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统计代写|统计推断作业代写statistics interference代考| Exponential family

Posted on 2022年4月14日2022年4月14日 by statistics-lab

如果你也在怎样代写统计推断statistics interference这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计推断是利用数据分析来推断概率基础分布的属性的过程。推断性统计分析推断人口的属性，例如通过测试假设和得出估计值。

statistics-lab™ 为您的留学生涯保驾护航在代写统计推断statistics interference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。我们的专家在代写统计推断statistics interference方面经验极为丰富，各种代写统计推断statistics interference相关的作业也就用不着说。

我们提供的属性统计推断statistics interference及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|统计推断作业代写statistics interference代考|Exponential family

We now consider a family of models that are important both because they have relatively simple properties and because they capture in one discussion many,

although by no means all, of the inferential properties connected with important standard distributions, the binomial, Poisson and geometric distributions and the normal and gamma distributions, and others too.

Suppose that $\theta$ takes values in a well-behaved region in $R^{d}$, and not of lower dimension, and that we can find a $(d \times 1)$-dimensional statistic $s$ and a parameterization $\phi$, i.e., a $(1,1)$ transformation of $\theta$, such that the model has the form
$$
m(y) \exp \left{s^{T} \phi-k(\phi)\right}
$$
where $s=s(y)$ is a function of the data. Then $S$ is sufficient; subject to some important regularity conditions this is called a regular or full $(d, d)$ exponential family of distributions. The statistic $S$ is called the canonical statistic and $\phi$ the canonical parameter. The parameter $\eta=E(S ; \phi)$ is called the mean parameter. Because the stated function defines a distribution, it follows that
$$
\begin{aligned}
&\int m(y) \exp \left{s^{T} \phi-k(\phi)\right} d y=1 \
&\int m(y) \exp \left{s^{T}(\phi+p)-k(\phi+p)\right} d y=1 .
\end{aligned}
$$
Hence, noting that $s^{T} p=p^{T} s$, we have from (2.11) that the moment generating function of $S$ is
$$
E\left{\exp \left(p^{T} S\right)\right}=\exp {k(\phi+p)-k(\phi)}
$$
Therefore the cumulant generating function of $S$, defined as the log of the moment generating function, is
$$
k(\phi+p)-k(\phi),
$$
providing a fairly direct interpretation of the function $k$ (.). Because the mean is given by the first derivatives of that generating function, we have that $\eta=$ $\nabla k(\phi)$, where $\nabla$ is the gradient operator $\left(\partial / \partial \phi_{1}, \ldots, \partial / \partial \phi_{d}\right)^{T}$. See Note $2.3$ for a brief account of both cumulant generating functions and the $\nabla$ notation.
Example 2.5. Binomial distribution. If $R$ denotes the number of successes in $n$ independent binary trials each with probability of success $\pi$, its density can be written
$$
n ! /{r !(n-r) !}^{\pi r}(1-\pi)^{n-r}=m(r) \exp \left{r \phi-n \log \left(1+e^{\phi}\right)\right},
$$
say, where $\phi=\log {\pi /(1-\pi)}$, often called the $\log$ odds, is the canonical parameter and $r$ the canonical statistic. Note that the mean parameter is $E(R)=$ $n \pi$ and can be recovered also by differentiating $k(\phi)$.

统计代写|统计推断作业代写statistics interference代考|Choice of priors for exponential family problems

While in Bayesian theory choice of prior is in principle not an issue of achieving mathematical simplicity, nevertheless there are gains in using reasonably simple and flexible forms. In particular, if the likelihood has the full exponential family form
$$
m(y) \exp \left{s^{T} \phi-k(\phi)\right}
$$
a prior for $\phi$ proportional to
$$
\exp \left{s_{0}^{T} \phi-a_{0} k(\phi)\right}
$$
leads to a posterior proportional to
$$
\exp \left{\left(s+s_{0}\right)^{T} \phi-\left(1+a_{0}\right) k(\phi)\right}
$$
Such a prior is called conjugate to the likelihood, or sometimes closed under sampling. The posterior distribution has the same form as the prior with $s_{0}$ replaced by $s+s_{0}$ and $a_{0}$ replaced by $1+a_{0}$.

Example 2.8. Binomial distribution (ctd). This continues the discussion of Example 2.5. If the prior for $\pi$ is proportional to
$$
\pi^{r_{0}}(1-\pi)^{n_{0}-r_{0}}
$$
i.e., is a beta distribution, then the posterior is another beta distribution corresponding to $r+r_{0}$ successes in $n+n_{0}$ trials. Thus both prior and posterior are beta distributions. It may help to think of $\left(r_{0}, n_{0}\right)$ as fictitious data! If the prior information corresponds to fairly small values of $n_{0}$ its effect on the conclusions will be small if the amount of real data is appreciable.

统计代写|统计推断作业代写statistics interference代考|Simple frequentist discussion

In Bayesian approaches sufficiency arises as a convenient simplification of the likelihood; whatever the prior the posterior is formed from the likelihood and hence depends on the data only via the sufficient statistic.

In frequentist approaches the issue is more complicated. Faced with a new model as the basis for analysis, we look for a Fisherian reduction, defined as follows:

find the likelihood function;
reduce to a sufficient statistic $S$ of the same dimension as $\theta$;
find a function of $S$ that has a distribution depending only on $\psi$;
invert that distribution to obtain limits for $\psi$ at an arbitrary set of probability levels;
use the conditional distribution of the data given $S=s$ informally or formally to assess the adequacy of the formulation.
Immediate application is largely confined to regular exponential family models. While most of our discussion will centre on inference about the parameter of interest, $\psi$, the complementary role of sufficiency of providing an explicit base for model checking is in principle very important. It recognizes that our formulations are always to some extent provisional, and usually capable to some extent of empirical check; the universe of discussion is not closed. In general there is no specification of what to do if the initial formulation is inadequate but, while that might sometimes be clear in broad outline, it seems both in practice and in principle unwise to expect such a specification to be set out in detail in each application.

The next phase of the analysis is to determine how to use $s$ to answer more focused questions, for example about the parameter of interest $\psi$. The simplest possibility is that there are no nuisance parameters, just a single parameter $\psi$ of interest, and reduction to a single component $s$ occurs. We then have one observation on a known density $f_{S}(s ; \psi)$ and distribution function $F_{S}(s ; \psi)$. Subject to some monotonicity conditions which, in applications, are typically satisfied, the probability statement
$$
P\left(S \leq a_{c}(\psi)\right)=F_{S}\left(a_{c}(\psi) ; \psi\right)=1-c
$$
can be inverted for continuous random variables into
$$
P\left{\psi \leq b_{c}(S)\right}=1-c
$$
Thus the statement on the basis of data $y$, yielding sufficient statistic $s$, that
$$
\psi \leq b_{c}(s)
$$provides an upper bound for $\psi$, that is a single member of a hypothetical long run of statements a proportion $1-c$ of which are true, generating a set of statements in principle at all values of $c$ in $(0,1)$.

Exponential distribution - Wikipedia — 统计代写|统计推断作业代写statistics interference代考| Exponential family

属性数据分析

统计代写|统计推断作业代写statistics interference代考|Exponential family

我们现在考虑一系列重要的模型，因为它们具有相对简单的属性，并且因为它们在一次讨论中捕获了许多，

尽管绝不是所有与重要标准分布、二项式分布、泊松分布和几何分布以及正态分布和伽马分布等相关的推理性质。

假设θ在行为良好的区域中取值Rd，而不是低维，我们可以找到一个(d×1)维统计s和参数化φ，即一个(1,1)的转变θ，使得模型具有形式
m(y) \exp \left{s^{T} \phi-k(\phi)\right}m(y) \exp \left{s^{T} \phi-k(\phi)\right}
在哪里s=s(是)是数据的函数。然后小号足够了; 根据一些重要的规律性条件，这被称为规律性或完全性(d,d)指数分布族。统计数据小号称为典型统计量，并且φ规范参数。参数这=和(小号;φ)称为均值参数。因为所述函数定义了一个分布，所以它遵循
\begin{对齐} &\int m(y) \exp \left{s^{T} \phi-k(\phi)\right} d y=1 \ &\int m(y) \exp \left{s ^{T}(\phi+p)-k(\phi+p)\right} d y=1 。\end{对齐}\begin{对齐} &\int m(y) \exp \left{s^{T} \phi-k(\phi)\right} d y=1 \ &\int m(y) \exp \left{s ^{T}(\phi+p)-k(\phi+p)\right} d y=1 。\end{对齐}
因此，注意到s吨p=p吨s, 我们从 (2.11) 得到矩生成函数小号是
E\left{\exp \left(p^{T} S\right)\right}=\exp {k(\phi+p)-k(\phi)}E\left{\exp \left(p^{T} S\right)\right}=\exp {k(\phi+p)-k(\phi)}
因此，累积生成函数小号，定义为矩生成函数的对数，是
到(φ+p)−到(φ),
提供对功能的相当直接的解释到(.)。因为均值是由该生成函数的一阶导数给出的，所以我们有这= ∇到(φ)，在哪里∇是梯度算子(∂/∂φ1,…,∂/∂φd)吨. 见说明2.3简要说明累积量生成函数和∇符号。
例 2.5。二项分布。如果R表示成功的次数n独立的二元试验，每个试验都有成功的概率圆周率, 它的密度可以写成
！/{r !(nr) !}^{\pi r}(1-\pi)^{nr}=m(r) \exp \left{r \phi-n \log \left(1+e^{ \phi}\right)\right},！/{r !(nr) !}^{\pi r}(1-\pi)^{nr}=m(r) \exp \left{r \phi-n \log \left(1+e^{ \phi}\right)\right},
说，在哪里φ=日志⁡圆周率/(1−圆周率)，通常称为日志几率，是规范参数，并且r典型统计量。请注意，平均参数是和(R)= n圆周率也可以通过微分恢复到(φ).

统计代写|统计推断作业代写statistics interference代考|Choice of priors for exponential family problems

虽然在贝叶斯理论中，先验的选择原则上不是实现数学简单性的问题，但是使用相当简单和灵活的形式是有好处的。特别是，如果可能性具有完整的指数族形式
m(y) \exp \left{s^{T} \phi-k(\phi)\right}m(y) \exp \left{s^{T} \phi-k(\phi)\right}
先验φ成正比
\exp \left{s_{0}^{T} \phi-a_{0} k(\phi)\right}\exp \left{s_{0}^{T} \phi-a_{0} k(\phi)\right}
导致后验比例
\exp \left{\left(s+s_{0}\right)^{T} \phi-\left(1+a_{0}\right) k(\phi)\right}\exp \left{\left(s+s_{0}\right)^{T} \phi-\left(1+a_{0}\right) k(\phi)\right}
这样的先验被称为可能性的共轭，或者有时在采样下关闭。后验分布具有与先验相同的形式s0取而代之s+s0和一种0取而代之1+一种0.

例 2.8。二项分布 (ctd)。这将继续对示例 2.5 的讨论。如果先于圆周率正比于
圆周率r0(1−圆周率)n0−r0
即，是一个β分布，那么后验是另一个β分布对应于r+r0成功n+n0试验。因此，先验和后验都是 beta 分布。想一想可能会有所帮助(r0,n0)作为虚构数据！如果先验信息对应于相当小的值n0如果实际数据量可观，它对结论的影响将很小。

统计代写|统计推断作业代写statistics interference代考|Simple frequentist discussion

在贝叶斯方法中，充分性作为可能性的方便简化而出现；无论先验后验是由可能性形成的，因此仅通过足够的统计量依赖于数据。

在频率论方法中，这个问题更加复杂。面对一个新模型作为分析的基础，我们寻找Fisherian约简，定义如下：

找到似然函数；
减少到足够的统计量小号尺寸相同θ;
找到一个函数小号它的分布仅取决于ψ;
反转该分布以获得限制ψ在任意一组概率水平上；
使用给定数据的条件分布小号=s非正式或正式地评估配方的充分性。
即时应用主要限于常规指数族模型。虽然我们的大部分讨论将集中在对感兴趣参数的推断上，ψ，为模型检查提供明确基础的充分性的补充作用原则上非常重要。它承认我们的公式在某种程度上总是临时的，并且通常能够在某种程度上进行经验检查；讨论的范围不是封闭的。一般来说，如果最初的表述不充分，没有具体说明该怎么做，虽然有时可能很清楚，但在实践和原则上，期望这样的说明在每篇文章中都详细列出似乎是不明智的。应用。

分析的下一阶段是确定如何使用s回答更有针对性的问题，例如关于感兴趣的参数ψ. 最简单的可能是没有讨厌的参数，只有一个参数ψ感兴趣，并减少到单个组件s发生。然后我们对已知密度进行一次观察F小号(s;ψ)和分布函数F小号(s;ψ). 受限于在应用中通常满足的一些单调性条件，概率陈述
磷(小号≤一种C(ψ))=F小号(一种C(ψ);ψ)=1−C
可以将连续随机变量反转为
P\left{\psi \leq b_{c}(S)\right}=1-cP\left{\psi \leq b_{c}(S)\right}=1-c
因此，基于数据的声明是, 产生足够的统计量s，那
ψ≤bC(s)提供了一个上限ψ, 那是假设的长期陈述的单个成员 a 比例1−C其中是正确的，原则上在所有值下生成一组陈述C在(0,1).

