### 统计代写|广义线性模型代写generalized linear model代考|STAT3030

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

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

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。