_i\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left{-\frac{1}{2} \frac{\left(y_i-\ mu_i\right)^2}{\sigma^2}\right} 。

## 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|STAT6175

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

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

As mentioned earlier, we cannot use the deviance for a binary response GLM as a measure of fit. We can use diagnostic plots of the binned residuals to help us identify inadequacies in the model but these cannot tell us whether the model fits or not. Even so the process of binning can help us develop a test for this purpose. We divide the observations up into $J$ bins based on the linear predictor. Let the mean response in the $j^{t h}$ bin be $y_j$ and the mean predicted probability be $\hat{p}_j$ with $m_j$ observations within the bin. We compute these values:
wcgsm <- na. omit (wcgs)
wcgsm <- mutate (wcgsm, predprob=predict (1mod, type=” response”))
gdf <- group_by (wcgsm, cut (1inpred, breaks=unique (quant ile (linpred,
$\hookrightarrow(1: 100) / 101))))$
hldf <- summarise (gdf, $y=$ sum $(y)$, ppred=mean (predprob), count=n ()$)$
There are a few missing values in the data. The default method is to ignore these cases. The na.omit command drops these cases from the data frame for the purposes of this calculation. We use the same method of binning the data as for the residuals but now we need to compute the number of observed cases of heart disease and total observations within each bin. We also need the mean predicted probability within each bin.

When we make a prediction with probability $p$, we would hope that the event occurs in practice with that proportion. We can check that by plotting the observed proportions against the predicted probabilities as seen in Figure $2.9$. For a wellcalibrated prediction model, the observed proportions and predicted probabilities should be close.

## 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◦F.

# 广义线性模型代考

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

wcgsm <- na。省略 (wcgs)
wcgsm <- mutate (wcgsm, predprob=predict ( $1 \mathrm{mod}$, type $=$ ” response”))
gdf <-group_by (wcgsm, cut (1inpred, breaks=unique (quant ile (linpred,
$\hookrightarrow(1: 100) / 101))))$
hldf <-总结 (gdf， $y=$ 和 $(y)$, ppred=均值 (predprob), count=n ())

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

$$P\left(Y_i=y_i\right)=\left(m_i y_i\right) p_i^{y_i}\left(1-p_i\right)^{m_i-y_i}$$

$$\eta_i=\beta_0+\beta_1 x_{i 1}+\cdots+\beta_q x_{i q}$$

$$l(\beta)=\sum_{i=1}^n\left[y_i \eta_i-m_i \log \left(1+e_i^\eta\right)+\log \left(m_i y_i\right)\right]$$

1986 年 1 月，挑战者号航天飞机在发射后不久就爆炸了。对坠机原因展开了调查，并将注意力集中在火箭助推 器中的橡胶 $O$ 形密封圈上。在较低的温度下，橡胶变得更脆并且是一种效果较差的密封剂。发射时，温度为 $31^{\circ} \mathrm{F}$ 。

## 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。