统计代写|统计推断作业代写statistics interference代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

在概率论概念中，随机过程是随机变量的集合。若一随机系统的样本点是随机函数，则称此函数为样本函数，这一随机系统全部样本函数的集合是一个随机过程。实际应用中，样本函数的一般定义在时间域或者空间域。 随机过程的实例如股票和汇率的波动、语音信号、视频信号、体温的变化，随机运动如布朗运动、随机徘徊等等。

贝叶斯方法代考

贝叶斯统计概念及数据分析表示使用概率陈述回答有关未知参数的研究问题以及统计范式。后验分布包括关于参数的先验分布，和基于观测数据提供关于参数的信息似然模型。根据选择的先验分布和似然模型，后验分布可以解析或近似，例如，马尔科夫链蒙特卡罗 (MCMC) 方法之一。贝叶斯统计概念及数据分析使用后验分布来形成模型参数的各种摘要，包括点估计，如后验平均值、中位数、百分位数和称为可信区间的区间估计。此外，所有关于模型参数的统计检验都可以表示为基于估计后验分布的概率报表。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

statistics-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。

机器学习代写

随着AI的大潮到来，Machine Learning逐渐成为一个新的学习热点。同时与传统CS相比，Machine Learning在其他领域也有着广泛的应用，因此这门学科成为不仅折磨CS专业同学的“小恶魔”，也是折磨生物、化学、统计等其他学科留学生的“大魔王”。学习Machine learning的一大绊脚石在于使用语言众多，跨学科范围广，所以学习起来尤其困难。但是不管你在学习Machine Learning时遇到任何难题，StudyGate专业导师团队都能为你轻松解决。

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|统计推断作业代写statistics interference代考| Some concepts and simple applications

Posted on 2022年4月14日2022年4月14日 by statistics-lab

如果你也在怎样代写统计推断statistics interference这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计推断是利用数据分析来推断概率基础分布的属性的过程。推断性统计分析推断人口的属性，例如通过测试假设和得出估计值。

我们提供的属性统计推断statistics interference及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|统计推断作业代写statistics interference代考| Some concepts and simple applications

统计代写|统计推断作业代写statistics interference代考|Likelihood

The likelihood for the vector of observations $y$ is defined as
$$
\operatorname{lik}(\theta ; y)=f_{Y}(y ; \theta),
$$
considered in the first place as a function of $\theta$ for given $y$. Mostly we work with its logarithm $l(\theta ; y)$, often abbreviated to $l(\theta)$. Sometimes this is treated as a function of the random vector $Y$ rather than of $y$. The log form is convenient, in particular because $f$ will often be a product of component terms. Occasionally we work directly with the likelihood function itself. For nearly all purposes multiplying the likelihood formally by an arbitrary function of $y$, or equivalently adding an arbitrary such function to the log likelihood, would leave unchanged that part of the analysis hinging on direct calculations with the likelihood.

Any calculation of a posterior density, whatever the prior distribution, uses the data only via the likelihood. Beyond that, there is some intuitive appeal in the idea that differences in $I(\theta)$ measure the relative effectiveness of different parameter values $\theta$ in explaining the data. This is sometimes elevated into a principle called the law of the likelihood.

A key issue concerns the additional arguments needed to extract useful information from the likelihood, especially in relatively complicated problems possibly with many nuisance parameters. Likelihood will play a central role in almost all the arguments that follow.

统计代写|统计推断作业代写statistics interference代考|Sufficiency

The term statistic is often used (rather oddly) to mean any function of the observed random variable $Y$ or its observed counterpart. A statistic $S=S(Y)$ is called sufficient under the model if the conditional distribution of $Y$ given $S=s$ is independent of $\theta$ for all $s, \theta$. Equivalently
$$
l(\theta ; y)=\log h(s, \theta)+\log m(y),
$$
for suitable functions $h$ and $m$. The equivalence forms what is called the Neyman factorization theorem. The proof in the discrete case follows most explicitly by defining any new variable $W$, a function of $Y$, such that $Y$ is in $(1,1)$ correspondence with $(S, W)$, i.e., such that $(S, W)$ determines $Y$. The individual atoms of probability are unchanged by transformation. That is,
$$
f_{Y}(y ; \theta)=f_{S, W}(s, w ; \theta)=f_{S}(s ; \theta) f_{W \mid S}(w ; s),
$$
where the last term is independent of $\theta$ by definition. In the continuous case there is the minor modification that a Jacobian, not involving $\theta$, is needed when transforming from $Y$ to $(S, W)$. See Note $2.2$.

We use the minimal form of $S$; i.e., extra components could always be added to any given $S$ and the sufficiency property retained. Such addition is undesirable and is excluded by the requirement of minimality. The minimal form always exists and is essentially unique.

Any Bayesian inference uses the data only via the minimal sufficient statistic. This is because the calculation of the posterior distribution involves multiplying the likelihood by the prior and normalizing. Any factor of the likelihood that is a function of $y$ alone will disappear after normalization.

In a broader context the importance of sufficiency can be considered to arise as follows. Suppose that instead of observing $Y=y$ we were equivalently to be given the data in two stages:

first we observe $S=s$, an observation from the density $f_{S}(s ; \theta)$;
then we are given the remaining data, in effect an observation from the density $f_{Y \mid S}(y ; s)$.
Now, so long as the model holds, the second stage is an observation on a fixed and known distribution which could as well have been obtained from a random number generator. Therefore $S=s$ contains all the information about $\theta$ given the model, whereas the conditional distribution of $Y$ given $S=s$ allows assessment of the model.

统计代写|统计推断作业代写statistics interference代考|Simple examples

Example 2.1. Exponential distribution (ctd). The likelihood for Example $1.6$ is
$$
\rho^{n} \exp \left(-\rho \Sigma y_{k}\right),
$$
so that the log likelihood is
$$
n \log \rho-\rho \Sigma y_{k},
$$
and, assuming $n$ to be fixed, involves the data only via $\Sigma y_{k}$ or equivalently via $\bar{y}=\Sigma y_{k} / n$. By the factorization theorem the sum (or mean) is therefore sufficient. Note that had the sample size also been random the sufficient statistic would have been $\left(n, \Sigma y_{k}\right)$; see Example $2.4$ for further discussion.

In this example the density of $S=\Sigma Y_{k}$ is $\rho(\rho s)^{n-1} e^{-\rho s} /(n-1)$ !, a gamma distribution. It follows that $\rho S$ has a fixed distribution. It follows also that the joint conditional density of the $Y_{k}$ given $S=s$ is uniform over the simplex $0 \leq y_{k} \leq s ; \Sigma y_{k}=s$. This can be used to test the adequacy of the model.
Example 2.2. Linear model (ctd). A minimal sufficient statistic for the linear model, Example 1.4, consists of the least squares estimates and the residual sum of squares. This strong justification of the use of least squares estimates depends on writing the log likelihood in the form
$$
-n \log \sigma-(y-z \beta)^{T}(y-z \beta) /\left(2 \sigma^{2}\right)
$$
and then noting that
$$
(y-z \beta)^{T}(y-z \beta)=(y-z \hat{\beta})^{T}(y-z \hat{\beta})+(\hat{\beta}-\beta)^{T}\left(z^{T} z\right)(\hat{\beta}-\beta),
$$
in virtue of the equations defining the least squares estimates. This last identity has a direct geometrical interpretation. The squared norm of the vector defined by the difference between $Y$ and its expected value $z \beta$ is decomposed into a component defined by the difference between $Y$ and the estimated mean $z \hat{\beta}$ and an orthogonal component defined via $\hat{\beta}-\beta$. See Figure 1.1.

It follows that the log likelihood involves the data only via the least squares estimates and the residual sum of squares. Moreover, if the variance $\sigma^{2}$ were

known, the residual sum of squares would be a constant term in the log likelihood and hence the sufficient statistic would be reduced to $\hat{\beta}$ alone.

This argument fails for a regression model nonlinear in the parameters, such as the exponential regression (1.5). In the absence of error the $n \times 1$ vector of observations then lies on a curved surface and while the least squares estimates are still given by orthogonal projection they satisfy nonlinear equations and the decomposition of the log likelihood which is the basis of the argument for sufficiency holds only as an approximation obtained by treating the curved surface as locally flat.

Simple Random Sampling: Definition and Examples — 统计代写|统计推断作业代写statistics interference代考| Some concepts and simple applications

属性数据分析

统计代写|统计推断作业代写statistics interference代考|Likelihood

观测向量的可能性是定义为
平等的⁡(θ;是)=F是(是;θ),
首先被认为是θ给定的是. 大多数情况下，我们使用它的对数一世(θ;是), 通常缩写为一世(θ). 有时这被视为随机向量的函数是而不是是. 日志形式很方便，特别是因为F通常是组件项的乘积。有时我们会直接使用似然函数本身。对于几乎所有目的，将可能性正式乘以任意函数是，或者等价地向对数似然添加任意这样的函数，将保持分析中依赖于可能性的直接计算的部分不变。

后验密度的任何计算，无论先验分布如何，都仅通过可能性使用数据。除此之外，还有一些直觉上的吸引力，即差异一世(θ)衡量不同参数值的相对有效性θ在解释数据时。这有时被提升为称为可能性法则的原则。

一个关键问题涉及从可能性中提取有用信息所需的额外参数，特别是在可能具有许多令人讨厌的参数的相对复杂的问题中。可能性将在接下来的几乎所有论点中发挥核心作用。

统计代写|统计推断作业代写statistics interference代考|Sufficiency

统计量这个术语经常（相当奇怪地）用来表示观察到的随机变量的任何函数是或其观察到的对应物。一个统计小号=小号(是)如果条件分布是给定小号=s独立于θ对全部s,θ. 等效地
一世(θ;是)=日志⁡H(s,θ)+日志⁡米(是),
适合功能H和米. 等价形成了所谓的内曼分解定理。离散情况下的证明最明确地遵循定义任何新变量在，一个函数是, 这样是在(1,1)与(小号,在)，即，这样(小号,在)决定是. 概率的单个原子不会因变换而改变。那是，
F是(是;θ)=F小号,在(s,在;θ)=F小号(s;θ)F在∣小号(在;s),
最后一项独立于θ根据定义。在连续情况下，雅可比行列式存在较小的修改，不涉及θ, 转换时需要是到(小号,在). 见说明2.2.

我们使用最小形式小号; 即，总是可以将额外的组件添加到任何给定的小号并保留充足的财产。这种添加是不希望的，并且被最小化的要求排除在外。最小的形式总是存在并且本质上是独一无二的。

任何贝叶斯推理都仅通过最小足够统计量使用数据。这是因为后验分布的计算涉及将似然乘以先验和归一化。可能性的任何因素，它是是归一化后单独消失。

在更广泛的背景下，充足的重要性可以被认为是如下出现的。假设不是观察是=是我们等效地分两个阶段获得数据：

首先我们观察小号=s, 从密度观察F小号(s;θ);
然后我们得到剩余的数据，实际上是对密度的观察F是∣小号(是;s).
现在，只要模型成立，第二阶段就是对固定且已知分布的观察，该分布也可以从随机数生成器中获得。所以小号=s包含有关的所有信息θ给定模型，而条件分布是给定小号=s允许评估模型。

统计代写|统计推断作业代写statistics interference代考|Simple examples

例 2.1。指数分布 (ctd)。示例的可能性1.6是
ρn经验⁡(−ρΣ是到),
所以对数似然是
n日志⁡ρ−ρΣ是到,
并且，假设n待修复，仅通过以下方式涉及数据Σ是到或等效地通过是¯=Σ是到/n. 因此，通过因式分解定理，总和（或均值）就足够了。请注意，如果样本量也是随机的，那么足够的统计量将是(n,Σ是到); 见例子2.4进一步讨论。

在这个例子中，密度小号=Σ是到是ρ(ρs)n−1和−ρs/(n−1)!，伽马分布。它遵循ρ小号有固定的分布。还可以得出，联合条件密度是到给定小号=s在单纯形上是一致的0≤是到≤s;Σ是到=s. 这可以用来测试模型的充分性。
例 2.2。线性模型 (ctd)。例 1.4 线性模型的最小足够统计量由最小二乘估计和残差平方和组成。使用最小二乘估计的这种强有力的理由取决于将对数似然写成形式
−n日志⁡σ−(是−和b)吨(是−和b)/(2σ2)
然后注意到
(是−和b)吨(是−和b)=(是−和b^)吨(是−和b^)+(b^−b)吨(和吨和)(b^−b),
凭借定义最小二乘估计的方程。最后一个恒等式具有直接的几何解释。由两者之差定义的向量的平方范数是及其期望值和b被分解为由两者之间的差异定义的组件是和估计的平均值和b^和通过定义的正交分量b^−b. 请参见图 1.1。

因此，对数似然仅通过最小二乘估计和残差平方和涉及数据。此外，如果方差σ2是

已知，残差平方和将是对数似然中的常数项，因此充分的统计量将减少为b^独自的。

对于参数中的非线性回归模型，例如指数回归 (1.5)，此论点失败。在没有错误的情况下n×1然后，观测向量位于曲面上，虽然最小二乘估计仍然由正交投影给出，但它们满足非线性方程，并且作为充分性论证基础的对数似然分解仅作为通过处理曲面局部平坦。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|统计推断作业代写statistics interference代考| Bayesian discussion

Posted on 2022年4月14日2022年4月14日 by statistics-lab

如果你也在怎样代写统计推断statistics interference这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计推断是利用数据分析来推断概率基础分布的属性的过程。推断性统计分析推断人口的属性，例如通过测试假设和得出估计值。

我们提供的属性统计推断statistics interference及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|统计推断作业代写statistics interference代考|Bayesian discussion

In the second approach to the problem we treat $\mu$ as having a probability distribution both with and without the data. This raises two questions: what is the meaning of probability in such a context, some extended or modified notion of probability usually being involved, and how do we obtain numerical values for the relevant probabilities? This is discussed further later, especially in Chapter $5 .$ For the moment we assume some such notion of probability concerned with measuring uncertainty is available.

If indeed we can treat $\mu$ as the realized but unobserved value of a random variable $M$, all is in principle straightforward. By Bayes’ theorem, i.e., by simple laws of probability,
$$
f_{M \mid Y}(\mu \mid y)=f_{Y \mid M}(y \mid \mu) f_{M}(\mu) / \int f_{Y \mid M}(y \mid \phi) f_{M}(\phi) d \phi .
$$
The left-hand side is called the posterior density of $M$ and of the two terms in the numerator the first is determined by the model and the other, $f_{M}(\mu)$, forms the prior distribution summarizing information about $M$ not arising from $y$. Any method of inference treating the unknown parameter as having a probability distribution is called Bayesian or, in an older terminology, an argument of inverse probability. The latter name arises from the inversion of the order of target and conditioning events as between the model and the posterior density.
The intuitive idea is that in such cases all relevant information about $\mu$ is then contained in the conditional distribution of the parameter given the data, that this is determined by the elementary formulae of probability theory and that remaining problems are solely computational.

In our example suppose that the prior for $\mu$ is normal with known mean $m$ and variance $v$. Then the posterior density for $\mu$ is proportional to
$$
\exp \left{-\Sigma\left(y_{k}-\mu\right)^{2} /\left(2 \sigma_{0}^{2}\right)-(\mu-m)^{2} /(2 v)\right}
$$
considered as a function of $\mu$. On completing the square as a function of $\mu$, there results a normal distribution of mean and variance respectively
$$
\begin{gathered}
\frac{\bar{y} /\left(\sigma_{0}^{2} / n\right)+m / v}{1 /\left(\sigma_{0}^{2} / n\right)+1 / v} \
\frac{1}{1 /\left(\sigma_{0}^{2} / n\right)+1 / v}
\end{gathered}
$$
for more details of the argument, see Note 1.5. Thus an upper limit for $\mu$ satisfied with posterior probability $1-c$ is
$$
\frac{\bar{y} /\left(\sigma_{0}^{2} / n\right)+m / v}{1 /\left(\sigma_{0}^{2} / n\right)+1 / v}+k_{c}^{*} \sqrt{\frac{1}{1 /\left(\sigma_{0}^{2} / n\right)+1 / v}}
$$

统计代写|统计推断作业代写statistics interference代考|Some further discussion

We now give some more detailed discussion especially of Example $1.4$ and outline a number of special models that illustrate important issues.

The linear model of Example $1.4$ and methods of analysis of it stemming from the method of least squares are of much direct importance and also are the base of many generalizations. The central results can be expressed in matrix form centring on the least squares estimating equations
$$
z^{T} z \hat{\beta}=z^{T} Y,
$$
the vector of fitted values
$$
\hat{Y}=z \hat{\beta},
$$
and the residual sum of squares
$$
\text { RSS }=(Y-\hat{Y})^{T}(Y-\hat{Y})=Y^{T} Y-\hat{\beta}^{T}\left(z^{T} z\right) \hat{\beta} .
$$
Insight into the form of these results is obtained by noting that were it not for random error the vector $Y$ would lie in the space spanned by the columns of $z$, that $\hat{Y}$ is the orthogonal projection of $Y$ onto that space, defined thus by
$$
z^{T}(Y-\hat{Y})=z^{T}(Y-z \hat{\beta})=0
$$
and that the residual sum of squares is the squared norm of the component of $Y$ orthogonal to the columns of $z$. See Figure 1.1.

There is a fairly direct generalization of these results to the nonlinear regression model of Example 1.5. Here if there were no error the observations would lie on the surface defined by the vector $\mu(\beta)$ as $\beta$ varies. Orthogonal projection involves finding the point $\mu(\hat{\beta})$ closest to $Y$ in the least squares sense, i.e., minimizing the sum of squares of deviations ${Y-\mu(\beta)}^{T}{Y-\mu(\beta)}$. The resulting equations defining $\hat{\beta}$ are best expressed by defining
$$
z^{T}(\beta)=\nabla \mu^{T}(\beta),
$$
where $\nabla$ is the $q \times 1$ gradient operator with respect to $\beta$, i.e., $\nabla^{T}=$ $\left(\partial / \partial \beta_{1}, \ldots, \partial / \partial \beta_{q}\right)$. Thus $z(\beta)$ is an $n \times q$ matrix, reducing to the previous $z$

in the linear case. Just as the columns of $z$ define the linear model, the columns of $z(\beta)$ define the tangent space to the model surface evaluated at $\beta$. The least squares estimating equation is thus
$$
z^{T}(\hat{\beta}){Y-\mu(\hat{\beta})}=0 .
$$
The local linearization implicit in this is valuable for numerical iteration. One of the simplest special cases arises when $E\left(Y_{k}\right)=\beta_{0} \exp \left(-\beta_{1} z_{k}\right)$ and the geometry underlying the nonlinear least squares equations is summarized in Figure 1.2.

The simple examples used here in illustration have one component random variable attached to each observation and all random variables are mutually independent. In many situations random variation comes from several sources and random components attached to different component observations may not be independent, showing for example temporal or spatial dependence.

统计代写|统计推断作业代写statistics interference代考|Parameters

A central role is played throughout the book by the notion of a parameter vector, $\theta$. Initially this serves to index the different probability distributions making up the full model. If interest were exclusively in these probability distributions as such, any $(1,1)$ transformation of $\theta$ would serve equally well and the choice of a particular version would be essentially one of convenience. For most of the applications in mind here, however, the interpretation is via specific parameters and this raises the need both to separate parameters of interest, $\psi$, from nuisance parameters, $\lambda$, and to choose specific representations. In relatively complicated problems where several different research questions are under study different parameterizations may be needed for different purposes.

There are a number of criteria that may be used to define the individual component parameters. These include the following:

the components should have clear subject-matter interpretations, for example as differences, rates of change or as properties such as in a physical context mass, energy and so on. If not dimensionless they should be measured on a scale unlikely to produce very large or very small values;
it is desirable that this interpretation is retained under reasonable perturbations of the model;
different components should not have highly correlated errors of estimation;
statistical theory for estimation should be simple;
if iterative methods of computation are needed then speedy and assured convergence is desirable.
The first criterion is of primary importance for parameters of interest, at least in the presentation of conclusions, but for nuisance parameters the other criteria are of main interest. There are considerable advantages in formulations leading to simple methods of analysis and judicious simplicity is a powerful aid
14
Preliminaries
to understanding, but for parameters of interest subject-matter meaning must have priority.

属性数据分析

统计代写|统计推断作业代写statistics interference代考|Bayesian discussion

在我们处理的问题的第二种方法中μ作为有和没有数据的概率分布。这提出了两个问题：在这种情况下概率的含义是什么，通常涉及一些扩展或修改的概率概念，以及我们如何获得相关概率的数值？这将在后面进一步讨论，尤其是在第5.目前，我们假设一些与测量不确定性有关的概率概念是可用的。

如果我们真的可以治疗μ作为随机变量的已实现但未观察到的值米，原则上一切都很简单。通过贝叶斯定理，即通过简单的概率定律，
F米∣是(μ∣是)=F是∣米(是∣μ)F米(μ)/∫F是∣米(是∣φ)F米(φ)dφ.
左侧称为后验密度米在分子中的两项中，第一项由模型确定，另一项由模型确定，F米(μ), 形成先验分布总结关于米不是产生于是. 任何将未知参数视为具有概率分布的推理方法都称为贝叶斯，或者在较早的术语中，称为逆概率参数。后一个名称源于模型和后验密度之间的目标和条件事件顺序的倒置。
直观的想法是，在这种情况下，所有关于μ然后包含在给定数据的参数的条件分布中，这是由概率论的基本公式确定的，剩下的问题完全是计算的。

在我们的例子中，假设先验μ是正常的，均值已知米和方差v. 然后后验密度为μ正比于
\exp \left{-\Sigma\left(y_{k}-\mu\right)^{2} /\left(2 \sigma_{0}^{2}\right)-(\mu-m)^ {2} /(2 v)\right}\exp \left{-\Sigma\left(y_{k}-\mu\right)^{2} /\left(2 \sigma_{0}^{2}\right)-(\mu-m)^ {2} /(2 v)\right}
被认为是一个函数μ. 在完成平方作为函数μ, 分别得到均值和方差的正态分布
是¯/(σ02/n)+米/v1/(σ02/n)+1/v 11/(σ02/n)+1/v
有关参数的更多详细信息，请参见注释 1.5。因此上限为μ满足后验概率1−C是
是¯/(σ02/n)+米/v1/(σ02/n)+1/v+到C∗11/(σ02/n)+1/v

统计代写|统计推断作业代写statistics interference代考|Some further discussion

我们现在给出一些更详细的讨论，尤其是示例1.4并概述一些说明重要问题的特殊模型。

Example 的线性模型1.4以及源自最小二乘法的分析方法具有直接的重要性，也是许多概括的基础。中心结果可以表示为以最小二乘估计方程为中心的矩阵形式
和吨和b^=和吨是,
拟合值的向量
是^=和b^,
和残差平方和
RSS =(是−是^)吨(是−是^)=是吨是−b^吨(和吨和)b^.
通过注意到如果不是随机误差向量是将位于由列所跨越的空间中和，那是^是的正交投影是到那个空间上，因此定义为
和吨(是−是^)=和吨(是−和b^)=0
并且残差平方和是分量的平方范数是正交于的列和. 请参见图 1.1。

这些结果可以相当直接地推广到示例 1.5 的非线性回归模型。在这里，如果没有错误，观察结果将位于向量定义的表面上μ(b)作为b变化。正交投影涉及找到点μ(b^)最靠近是在最小二乘意义上，即最小化偏差的平方和是−μ(b)吨是−μ(b). 结果方程定义b^最好通过定义来表达
和吨(b)=∇μ吨(b),
在哪里∇是个q×1关于梯度算子b， IE，∇吨= (∂/∂b1,…,∂/∂bq). 因此和(b)是一个n×q矩阵，归约到前一个和

在线性情况下。就像列和定义线性模型，列和(b)定义模型曲面的切线空间b. 因此，最小二乘估计方程是
和吨(b^)是−μ(b^)=0.
其中隐含的局部线性化对于数值迭代很有价值。最简单的特殊情况之一出现在和(是到)=b0经验⁡(−b1和到)图 1.2 总结了非线性最小二乘方程的几何结构。

此处用于说明的简单示例将一个分量随机变量附加到每个观察值，并且所有随机变量都是相互独立的。在许多情况下，随机变化来自多个来源，附加到不同分量观察的随机分量可能不是独立的，例如显示时间或空间依赖性。

统计代写|统计推断作业代写statistics interference代考|Parameters

参数向量的概念在整本书中起着核心作用，θ. 最初，这用于索引构成完整模型的不同概率分布。如果只对这些概率分布感兴趣，那么任何(1,1)的转变θ将同样有效，并且选择特定版本本质上是一种方便。然而，对于这里考虑的大多数应用程序，解释是通过特定参数进行的，这提出了对分离感兴趣参数的需求，ψ，从讨厌的参数，λ，并选择特定的表示。在研究几个不同研究问题的相对复杂的问题中，可能需要针对不同目的进行不同的参数化。

有许多标准可用于定义各个组件参数。其中包括：

组件应具有明确的主题解释，例如差异、变化率或物理环境中的质量、能量等属性。如果不是无量纲的，它们应该在一个不可能产生非常大或非常小的值的尺度上进行测量；
在模型的合理扰动下保留这种解释是可取的；
不同组成部分不应有高度相关的估计误差；
估计的统计理论应该简单；
如果需要迭代计算方法，则需要快速且可靠的收敛。
第一个标准对于感兴趣的参数至关重要，至少在结论的呈现中，但对于有害参数，其他标准是主要关注的。有相当大的优势，导致简单的分析方法和明智的简单性是一个强大的帮助
14
初步
理解，但对于感兴趣的参数，主题意义必须优先。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|统计推断作业代写statistics interference代考| Formulation of objectives

Posted on 2022年4月14日2022年4月14日 by statistics-lab

如果你也在怎样代写统计推断statistics interference这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计推断是利用数据分析来推断概率基础分布的属性的过程。推断性统计分析推断人口的属性，例如通过测试假设和得出估计值。

我们提供的属性统计推断statistics interference及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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

Frontiers | Errors in Statistical Inference Under Model Misspecification: Evidence, Hypothesis Testing, and AIC | Ecology and Evolution — 统计代写|统计推断作业代写statistics interference代考| Formulation of objectives

统计代写|统计推断作业代写statistics interference代考|Formulation of objectives

We can, as already noted, formulate possible objectives in two parts as follows.
Part I takes the family of models as given and aims to:

give intervals or in general sets of values within which $\psi$ is in some sense likely to lie;
assess the consistency of the data with a particular parameter value $\psi_{0}$;
predict as yet unobserved random variables from the same random system that generated the data;
use the data to choose one of a given set of decisions $\mathcal{D}$, requiring the specification of the consequences of various decisions.
Part II uses the data to examine the family of models via a process of model criticism. We return to this issue in Section 3.2.

We shall concentrate in this book largely but not entirely on the first two of the objectives in Part I, interval estimation and measuring consistency with specified values of $\psi$.

To an appreciable extent the theory of inference is concerned with generalizing to a wide class of models two approaches to these issues which will be outlined in the next section and with a critical assessment of these approaches.

统计代写|统计推断作业代写statistics interference代考|General remarks

Consider the first objective above, that of providing intervals or sets of values likely in some sense to contain the parameter of interest, $\psi$.

There are two broad approaches, called frequentist and Bayesian, respectively, both with variants. Alternatively the former approach may be said to be based on sampling theory and an older term for the latter is that it uses imverse probability. Much of the rest of the book is concerned with the similarities and differences between these two approaches. As a prelude to the general development we show a very simple example of the arguments involved.

We take for illustration Example 1.1, which concerns a normal distribution with unknown mean $\mu$ and known variance. In the formulation probability is used to model variability as experienced in the phenomenon under study and its meaning is as a long-run frequency in repetitions, possibly, or indeed often, hypothetical, of that phenomenon.

What can reasonably be said about $\mu$ on the basis of observations $y_{1}, \ldots, y_{n}$ and the assumptions about the model?

统计代写|统计推断作业代写statistics interference代考|Frequentist discussion

In the first approach we make no further probabilistic assumptions. In particular we treat $\mu$ as an unknown constant. Strong arguments can be produced for reducing the data to their mean $\bar{y}=\Sigma y_{k} / n$, which is the observed value of the corresponding random variable $\bar{Y}$. This random variable has under the assumptions of the model a normal distribution of mean $\mu$ and variance $\sigma_{0}^{2} / n$, so that in particular
$$
P\left(\bar{Y}>\mu-k_{c}^{} \sigma_{0} / \sqrt{n}\right)=1-c $$ where, with $\Phi\left(\right.$.) denoting the standard normal integral, $\Phi\left(k_{c}^{}\right)=1-c$. For example with $c=0.025, k_{c}^{}=1.96$. For a sketch of the proof, see Note $1.5$. Thus the statement equivalent to (1.9) that $$ P\left(\mu<\bar{Y}+k_{c}^{} \sigma_{0} / \sqrt{n}\right)=1-c,
$$
can be interpreted as specifying a hypothetical long run of statements about $\mu$ a proportion $1-c$ of which are correct. We have observed the value $\bar{y}$ of the random variable $\bar{Y}$ and the statement
$$
\mu<\bar{y}+k_{c}^{*} \sigma_{0} / \sqrt{n}
$$
is thus one of this long run of statements, a specified proportion of which are correct. In the most direct formulation of this $\mu$ is fixed and the statements vary and this distinguishes the statement from a probability distribution for $\mu$. In fact a similar interpretation holds if the repetitions concern an arbitrary sequence of fixed values of the mean.

There are a large number of generalizations of this result, many underpinning standard elementary statistical techniques. For instance, if the variance $\sigma^{2}$ is unknown and estimated by $\Sigma\left(y_{k}-\bar{y}\right)^{2} /(n-1)$ in $(1.9)$, then $k_{c}^{*}$ is replaced by the corresponding point in the Student $t$ distribution with $n-1$ degrees of freedom.

There is no need to restrict the analysis to a single level $c$ and provided concordant procedures are used at the different $c$ a formal distribution is built up.
Arguments involving probability only via its (hypothetical) long-run frequency interpretation are called frequentist. That is, we define procedures for assessing evidence that are calibrated by how they would perform were they used repeatedly. In that sense they do not differ from other measuring instruments. We intend, of course, that this long-run behaviour is some assurance that with our particular data currently under analysis sound conclusions are drawn. This raises important issues of ensuring, as far as is feasible, the relevance of the long run to the specific instance.

The Importance of Statistics - Statistics By Jim — 统计代写|统计推断作业代写statistics interference代考| Formulation of objectives

属性数据分析

统计代写|统计推断作业代写statistics interference代考|Formulation of objectives

如前所述，我们可以将可能的目标分为以下两部分。
第一部分将模型系列作为给定的，旨在：

给出区间或一般的一组值，其中ψ在某种意义上可能会撒谎；
评估数据与特定参数值的一致性ψ0;
从生成数据的同一随机系统中预测尚未观察到的随机变量；
使用数据来选择一组给定的决策D，要求说明各种决定的后果。
第二部分通过模型批评过程使用数据来检查模型族。我们在第 3.2 节中回到这个问题。

我们将在本书中主要但不完全集中于第一部分中的前两个目标，区间估计和测量与指定值的一致性ψ.

在一定程度上，推理理论涉及将解决这些问题的两种方法推广到广泛的模型中，这将在下一节中概述，并对这些方法进行批判性评估。

统计代写|统计推断作业代写statistics interference代考|General remarks

考虑上面的第一个目标，即提供在某种意义上可能包含感兴趣参数的区间或值集，ψ.

有两种广泛的方法，分别称为常客和贝叶斯，两者都有变体。或者，前一种方法可以说是基于抽样理论，而后者的旧术语是它使用逆概率。本书其余部分的大部分内容都涉及这两种方法之间的异同。作为一般发展的前奏，我们展示了一个非常简单的例子来说明所涉及的论点。

我们以示例 1.1 为例，该示例涉及均值未知的正态分布μ和已知的方差。在公式中，概率用于模拟所研究现象中所经历的可变性，其含义是重复的长期频率，可能或实际上经常是该现象的假设。

什么可以合理地说μ根据观察是1,…,是n以及关于模型的假设？

统计代写|统计推断作业代写statistics interference代考|Frequentist discussion

在第一种方法中，我们不做进一步的概率假设。特别是我们对待μ作为一个未知常数。可以产生强有力的论据来将数据减少到它们的平均值是¯=Σ是到/n，即对应随机变量的观测值是¯. 该随机变量在模型的假设下具有均值的正态分布μ和方差σ02/n，所以特别是
磷(是¯>μ−到Cσ0/n)=1−C在哪里，与披(.) 表示标准正态积分，披(到C)=1−C. 例如与C=0.025,到C=1.96. 有关证明的草图，请参阅注1.5. 因此等价于 (1.9) 的陈述磷(μ<是¯+到Cσ0/n)=1−C,
可以解释为指定一个假设的长期陈述μ一个比例1−C其中是正确的。我们观察到了价值是¯随机变量是¯和声明
μ<是¯+到C∗σ0/n
因此，它是这一长期陈述之一，其中特定比例是正确的。在这个最直接的表述中μ是固定的并且陈述是变化的，这将陈述与概率分布区分开来μ. 事实上，如果重复涉及平均值的固定值的任意序列，则类似的解释成立。

这个结果有大量的概括，许多支持标准的基本统计技术。例如，如果方差σ2是未知的，估计由Σ(是到−是¯)2/(n−1)在(1.9)，然后到C∗被Student中的对应点替换吨分布与n−1自由程度。

无需将分析限制在单一级别C并提供一致的程序用于不同的C建立了正式的分配。
仅通过其（假设的）长期频率解释涉及概率的论点称为频率论者。也就是说，我们定义了评估证据的程序，这些程序是根据它们在重复使用时的表现来校准的。从这个意义上说，它们与其他测量仪器没有区别。当然，我们打算通过这种长期行为来确保我们目前正在分析的特定数据能够得出合理的结论。这提出了在可行的情况下确保长期与具体实例的相关性的重要问题。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|统计推断作业代写statistics interference代考|Preliminaries

Posted on 2022年4月14日2022年4月14日 by statistics-lab

如果你也在怎样代写统计推断statistics interference这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

统计推断是利用数据分析来推断概率基础分布的属性的过程。推断性统计分析推断人口的属性，例如通过测试假设和得出估计值。

我们提供的属性统计推断statistics interference及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|统计推断作业代写statistics interference代考|Preliminaries

统计代写|统计推断作业代写statistics interference代考|Starting point

We typically start with a subject-matter question. Data are or become available to address this question. After preliminary screening, checks of data quality and simple tabulations and graphs, more formal analysis starts with a provisional model. The data are typically split in two parts $(y: z)$, where $y$ is regarded as the observed value of a vector random variable $Y$ and $z$ is treated as fixed. Sometimes the components of $y$ are direct measurements of relevant properties on study individuals and sometimes they are themselves the outcome of some preliminary analysis, such as means, measures of variability, regression coefficients and so on. The set of variables $z$ typically specifies aspects of the system under study that are best treated as purely explanatory and whose observed values are not usefully represented by random variables. That is, we are interested solely in the distribution of outcome or response variables conditionally on the variables $z$; a particular example is where $z$ represents treatments in a randomized experiment.
We use throughout the notation that observable random variables are represented by capital letters and observations by the corresponding lower case letters.
A model, or strictly a family of models, specifies the density of $Y$ to be
$$
f_{Y}(y: z ; \theta)
$$

where $\theta \subset \Omega_{\theta}$ is unknown. The distribution may depend also on design features of the study that generated the data. We typically simplify the notation to $f_{Y}(y ; \theta)$, although the explanatory variables $z$ are frequently essential in specific applications.
To choose the model appropriately is crucial to fruitful application.
We follow the very convenient, although deplorable, practice of using the term density both for continuous random variables and for the probability function of discrete random variables. The deplorability comes from the functions being dimensionally different, probabilities per unit of measurement in continuous problems and pure numbers in discrete problems. In line with this convention in what follows integrals are to be interpreted as sums where necessary. Thus we write
$$
E(Y)=E(Y ; \theta)=\int y f_{Y}(y ; \theta) d y
$$
for the expectation of $Y$, showing the dependence on $\theta$ only when relevant. The integral is interpreted as a sum over the points of support in a purely discrete case. Next, for each aspect of the research question we partition $\theta$ as $(\psi, \lambda)$, where $\psi$ is called the parameter of interest and $\lambda$ is included to complete the specification and commonly called a nuisance parameter. Usually, but not necessarily, $\psi$ and $\lambda$ are variation independent in that $\Omega_{\theta}$ is the Cartesian product $\Omega_{\psi} \times \Omega_{\lambda}$. That is, any value of $\psi$ may occur in connection with any value of $\lambda$. The choice of $\psi$ is a subject-matter question. In many applications it is best to arrange that $\psi$ is a scalar parameter, i.e., to break the research question of interest into simple components corresponding to strongly focused and incisive research questions, but this is not necessary for the theoretical discussion.

统计代写|统计推断作业代写statistics interference代考|Role of formal theory of inference

The formal theory of inference initially takes the family of models as given and the objective as being to answer questions about the model in the light of the data. Choice of the family of models is, as already remarked, obviously crucial but outside the scope of the present discussion. More than one choice may be needed to answer different questions.

A second and complementary phase of the theory concerns what is sometimes called model criticism, addressing whether the data suggest minor or major modification of the model or in extreme cases whether the whole focus of the analysis should be changed. While model criticism is often done rather informally in practice, it is important for any formal theory of inference that it embraces the issues involved in such checking.

统计代写|统计推断作业代写statistics interference代考|Some simple models

General notation is often not best suited to special cases and so we use more conventional notation where appropriate.

Example 1.1. The normal mean. Whenever it is required to illustrate some point in simplest form it is almost inevitable to return to the most hackneyed of examples, which is therefore given first. Suppose that $Y_{1}, \ldots, Y_{n}$ are independently normally distributed with unknown mean $\mu$ and known variance $\sigma_{0}^{2}$. Here $\mu$ plays the role of the unknown parameter $\theta$ in the general formulation. In one of many possible generalizations, the variance $\sigma^{2}$ also is unknown. The parameter vector is then $\left(\mu, \sigma^{2}\right)$. The component of interest $\psi$ would often be $\mu$

but could be, for example, $\sigma^{2}$ or $\mu / \sigma$, depending on the focus of subject-matter interest.

Example 1.2. Linear regression. Here the data are $n$ pairs $\left(y_{1}, z_{1}\right), \ldots,\left(y_{n}, z_{n}\right)$ and the model is that $Y_{1}, \ldots, Y_{n}$ are independently normally distributed with variance $\sigma^{2}$ and with
$$
E\left(Y_{k}\right)=\alpha+\beta z_{k} .
$$
Here typically, but not necessarily, the parameter of interest is $\psi=\beta$ and the nuisance parameter is $\lambda=\left(\alpha, \sigma^{2}\right)$. Other possible parameters of interest include the intercept at $z=0$, namely $\alpha$, and $-\alpha / \beta$, the intercept of the regression line on the $z$-axis.

Example 1.3. Linear regression in semiparametric form. In Example $1.2$ replace the assumption of normality by an assumption that the $Y_{k}$ are uncorrelated with constant variance. This is semiparametric in that the systematic part of the variation, the linear dependence on $z_{k}$, is specified parametrically and the random part is specified only via its covariance matrix, leaving the functional form of its distribution open. A complementary form would leave the systematic part of the variation a largely arbitrary function and specify the distribution of error parametrically, possibly of the same normal form as in Example 1.2. This would lead to a discussion of smoothing techniques.

Example 1.4. Linear model. We have an $n \times 1$ vector $Y$ and an $n \times q$ matrix $z$ of fixed constants such that
$$
E(Y)=z \beta, \quad \operatorname{cov}(Y)=\sigma^{2} I,
$$
where $\beta$ is a $q \times 1$ vector of unknown parameters, $I$ is the $n \times n$ identity matrix and with, in the analogue of Example 1.2, the components independently normally distributed. Here $z$ is, in initial discussion at least, assumed of full rank $q<n$. A relatively simple but important generalization has $\operatorname{cov}(Y)=$ $\sigma^{2} V$, where $V$ is a given positive definite matrix. There is a corresponding semiparametric version generalizing Example 1.3.

Both Examples $1.1$ and $1.2$ are special cases, in the former the matrix $z$ consisting of a column of $1 \mathrm{~s}$.

Example 1.5. Normal-theory nonlinear regression. Of the many generalizations of Examples $1.2$ and 1.4, one important possibility is that the dependence on the parameters specifying the systematic part of the structure is nonlinear. For example, instead of the linear regression of Example $1.2$ we might wish to consider
$$
E\left(Y_{k}\right)=\alpha+\beta \exp \left(\gamma z_{k}\right)
$$

属性数据分析

统计代写|统计推断作业代写statistics interference代考|Starting point

我们通常从一个主题问题开始。已有数据或可用于解决这个问题。经过初步筛选、数据质量检查和简单的表格和图表，更正式的分析从临时模型开始。数据通常分为两部分(是:和)，在哪里是被视为向量随机变量的观测值是和和被视为固定。有时组件是是对研究个体相关属性的直接测量，有时它们本身就是一些初步分析的结果，例如平均值、变异性测量、回归系数等。变量集和通常指定所研究系统中最好被视为纯粹解释性的方面，并且其观察值不能用随机变量有用地表示。也就是说，我们只对以变量为条件的结果或响应变量的分布感兴趣和; 一个特定的例子是和代表随机实验中的处理。
我们在整个符号中使用可观察随机变量用大写字母表示，观察值用相应的小写字母表示。
一个模型，或者严格来说是一系列模型，指定了是成为
F是(是:和;θ)

在哪里θ⊂Ωθ是未知的。分布也可能取决于生成数据的研究的设计特征。我们通常将符号简化为F是(是;θ), 虽然解释变量和在特定应用中经常是必不可少的。
选择合适的模型对于有效的应用至关重要。
我们遵循非常方便但令人遗憾的做法，即对连续随机变量和离散随机变量的概率函数使用术语密度。可悲性来自于函数在维度上的不同，连续问题中每单位测量的概率以及离散问题中的纯数字。根据这个惯例，在必要的情况下，积分将被解释为总和。因此我们写
和(是)=和(是;θ)=∫是F是(是;θ)d是
为了期待是, 显示依赖θ仅在相关时。在纯离散情况下，积分被解释为支持点的总和。接下来，对于研究问题的每个方面，我们划分θ作为(ψ,λ)，在哪里ψ被称为感兴趣的参数，并且λ包括在内以完成规范，通常称为滋扰参数。通常，但不一定，ψ和λ是变化独立的Ωθ是笛卡尔积Ωψ×Ωλ. 也就是说，任何值ψ可能与任何价值有关λ. 的选择ψ是一个主题问题。在许多应用中，最好安排ψ是一个标量参数，即将感兴趣的研究问题分解为与重点突出和深刻的研究问题相对应的简单组件，但这对于理论讨论不是必需的。

统计代写|统计推断作业代写statistics interference代考|Role of formal theory of inference

正式的推理理论最初将模型族视为给定的，目标是根据数据回答有关模型的问题。如前所述，模型族的选择显然是至关重要的，但超出了当前讨论的范围。可能需要不止一种选择来回答不同的问题。

该理论的第二个补充阶段涉及有时被称为模型批评的内容，即解决数据是否表明模型的微小或重大修改，或者在极端情况下是否应该改变整个分析重点。虽然模型批评在实践中通常是相当非正式的，但对于任何正式的推理理论来说，重要的是它包含了这种检查所涉及的问题。

统计代写|统计推断作业代写statistics interference代考|Some simple models

一般表示法通常不适合特殊情况，因此我们在适当的情况下使用更传统的表示法。

例 1.1。正常的意思。每当需要用最简单的形式来说明某个观点时，几乎不可避免地会回到最陈腐的例子，因此首先给出了这个例子。假设是1,…,是n均值未知的独立正态分布μ和已知方差σ02. 这里μ扮演未知参数的角色θ在一般公式中。在许多可能的概括之一中，方差σ2也是未知数。那么参数向量就是(μ,σ2). 感兴趣的组件ψ经常是μ

但可能是，例如，σ2或者μ/σ，取决于主题兴趣的焦点。

例 1.2。线性回归。这里的数据是n对(是1,和1),…,(是n,和n)模型是这样的是1,…,是n具有方差独立正态分布σ2与
和(是到)=一种+b和到.
这里通常但不一定，感兴趣的参数是ψ=b和讨厌的参数是λ=(一种,σ2). 其他可能感兴趣的参数包括截距和=0，即一种，和−一种/b，回归线的截距和-轴。

例 1.3。半参数形式的线性回归。在示例中1.2将正态性假设替换为以下假设：是到与恒定方差不相关。这是半参数的，因为变化的系统部分，线性依赖于和到, 以参数方式指定，随机部分仅通过其协方差矩阵指定，使其分布的函数形式保持开放。补充形式将使变分的系统部分在很大程度上成为任意函数，并以参数方式指定误差分布，可能与示例 1.2 中的范式相同。这将导致对平滑技术的讨论。

例 1.4。线性模型。我们有一个n×1向量是和n×q矩阵和的固定常数使得
和(是)=和b,这⁡(是)=σ2一世,
在哪里b是一个q×1未知参数的向量，一世是个n×n单位矩阵，并且与示例 1.2 类似，分量独立正态分布。这里和至少在最初的讨论中，假定为全等级q<n. 一个相对简单但重要的概括有这⁡(是)= σ2五，在哪里五是给定的正定矩阵。有一个相应的半参数版本概括了示例 1.3。

两个例子1.1和1.2是特殊情况，在前者中，矩阵和由一列组成1 s.

例 1.5。正态理论非线性回归。例子的许多概括1.2和 1.4，一种重要的可能性是对指定结构系统部分的参数的依赖性是非线性的。例如，代替 Example 的线性回归1.2我们不妨考虑
和(是到)=一种+b经验⁡(C和到)

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|属性数据分析作业代写analysis of categorical data代考|Modeling and the Generalized Linear Model

Posted on 2022年4月13日2022年4月13日 by statistics-lab

如果你也在怎样代写属性数据分析analysis of categorical data这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

属性数据分析analysis of categorical data一属性变量和属性数据，通常所指属性数据，反映事物属性的数据，也称为定性数据或类别数据，它是属性变量取的值。分类数据是指将一个观察结果归入一个或多个类别的数据。例如，一个项目可能被评判为好或坏，或者对调查的反应可能包括同意、不同意或无意见等类别。Statgraphics包括许多处理这类数据的程序，包括包含在方差分析、回归分析和统计过程控制部分的建模程序。

statistics-lab™ 为您的留学生涯保驾护航在代写属性数据分析analysis of categorical data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。我们的专家在代写属性数据分析analysis of categorical data方面经验极为丰富，各种代写属性数据分析analysis of categorical data相关的作业也就用不着说。

我们提供的属性数据分析analysis of categorical data及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|属性数据分析作业代写analysis of categorical data代考|Modeling and the Generalized Linear Model

统计代写|属性数据分析作业代写analysis of categorical data代考|The Random Component

The random component of a GLM is the probability distribution assumed to underlie the dependent or outcome variable, predicted by the model. Recall from Chapter 2 that when we have continuous outcome variables, we typically assume that the values obtained for these variables are random observations that come from (or follow) a normal distribution. In other words, when the outcome or response variable is continuous, such as in simple linear regression or analysis of variance (ANOVA), we typically assume that the normal distribution is the random component or underlying probability distribution for the outcome variable.

When the outcome variable is categorical, we can no longer assume that its values in the population are normally distributed. In fact, in a GLM the random component can be any known probability distribution. As discussed in Chapter 2 , with categorical variables the Poisson or binomial is often the appropriate underlying distribution, and that distribution would indicate the random component when the outcome or response variable is categorical. For example, if the outcome variable is whether a student passed (rather than failed) a test, we would assume that the underlying probability distribution of the outcome is the binomial distribution rather than the normal distribution. As another example, if the outcome variable is the number of boats that dock at a particular marina in an hour, we would assume that the underlying probability distribution is the Poisson distribution rather than the normal distribution.

The random component of a GLM thus allows us to use outcome variables (Ys) that are not necessarily normally distributed. In addition, as was shown in Chapter 2 , the random component or distribution underlying the outcome variable $(Y)$ is instrumental in computing its expected value (or mean),
$$
E(Y)=\propto
$$
This expected value is also the outcome predicted by a model, using predictor variables.

统计代写|属性数据分析作业代写analysis of categorical data代考|The Systematic Component

The systematic component of a GLM consists of the independent, predictor, or explanatory variables (Xs) that a researcher hypothesizes will predict (or explain) differences in the dependent or outcome variable. The predictors are considered to be the systematic component of the model because they systematically explain differences in the outcome variable and are generally treated as fixed, rather than random, variables. These variables may be subject to experimental control, or systematic manipulation, although this is not a necessary condition for the systematic component.

The predictor variables are combined to form the linear predictor, which is simply a linear combination of the predictors or the “right-hand side” of the model equation.

where the coefficients of the model ( $\alpha$ and $\beta$ s) are estimated based on the observed data. The systematic component of a GLM thus specifies the way in which the explanatory variables or predictors are expected to linearly influence the predicted or expected value of the outcome, $E(Y)$.

It should be noted that each of the predictors may be a combination of other predictors. For example, an interaction term can be represented by a predictor that is the product of two variables, such as $X_{4}=X_{1} X_{3}$, or a nonlinear trend can be represented by a predictor that is a function of a variable, such as using $X_{2}=X_{1}^{2}$ to represent a quadratic trend by squaring a variable. The key is that the predictors are represented as a linear combination in the GLM to ensure that it is indeed a linear model.

统计代写|属性数据分析作业代写analysis of categorical data代考|The Link Function

The key to GLMs is to “link” the random and systematic components of the model with some mathematical function, which we will call $g(\cdot)$. This function is applied to the expected value of the outcome variable, $E(Y)$, so that it can be properly modeled or predicted using the systematic component; that is:
$$
\mathrm{g}(E(Y))=\alpha+\beta_{1} X_{1}+\beta_{2} X_{2}+\ldots+\beta_{p} X_{p}
$$
The link function allows us to relate the systematic component (consisting of a linear predictor) to the random component (which is based on the probability distribution of the outcome variable) in a linear manner. In other words, the link function is a mathematical function we use to transform the predicted or expected value of the outcome to produce a transformed variable, $\mathrm{g}(E(Y))$, that is linearly related to the predictors.

For example, suppose that we would like to use family income (in thousands of dollars) as a predictor, $X$, of a standardized test score (such as an ACT score). Figure $6.2$ provides an illustration of a possible relationship between these variables. In this case, if the relationship depicted in Figure $6.2$ provides a good representation of the actual relationship between these variables, the predicted outcome (ACT score), which is the expected value of $Y$ and is denoted as $E(Y)$, can be written as
$$
E(Y)=\alpha+\beta(X) . \mathrm{w}
$$
Figure $6.2$ shows that as $X$ increases by one unit, the predicted outcome, $E(Y)$, increases at a constant rate (represented by $\beta$ in Equation 6.1). In this case, the predicted or expected outcome, $E(Y)$, does not need to be transformed to be linearly related to the predictor. More technically, if $g(\cdot)$ represents the link function, the transformation of $E(Y)$ by $g$ in this case is$g(E(Y))=E(Y)$. This is referred to as the identity link function because applying the $g(\cdot)$ function to $E(Y)$ results in the same value, $E(Y)$. This would be a reasonable approach, in that it will represent the relationship appropriately, when the outcome variable is continuous. Thus, this is the link function that is used when the outcome or response variable is continuous and typically normally distributed, such as in regression and ANOVA models. In this case a link function is not truly necessary, though in the context of a GLM the link function would be the identity function.

When it cannot be assumed that the response variable follows a normal distribution, the predicted or expected outcome $E(Y)$ will not typically be linearly related to the predictors unless it is transformed. For example, suppose that the outcome variable was the probability that a student will pass (as opposed to fail) a specific test, so the predicted value is $E(Y)=\pi=$ predicted probability of passing. Using the same predictor as earlier $(X=$ family income), the graph shown in Figure 6.3a illustrates a possible relationship between these two variables. Note that in this case the outcome variable, a probability, cannot be lower than 0 or greater than 1 (by definition) no matter how high or low the value of the predictor gets. In addition, family income tends to be more strongly associated with the probability of passing the test for students in the middle of the family income range than at more extreme (very high or very low) income levels. In this case, using the identity link as in Equation $6.1$ to link the random and systematic components of the GLM would amount to using the model $E(Y)=\pi=\alpha+\beta(X)$ or fitting a straight line to the points in Figure 6.3a. This would result in a poor representation of the association between the variables, especially for certain income ranges. It would also then be theoretically possible for the prediction obtained from the model to exceed 1 or fall below 0 (for high or low enough values of $X$, respectively), which is nonsensical because probabilities must fall between 0 and 1 . If, however, the predicted probability $(E(Y)$ or $\pi)$ is transformed using the equation
$\mathrm{g}(E(Y))=\mathrm{g}(\pi)=\ln \left(\frac{\pi}{1-\pi}\right)=\operatorname{logit}$ of $\pi$,
then the resulting relationship between the transformed value, $\ln (\pi /(1-\pi))$, and income level $(\mathrm{X})$ will be linear, as illustrated in Figure 6.3b. Therefore, the transformed outcome variable can be related (or linked) to the predictor in a linear fashion by the following model:
$$
\mathrm{g}(E(Y))=\ln \left(\frac{\pi}{1-\pi}\right)=\alpha+\beta(X)
$$
This particular link function (or transformation) is called the logit link function, and the resulting GLM is called the logistic regression model (discussed in detail in Chapters 8,9 , and 10 ). The logit function typically works well with a binary outcome variable or a random component that is assumed to follow a binomial distribution.

属性数据分析

统计代写|属性数据分析作业代写analysis of categorical data代考|The Random Component

GLM 的随机分量是假设为模型预测的因变量或结果变量的概率分布。回想一下第 2 章，当我们有连续的结果变量时，我们通常假设为这些变量获得的值是来自（或遵循）正态分布的随机观察值。换句话说，当结果或响应变量是连续的时，例如在简单线性回归或方差分析 (ANOVA) 中，我们通常假设正态分布是结果变量的随机分量或潜在概率分布。

当结果变量是分类变量时，我们不能再假设它在总体中的值是正态分布的。事实上，在 GLM 中，随机分量可以是任何已知的概率分布。正如第 2 章所讨论的，对于分类变量，泊松或二项式通常是适当的基础分布，并且当结果或响应变量是分类变量时，该分布将指示随机分量。例如，如果结果变量是学生是否通过（而不是失败）测试，我们将假设结果的潜在概率分布是二项分布而不是正态分布。再举一个例子，如果结果变量是一小时内停靠在特定码头的船只数量，

因此，GLM 的随机分量允许我们使用不一定是正态分布的结果变量 (Ys)。此外，如第 2 章所示，结果变量的随机分量或分布(是)有助于计算其预期值（或平均值），
和(是)=∝
该预期值也是模型使用预测变量预测的结果。

统计代写|属性数据分析作业代写analysis of categorical data代考|The Systematic Component

GLM 的系统组件由独立变量、预测变量或解释变量 (X) 组成，研究人员假设这些变量将预测（或解释）因变量或结果变量的差异。预测变量被认为是模型的系统组成部分，因为它们系统地解释了结果变量的差异，并且通常被视为固定变量，而不是随机变量。这些变量可能受到实验控制或系统操作，尽管这不是系统组件的必要条件。

预测变量组合起来形成线性预测变量，它只是预测变量的线性组合或模型方程的“右手边”。

其中模型的系数 (一种和bs) 根据观察到的数据进行估计。因此，GLM 的系统组件指定了解释变量或预测变量预期线性影响结果的预测值或预期值的方式，和(是).

应当注意，每个预测器可以是其他预测器的组合。例如，一个交互项可以由一个预测变量表示，该预测变量是两个变量的乘积，例如X4=X1X3, 或者非线性趋势可以用作为变量函数的预测变量来表示，例如使用X2=X12通过对变量进行平方来表示二次趋势。关键是预测变量在 GLM 中表示为线性组合，以确保它确实是一个线性模型。

统计代写|属性数据分析作业代写analysis of categorical data代考|The Link Function

GLM 的关键是将模型的随机和系统组件与一些数学函数“联系起来”，我们将其称为G(⋅). 该函数应用于结果变量的期望值，和(是)，以便可以使用系统组件对其进行适当的建模或预测；那是：
G(和(是))=一种+b1X1+b2X2+…+bpXp
链接函数允许我们以线性方式将系统分量（由线性预测变量组成）与随机分量（基于结果变量的概率分布）联系起来。换句话说，链接函数是我们用来转换结果的预测值或期望值以产生转换变量的数学函数，G(和(是))，即与预测变量线性相关。

例如，假设我们想使用家庭收入（以千美元计）作为预测变量，X，标准化考试成绩（如 ACT 成绩）。数字6.2说明了这些变量之间可能存在的关系。在这种情况下，如果如图所示的关系6.2提供了这些变量之间实际关系的良好表示，即预测结果（ACT 分数），即是并表示为和(是), 可以写成
和(是)=一种+b(X).在
数字6.2表明作为X增加一个单位，预测结果，和(是)，以恒定速率增加（表示为b在公式 6.1)。在这种情况下，预测或预期的结果，和(是), 不需要转换为与预测变量线性相关。从技术上讲，如果G(⋅)表示链接函数，变换和(是)经过G在这种情况下是G(和(是))=和(是). 这被称为身份链接功能，因为应用G(⋅)作用于和(是)产生相同的值，和(是). 这将是一种合理的方法，因为当结果变量是连续的时，它将适当地表示关系。因此，这是当结果或响应变量是连续的并且通常是正态分布时使用的链接函数，例如在回归和方差分析模型中。在这种情况下，链接函数并不是真正需要的，尽管在 GLM 的上下文中，链接函数将是恒等函数。

当不能假设响应变量服从正态分布时，预测或预期结果和(是)除非它被转换，否则它通常不会与预测变量线性相关。例如，假设结果变量是学生通过（而不是不及格）特定测试的概率，因此预测值为和(是)=圆周率=预测的通过概率。使用与之前相同的预测器(X=家庭收入），图 6.3a 中的图表说明了这两个变量之间可能存在的关系。请注意，在这种情况下，无论预测变量的值有多高或多低，结果变量（概率）都不能小于 0 或大于 1（根据定义）。此外，与极端（非常高或非常低）收入水平的学生相比，家庭收入中等的学生与通过考试的概率之间的联系更紧密。在这种情况下，使用等式中的身份链接6.1将 GLM 的随机和系统成分联系起来相当于使用该模型和(是)=圆周率=一种+b(X)或将直线拟合到图 6.3a 中的点。这将导致变量之间的关联表现不佳，特别是对于某些收入范围。从理论上讲，从模型获得的预测也有可能超过 1 或低于 0（对于足够高或足够低的X，分别），这是无意义的，因为概率必须落在 0 和 1 之间。但是，如果预测的概率(和(是)或者圆周率)使用等式转换
G(和(是))=G(圆周率)=ln⁡(圆周率1−圆周率)=罗吉特的圆周率，
然后是转换后的值之间的关系，ln⁡(圆周率/(1−圆周率)), 和收入水平(X)将是线性的，如图 6.3b 所示。因此，转换后的结果变量可以通过以下模型以线性方式与预测变量相关（或链接）：
G(和(是))=ln⁡(圆周率1−圆周率)=一种+b(X)
这个特定的链接函数（或转换）称为 logit 链接函数，生成的 GLM 称为逻辑回归模型（在第 8,9 和 10 章中详细讨论）。logit 函数通常适用于二元结果变量或假定遵循二项分布的随机分量。

统计代写|属性数据分析作业代写analysis of categorical data代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Independence

Posted on 2022年4月13日2022年4月13日 by statistics-lab

如果你也在怎样代写属性数据分析analysis of categorical data这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的属性数据分析analysis of categorical data及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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

A = independent marginal distribution P (x); B = independent marginal... | Download Scientific Diagram — 统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Independence

统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Independence

Marginal independence implies that the there is no association in the marginal table, whereas marginal dependence or marginal association implies that there is an association in the marginal table. The terms marginal dependence and marginal association can thus be used interchangeably. For a $2 \times 2$ marginal table representing the relationship between two variables, $X$ and $Y$ (across all levels of $Z$ ), marginal independence implies that (in the population) the marginal odds ratio, $\theta_{X Y}$ is equal to 1 ; similarly, marginal dependence implies that (in the population) $\theta_{X Y}$ is not equal to 1 . In our second example (Table 5.5), for instance, there was marginal dependence between smoking status and the ability to breathe normally (in the sample) because the estimated marginal odds ratio was, $\hat{\theta}_{X Y}=2.756$. This association (odds ratio) was statistically significant, indicating that the presence of a marginal association (i.e., a marginal odds ratio that is greater than 1) generalizes to the population.
In general, for any $I \times J$ marginal table, marginal independence implies that all of the odds ratios that can be formed using any two levels of the variables, $X$ and $Y$, will be equal to 1 .
92 Associations, Three Categorical Variables
On the other hand, marginal dependence implies that at least one of the odds ratios formed by using two levels of the variables $X$ and $Y$ is not equal to 1 . In all cases, these marginal associations (between $X$ and $Y$ ) ignore the third variable ( $Z$ ).

统计代写|属性数据分析作业代写analysis of categorical data代考|Conditional Independence

Conditional independence implies that there is no association between the variables $X$ and $Y$ in $a n y$ of the $K$ partial tables that are conditional on each level of the third variable, $Z$. For a $2 \times 2$ partial table, this implies that, in the population, the odds ratios in all of the $K$ partial tables are equal to 1 , or $\theta_{X Y \mid \mathbb{Z}{k}}=1$ for all $k=1,2, \ldots, K$. We use the conditional odds ratio notation $\theta{X Y \chi}$ to represent the association between $X$ and $Y$ conditional on the $k^{\text {th }}$ level of $Z$. Note that in conditional notation the variables to the left of the vertical line represent the association of interest, and the variables to the right of the vertical line represent the variables on which the association is conditioned. In general, for any $I \times J$ partial table, conditional independence implies that all odds ratios that can be formed by using any two levels of $X$ and $Y$ will be equal to 1 for all $K$ partial tables (i.e., conditional on the levels of $Z$ ).

Conditional dependence or conditional association implies that there is an association in at least one of the partial tables. In the case of $2 \times 2$ partial tables, conditional dependence implies that, in the population, the odds ratio in at least one of the partial tables, or $\theta_{X Y \mid z_{k}}$ for at least one $k=1,2, \ldots, K$, is not equal to 1 . In general, for any $I \times J$ partial table, conditional dependence implies that at least one of the odds ratios that can be formed by using any two levels of two variables, $X$ and $Y$, is not equal to 1 for at least one of the partial tables conditional on $Z$.

Conditional dependence was evident in both of our earlier examples because the partial association between two of the variables was present in (at least) one of the partial tables. In our first example (Table 5.1), there was partial association between political affiliation and age for females $\left(\chi^{2}=24.496, d f=6, p<0.001\right)$, though not for males $\left(\chi^{2}=8.193, d f=6\right.$, $p=0.224)$. This implies that at least one of the conditional odds ratios that can be computed from the political affiliation and age group partial table for females is not equal to 1 in the population. In fact, given the residual analysis described previously (Table 5.2), and examining the cells that most deviated from independence, it is likely that the odds ratio formed by considering the $2 \times 2$ table for liberal and conservative females in the age groups 18-29 and 50 or older will reflect a statistically significant association. This is because these cells have the largest residuals and thus deviate most from what would be expected under independence. The frequency counts for these four cells are shown in Table $5.6$; the estimated odds ratio for this table is $2.83$, indicating that the odds of being affiliated as liberal rather than conservative are almost 3 times greater for females between the ages of 18 and 29 than for females who are at least 50 years old.

统计代写|属性数据分析作业代写analysis of categorical data代考|Homogeneous Association

When the conditional associations between $X$ and $Y$ are the same across all $K$ partial tables (representing levels of $Z$ ), we have homogeneous association between $X$ and $Y$. This is analogous to the absence of a three-way interaction in a three-way ANOVA, and implies that the two-way interaction between any two variables (or factors) is the same across all levels of the third variable (or factor).

Homogeneous association was not evident in the examples presented thus far because the partial associations between $X$ and $Y$ were not the same across all $K$ partial tables. In other words, in these examples there was a “three-way association” between the variables considered. Specifically, in our first example, there was a three-way association between gender, age, and political affiliation, because the degree of association between political affiliation and age differed between males and females. In other words, the association between political affiliation and age depended on one’s gender. Likewise, in our second example there was a three-way association between ability to breathe normally, smoking, and age, because the degree of association between smoking and the ability to breathe normally was stronger for respondents older than 50 years of age than for those 50 years of age or younger. In general, to reject the null hypothesis of homogeneous association, it is not necessary for some conditional associations to be statistically significant and others to be insignificant (as was the case in these examples). A rejection of this null hypothesis only implies that the partial associations are not equivalent in either strength or direction. It could be the case, for example, that both of the partial associations are statistically significant but one of them is also significantly stronger than another.
Formally, a homogeneous association implies that all of the following equalities hold:
$$
\begin{aligned}
&\theta_{X Y \mid Z_{1}}=\theta_{X Y \mid Z_{2}}=\cdots=\theta_{X Y \mid Z_{X}} \
&\theta_{X Z \mid Y_{1}}=\theta_{X Z Y_{2}}=\cdots=\theta_{X Z Y} \
&\theta_{Y Z \mid X_{1}}=\theta_{Y Z \mid X_{2}}=\cdots=\theta_{Y Z \mid X_{1}}
\end{aligned}
$$
If any one of the equalities (in Equations $5.1-5.3$ ) is true, then the other two equalities will also be true. For example, suppose that homogeneous association was found between writing proficiency ( $Y=$ yes or no), type of instruction ( $X=$ whole language or phonics), and school locale ( $Z=$ urban or rural). This would imply that the odds of being proficient in writing if taught using a whole language approach, as opposed to a phonics approach, would be statistically equivalent for students in urban and rural schools (i.e., all $\theta_{X Y \mid Z_{k}}$ are equal to each other). Moreover, the odds of being proficient in writing if one went to an urban school, as opposed to a rural school, would be statistically equivalent regardless of the method of instruction (i.e., all $\theta_{Y Z \mid X_{i}}$ are equal). Finally, the odds of being taught from a whole language approach if one went to an urban school, as opposed to a rural school, would be comparable for students who were proficient in writing and those who were not (i.e., all $\theta_{x z Y}$ are equal).

PDF] Binary models for marginal independence | Semantic Scholar — 统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Independence

属性数据分析

统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Independence

边际独立意味着在边际表中没有关联，而边际依赖或边际关联意味着在边际表中存在关联。因此，术语边际依赖和边际关联可以互换使用。为一个2×2表示两个变量之间关系的边际表，X和是（在所有级别从)，边际独立性意味着（在总体中）边际优势比，θX是等于 1 ；同样，边际依赖意味着（在人口中）θX是不等于 1 。例如，在我们的第二个示例（表 5.5）中，吸烟状况和正常呼吸能力（在样本中）之间存在边际依赖性，因为估计的边际优势比是，θ^X是=2.756. 这种关联（优势比）具有统计学意义，表明存在边际关联（即，大于 1 的边际优势比）可以推广到人群。
一般来说，对于任何一世×Ĵ边际表，边际独立性意味着可以使用任何两个变量水平形成的所有优势比，X和是, 将等于 1 。
92 关联，三个分类变量
另一方面，边际依赖意味着通过使用两个变量水平形成的优势比中的至少一个X和是不等于 1 。在所有情况下，这些边缘关联（在X和是) 忽略第三个变量 (从).

统计代写|属性数据分析作业代写analysis of categorical data代考|Conditional Independence

条件独立意味着变量之间没有关联X和是在一种n是的到以第三个变量的每个级别为条件的部分表，从. 为一个2×2部分表，这意味着在总体中，所有到部分表等于 1 ，或θX是∣从到=1对全部到=1,2,…,到. 我们使用条件优势比符号θX是χ表示之间的关联X和是有条件的到th 水平从. 请注意，在条件符号中，垂直线左侧的变量代表感兴趣的关联，垂直线右侧的变量代表关联所依赖的变量。一般来说，对于任何一世×Ĵ部分表，条件独立意味着所有优势比可以通过使用任何两个水平X和是将等于 1到部分表（即，以从).

条件依赖或条件关联意味着在至少一个部分表中存在关联。如果是2×2部分表，条件依赖意味着，在总体中，至少有一个部分表中的优势比，或θX是∣和到对于至少一个到=1,2,…,到, 不等于 1 。一般来说，对于任何一世×Ĵ部分表，条件依赖意味着至少一个优势比可以通过使用两个变量的任何两个水平形成，X和是, 对于至少一个部分表不等于 1从.

在我们之前的两个示例中，条件依赖都很明显，因为两个变量之间的部分关联存在于（至少）一个部分表中。在我们的第一个示例（表 5.1）中，女性的政治派别与年龄之间存在部分关联(χ2=24.496,dF=6,p<0.001), 虽然不适合男性(χ2=8.193,dF=6,p=0.224). 这意味着可以从女性的政治派别和年龄组部分表中计算出的条件优势比中的至少一个在总体中不等于 1。事实上，考虑到前面描述的残差分析（表 5.2），并检查最偏离独立性的单元格，很可能通过考虑2×218-29 岁和 50 岁或以上年龄组的自由派和保守派女性的表格将反映具有统计学意义的关联。这是因为这些单元格具有最大的残差，因此与独立时的预期偏差最大。这四个细胞的频率计数显示在表中5.6; 该表的估计优势比为2.83，表明 18 至 29 岁的女性加入自由派而非保守派的几率几乎是 50 岁以上女性的 3 倍。

统计代写|属性数据分析作业代写analysis of categorical data代考|Homogeneous Association

当之间的条件关联X和是都是一样的到部分表（代表级别从)，我们之间存在同质关联X和是. 这类似于三因素方差分析中不存在三因素交互作用，并暗示任何两个变量（或因子）之间的双向交互作用在第三个变量（或因子）的所有水平上都是相同的。

迄今为止的例子中，同质关联并不明显，因为之间的部分关联X和是所有人都不一样到部分表。换句话说，在这些示例中，所考虑的变量之间存在“三向关联”。具体来说，在我们的第一个例子中，性别、年龄和政治派别之间存在三向关联，因为政治派别和年龄之间的关联程度在男性和女性之间是不同的。换句话说，政治派别和年龄之间的关联取决于一个人的性别。同样，在我们的第二个示例中，正常呼吸能力、吸烟和年龄之间存在三向关联，因为 50 岁以上的受访者吸烟与正常呼吸能力之间的关联程度要强于那些50 岁或以下。一般来说，要拒绝同质关联的原假设，一些条件关联没有必要在统计上显着，而另一些则无关紧要（如这些示例中的情况）。拒绝该零假设仅意味着部分关联在强度或方向上不相等。例如，可能的情况是，两个部分关联都具有统计显着性，但其中一个也明显强于另一个。
形式上，同质关联意味着以下所有等式都成立：
θX是∣从1=θX是∣从2=⋯=θX是∣从X θX从∣是1=θX从是2=⋯=θX从是 θ是从∣X1=θ是从∣X2=⋯=θ是从∣X1
如果任何一个等式（在等式5.1−5.3) 为真，那么其他两个等式也为真。例如，假设在写作能力（是=是或否），指令类型（X=整个语言或语音）和学校语言环境（从=城市或农村）。这意味着，如果使用全语言教学法而不是拼音法教学，精通写作的几率对于城市和农村学校的学生在统计上是相等的（即，所有θX是∣从到彼此相等）。此外，如果一个人上城市学校而不是农村学校，那么无论教学方法如何（即所有θ是从∣X一世相等）。最后，如果一个人去城市学校而不是农村学校，那么从整体语言方法学习的几率对于熟练写作的学生和不熟练写作的学生（即所有θX和是相等）。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|属性数据分析作业代写analysis of categorical data代考|Contingency Tables for Three Categorical Variables

Posted on 2022年4月13日2022年4月13日 by statistics-lab

如果你也在怎样代写属性数据分析analysis of categorical data这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的属性数据分析analysis of categorical data及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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

Chapter 6 — 统计代写|属性数据分析作业代写analysis of categorical data代考|Contingency Tables for Three Categorical Variables

统计代写|属性数据分析作业代写analysis of categorical data代考|Partial Tables and Conditional Associations

Three-way contingency tables depict the relationship between three categorical variables by considering two-way contingency tables, called partial tables, at the different levels of
Associations, Three Categorical Variables 87 the third variable. While the notation and terminology introduced in the previous chapter for two-way contingency tables generalize to three-way contingency tables, they are here extended to take into consideration the third variable.

When we have three categorical variables, the total number of categories for the row variable, $X$, is still denoted by $I$, with each category indexed by $i$; the total number of categories for the column variable, $Y$, is still denoted by $J$, with each category indexed by $j$; but now we have a third variable, $Z$, for which the total number of categories is denoted by $K$, with each category indexed by $k$. Figure $5.1$ illustrates a three-way table, which can be partitioned or “sliced up” in three different ways to create partial tables. One could either create $K$ partial tables, one for each level of the variable $Z$; J partial tables, one for each level of $Y$; or $I$ partial tables, one for each level of $X$. The slices for each level of $Z$ are depicted in Figure 5.1. The “slices” are often displayed side-by-side or stacked on top of each other when presenting the data. In general, the size of three-way contingency tables is denoted as $I \times J \times K$ and the frequency in each cell of the table (i.e., the number of observations falling into the $i^{\text {th }}$ category of $X, j^{\text {th }}$ category of $Y$, and $k^{\text {th }}$ category of $Z$ ) is denoted by $n_{i j k}$.

A substantive example of a three-way contingency table depicting the relationship between political affiliation, age, and gender is illustrated in Table 5.1. In this example, $X$ is political affiliation and has $I=3$ categories ( $i=1$ for liberal; $i=2$ for moderate; and $i=3$ for conservative), $Y$ is age group and has $J=4$ categories $(j=1$ for those $18-29$ years of age; $j=2$ for those $30-39$ years of age; $j=3$ for those $40-49$ years of age; and $j=4$ for those $50-$ plus years of age), and $Z$ is gender with $K=2$ categories ( $k=1$ for males; $k=2$ for females). The size of this three-way contingency table is $3 \times 4 \times 2$. The frequency in each cell of the table is denoted by $\mathrm{n}{\mathrm{ijl}}$ (where $i=1,2, \ldots, 3 ; j=1,2, \ldots, 4 ; k=1,2$ ). For example, $\mathrm{n}{142}$ in Table $5.1$ represents the number of respondents who are liberal $(i=1), 50$-plus years of age $(j=4)$, and female $(k=2)$, so $n_{142}=63$. Taken together, the cell frequencies represent the joint distribution of the three categorical variables.

统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Tables and Marginal Associations

A marginal table represents combined partial tables and is formed by adding their corresponding frequencies. That is, the marginal table contains marginal frequencies because the frequencies are summed across one of the three variables. Using the example in Table 5.1, a $3 \times 4$ marginal table (representing political affiliation and age category) can be formed by adding the frequencies across gender, as depicted in Table 5.3. For illustration, the first cell frequency in Table $5.3$ is $\mathrm{n}{11+}=86$ and was obtained by adding the frequencies of males and females who are liberal and $18-29$ years old; that is, $n{111}+n_{112}=27+59=86$. In general, each frequency in this marginal table can be represented as $n_{i j+}=n_{i j 1}+n_{i j 2}$.

The associations in marginal tables are called marginal associations. For readers familiar with analysis of variance (ANOVA), the conditional associations previously discussed are analogous to three-way interactions in ANOVA, where the interaction between any two factors depends on the level of the third factor, while the marginal associations are analogous to

two-way interactions in a three-way ANOVA, where the interaction between any two factors is averaged across all levels of the third factor. In other words, conditional associations examine two-way associations separately at each level of the third variable, whereas marginal associations examine two-way associations overall, essentially ignoring the third variable. Therefore, conditional associations can be very different from the marginal associations for the same data set. In our example, the marginal association between political affiliation and age group would essentially ignore one’s gender and may be very different from either of the conditional associations for these variables (which are obtained for each gender separately).

To further illustrate these concepts, Table $5.4$ depicts the results of a study, adapted from Agresti (1990), that examined the association between smoking status and the ability to breathe normally for two age groups. A marginal table that depicts the overall association between smoking status and the ability to breathe normally regardless of (or summed across) age is shown in Table 5.5. The estimated odds ratio for the marginal association between breathing normally and smoking status (computed using the frequencies in Table 5.5) is
$$
\hat{\theta}=\frac{741 \times 131}{927 \times 38}=2.756
$$
Associations, Three Categorical Variables 91 and it represents a statistically significant marginal association $\left(\chi^{2}=30.242, d f=1, p<0.001\right)$. In computing this association, we have ignored the effect of age, although it might be hypothesized to have an impact on the ability to breathe. In fact, using the partial tables shown in Table $5.4$, for those who were less than 50 years of age, the estimated odds ratio between breathing normally and smoking status is $\hat{\theta}=1.418$, which is not a statistically significant conditional association $\left(\chi^{2}=2.456, d f=1, p=0.112\right)$. On the other hand, for participants in the study who were 50 years of age or older, the estimated odds ratio is $\hat{\theta}=12.38$, which is a statistically significant conditional association $\left(\chi^{2}=35.45, d f=1, p<0.001\right)$. Therefore, age is an important covariate in studying the relationship between smoking status and the ability to breathe.

统计代写|属性数据分析作业代写analysis of categorical data代考|Patterns of Association

In this section, we discuss the relationship between two variables, $X$ and $Y$, either conditional on or combined across the levels of the third variable, $Z$. Although the labels given to the variables (i.e., which variable is called $X, Y$, or $Z$ ) are rather arbitrary, it is somewhat conventional to denote the primary variables of interest as $X$ and $Y$ while denoting the covariate as $Z$. This is the approach we take in the general discussion that follows.

属性数据分析

统计代写|属性数据分析作业代写analysis of categorical data代考|Partial Tables and Conditional Associations

三向列联表通过考虑双向列联表（称为部分表）来描述三个分类变量之间的关系，在不同的
关联级别，三分类变量 87 第三个变量。虽然前一章介绍的双向列联表的符号和术语可以推广到三路列联表，但在这里它们被扩展以考虑第三个变量。

当我们有三个分类变量时，行变量的类别总数，X, 仍表示为一世，每个类别由一世; 列变量的类别总数，是, 仍表示为Ĵ，每个类别由j; 但现在我们有了第三个变量，从, 其中类别总数表示为到，每个类别由到. 数字5.1说明了一个三向表，可以以三种不同的方式对其进行分区或“切片”以创建部分表。一个人可以创建到部分表，一个用于变量的每个级别从; J 个部分表，每个级别一个是; 或者一世部分表，每个级别一个X. 每个级别的切片从如图 5.1 所示。在呈现数据时，“切片”通常并排显示或堆叠在一起。通常，三向列联表的大小表示为一世×Ĵ×到以及表格每个单元格中的频率（即，落入一世th 类别X,jth 类别是，和到th 类别从) 表示为n一世j到.

描述政治派别、年龄和性别之间关系的三向列联表的一个实质性例子如表 5.1 所示。在这个例子中，X是政治派别，并且有一世=3类别（一世=1对于自由主义者；一世=2为中度；和一世=3保守），是是年龄组并且有Ĵ=4类别(j=1对于那些18−29岁;j=2对于那些30−39岁;j=3对于那些40−49岁; 和j=4对于那些50−加上年龄），和从是性别与到=2类别（到=1男性；到=2对于女性）。这个三向列联表的大小是3×4×2. 表中每个单元格中的频率用 $\mathrm{n} {\mathrm{ijl}} 表示(在H和r和i=1,2, \ldots, 3 ; j=1,2, \ldots, 4 ; k=1,2).F这r和X一种米p一世和,\mathrm{n} {142}一世n吨一种b一世和5.1r和pr和s和n吨s吨H和n你米b和r这Fr和sp这nd和n吨s在H这一种r和一世一世b和r一种一世(i=1), 50−p一世你s是和一种rs这F一种G和(j=4),一种ndF和米一种一世和(k = 2),s这n_{142}=63 美元。总之，单元频率代表三个分类变量的联合分布。

统计代写|属性数据分析作业代写analysis of categorical data代考|Marginal Tables and Marginal Associations

边缘表表示组合的部分表，并通过添加它们的相应频率形成。也就是说，边际表包含边际频率，因为频率是三个变量之一的总和。使用表 5.1 中的示例，a3×4边际表（代表政治派别和年龄类别）可以通过添加跨性别的频率来形成，如表 5.3 所示。为了说明，表中的第一个小区频率5.3是 $\mathrm{n} {11+}=86一种nd在一种s这b吨一种一世n和db是一种dd一世nG吨H和Fr和q你和nC一世和s这F米一种一世和s一种ndF和米一种一世和s在H这一种r和一世一世b和r一种一世一种nd18-29是和一种rs这一世d;吨H一种吨一世s,n {111}+n_{112}=27+59=86.一世nG和n和r一种一世,和一种CHFr和q你和nC是一世n吨H一世s米一种rG一世n一种一世吨一种b一世和C一种nb和r和pr和s和n吨和d一种sn_{i j+}=n_{ij 1}+n_{ij 2}$。

边缘表中的关联称为边缘关联。对于熟悉方差分析 (ANOVA) 的读者来说，前面讨论的条件关联类似于 ANOVA 中的三向交互作用，其中任意两个因素之间的交互作用取决于第三个因素的水平，而边际关联类似于

三向方差分析中的双向交互作用，其中任何两个因素之间的交互作用在第三个因素的所有水平上取平均值。换句话说，条件关联在第三个变量的每个级别分别检查双向关联，而边际关联总体上检查双向关联，基本上忽略了第三个变量。因此，条件关联可能与同一数据集的边缘关联非常不同。在我们的示例中，政治派别和年龄组之间的边际关联基本上会忽略一个人的性别，并且可能与这些变量的任何一个条件关联（分别针对每个性别获得）非常不同。

为了进一步说明这些概念，表5.4描述了改编自 Agresti (1990) 的一项研究的结果，该研究检查了两个年龄组的吸烟状况与正常呼吸能力之间的关系。表 5.5 显示了一个边际表，该表描述了吸烟状况与正常呼吸能力之间的总体关联，而与年龄无关（或总和）。正常呼吸与吸烟状态之间的边际关联的估计优势比（使用表 5.5 中的频率计算）为
θ^=741×131927×38=2.756
关联，三个分类变量 91 它代表了具有统计意义的边际关联(χ2=30.242,dF=1,p<0.001). 在计算这种关联时，我们忽略了年龄的影响，尽管可能假设它对呼吸能力有影响。实际上，使用 Table 所示的部分表5.4，对于年龄小于 50 岁的人，正常呼吸和吸烟状态之间的估计优势比为θ^=1.418，这不是统计显着的条件关联(χ2=2.456,dF=1,p=0.112). 另一方面，对于年龄在 50 岁或以上的研究参与者，估计优势比为θ^=12.38，这是一个统计显着的条件关联(χ2=35.45,dF=1,p<0.001). 因此，年龄是研究吸烟状况与呼吸能力之间关系的重要协变量。

统计代写|属性数据分析作业代写analysis of categorical data代考|Patterns of Association

在本节中，我们讨论两个变量之间的关系，X和是，以第三个变量的水平为条件或组合，从. 虽然赋予变量的标签（即调用哪个变量X,是，或者从) 是相当随意的，将感兴趣的主要变量表示为有些传统X和是同时将协变量表示为从. 这是我们在随后的一般性讨论中采用的方法。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|属性数据分析作业代写analysis of categorical data代考|Testing the Association Between Two Categorical Variables

Posted on 2022年4月13日2022年4月13日 by statistics-lab

如果你也在怎样代写属性数据分析analysis of categorical data这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的属性数据分析analysis of categorical data及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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|属性数据分析作业代写analysis of categorical data代考|Expected Frequencies Under Independence

Under the first approach to testing the association (or lack of association) between two categorical variables, the null hypothesis states that the two variables are statistically independent. This means (recall from Section 4.2) that the frequency or probability in a particular cell of the contingency table can be determined directly from the cell’s row and column (marginal) frequencies or probabilities. In other words, under statistical independence, the marginal probabilities (or frequencies) can be used to determine the joint probabilities (or frequencies); specifically, the cell (joint) probability is equal to the product of its row and column (marginal) probabilities: $\pi_{i j}=\pi_{i+} \pi_{+i}$

Using sample notation, the expected joint probability $p_{i j}$ for any given cell can be computed as
$$
p_{i j}=p_{i+} p_{+j}=\left(\frac{n_{i+}}{n_{++}}\right)\left(\frac{n_{+j}}{n_{++}}\right) .
$$
To convert this expected probability to the corresponding expected frequency, we multiply the probability by the total number of observations:
$$
n_{i j}=n_{++} p_{i j}=n_{++}\left(\frac{n_{i+}}{n_{++}}\right)\left(\frac{n_{+j}}{n_{++}}\right)=\frac{n_{i+} n_{+j}}{n_{++}} .
$$

Using our voter preference and gender example (Table 4.1), under the null hypothesis of independence the expected (joint) probability that a voter is male and voted for Clinton can be computed as follows:
$$
\begin{aligned}
&P(\text { voter is male and voted for Clinton })=p_{11} \
&=P(\text { voter is male }) \times P(\text { votes for Clinton })=p_{1+} p_{+1}=\left(\frac{n_{1+}}{n_{++}}\right)\left(\frac{n_{+1}}{n_{++}}\right) \
&=(606 / 1442)(618 / 1442)=(0.42)(0.43)=0.18 .
\end{aligned}
$$
To convert this probability to a frequency, we multiply it by the total number of observations (in our case, 1,442 ) to obtain $\mathrm{n}{11}=\mathrm{n}{++} p_{11}=(1442)(0.18)=259.71$. Alternatively, this expected frequency and all others can be obtained directly using the expected frequencies formula shown in Equation 4.4, as follows:
Males voting for Clinton $=n_{11}=\left(n_{1+} n_{+1}\right) / n_{++}=(606)(618) / 1442=259.71$;
Males voting for Obama $=n_{12}=\left(n_{1+} n_{+2}\right) / n_{++}=(606)(824) / 1442=346.29$;
Females voting for Clinton $=n_{21}=\left(n_{2+}{ }^{n}{ }{+1}\right) / n{++}=(836)(618) / 1442=358.29$; and
Females voting for Obama $=n_{22}=\left(n_{2+}{ }^{n}{ }{+2}\right) / n{++}=(836)(824) / 1442=477.71$.
These expected frequencies are summarized in Table $4.6$ (b). Note that the expected marginal frequencies are identical to the observed marginal frequencies, and this should always be the case (so you can use this fact to check your computations). The joint frequency distribution obtained from the sample (observed, see Table 4.6(a)) will be compared to the distribution obtained under the null hypothesis of independence (expected, see Table $4.6(\mathrm{~b})$ ) to determine whether the observed data are consistent with the hypothesis of independence.

统计代写|属性数据分析作业代写analysis of categorical data代考|Expected Frequencies Under Equal Proportion Distributions

Under the second approach to testing whether there is an association between two categorical variables, the null hypothesis of independence states that the probability distribution of the dependent variable (e.g., improvement) is the same in each category of the independent variable (e.g., treatment group). In our earlier example of comparing three treatment groups in terms of improvement, the null hypothesis would state that the distribution of the improvement outcome (yes/no) should be the same across all three treatment groups; hence, improvement is independent of (or unassociated with) group. If that is the case, then within

each treatment group we would expect the same probability distribution for the outcome, and this will also be reflected in the marginal probability distribution of the outcome.

Hypothetical observed frequencies for our example are presented in Table 4.7(a). From the observed frequencies, the marginal probability distribution of the outcome is as follows:
$$
\begin{aligned}
&P(\text { improvement }=\text { Yes })=p_{+1}=\frac{33}{75}=0.44 ; \
&P(\text { improvement }=\mathrm{No})=p_{+2}=\frac{42}{75}=0.56 .
\end{aligned}
$$
This indicates that the probability distribution of the outcome (improvement) is $44 \%$ yes and $56 \%$ no. Under independence, this probability distribution should hold for each of the treatment groups. For instance, of the 25 individuals who received the new drug, $44 \%$ would be expected to show improvement and $56 \%$ would be expected not to show improvement if treatment and outcome were independent. Therefore, the expected frequency distribution for that group (or in that row of the table) will be:
Expected frequency of a decrease in depressive symptoms $=(0.44)(25)=11$;
Expected frequency of no decrease in depressive symptoms $=(0.56)(25)=14$.
Moreover, assuming the null hypothesis is true, the marginal probabilities of $0.44$ and $0.56$ (for whether or not patients reported improvement, respectively) will hold for all three of the treatment groups. That is, in each of the three groups (or within each row), we expect $44 \%$ of those in the group to be in the “yes” column and $56 \%$ to be in the “no” column. Because we happen to have 25 individuals in each group, these expected probabilities result in the frequencies of 11 and 14 in each group; these expected frequencies are summarized in Table 4.7(b). Note once again that the observed and expected marginal frequencies are identical. To test the hypothesis, we now need to compare the cell frequencies obtained from the sample (observed) to those obtained under the null hypothesis (expected) to determine whether the observed data are consistent with the hypothesis of independence.

统计代写|属性数据分析作业代写analysis of categorical data代考|Test Statistics

To compute the test statistic for either approach, the observed and expected frequencies are compared using the goodness-of-fit test statistics discussed in Chapter 3 (Section 3.4). Specifically, the Pearson chi-squared test statistic is
$$
X^{2}=\sum_{i=1}^{I} \sum_{j=1}^{J} \frac{\left(O_{i j}-E_{i j}\right)^{2}}{E_{i j}}
$$

and the likelihood ratio test statistic is
$$
G^{2}=2 \sum_{i=1}^{I} \sum_{j=1}^{J} O_{i j} \ln \left(\frac{O_{i j}}{E_{i j}}\right),
$$
where $O_{i j}$ and $E_{i j}$ refer to the observed and expected joint frequencies (i.e., for the cell in the $i^{\text {th }}$ row and $j^{\text {th }}$ column), respectively, in a two-way contingency table.

The Pearson chi-squared test statistic for a contingency table consists of a summation over all cells and results in a test statistic with $(I-1)(J-1)$ degrees of freedom. The degrees of freedom can be determined using the same reasoning provided in Chapter 3 ; that is, given the marginal frequencies, only $(I-1)(J-1)$ cell frequencies are “free” to vary, while the remaining cell frequencies are determined based on the marginal frequencies. (Try it for yourself: how many cell frequencies could you “freely” choose while maintaining the marginal frequencies provided in Table 4.7?) For our drug treatment example (Table 4.7), $I=3$ and $J=2$, so the degrees of freedom are $(3-1)(2-1)=2$, and the test statistic is
$$
\begin{aligned}
X^{2} &=\sum_{i=1}^{3} \sum_{j=1}^{2} \frac{\left(O_{i j}-E_{i j}\right)^{2}}{E_{i j}} \
&=\frac{\left(O_{11}-E_{11}\right)^{2}}{E_{11}}+\frac{\left(O_{12}-E_{12}\right)^{2}}{E_{12}}+\frac{\left(O_{21}-E_{21}\right)^{2}}{E_{21}}+\frac{\left(O_{22}-E_{22}\right)^{2}}{E_{22}}+\frac{\left(O_{31}-E_{31}\right)^{2}}{E_{31}}+\frac{\left(O_{32}-E_{32}\right)^{2}}{E_{32}} \
&=\frac{(16-11)^{2}}{11}+\frac{(9-14)^{2}}{14}+\frac{(12-11)^{2}}{11}+\frac{(13-14)^{2}}{14}+\frac{(5-11)^{2}}{11}+\frac{(20-14)^{2}}{14}=10.065 .
\end{aligned}
$$

属性数据分析

统计代写|属性数据分析作业代写analysis of categorical data代考|Expected Frequencies Under Independence

在检验两个分类变量之间的关联（或缺乏关联）的第一种方法下，原假设表明这两个变量在统计上是独立的。这意味着（回顾第 4.2 节）列联表的特定单元格中的频率或概率可以直接从单元格的行和列（边际）频率或概率中确定。换句话说，在统计独立的情况下，边际概率（或频率）可以用来确定联合概率（或频率）；具体来说，单元格（联合）概率等于其行和列（边际）概率的乘积：圆周率一世j=圆周率一世+圆周率+一世

使用样本符号，预期联合概率p一世j对于任何给定的单元格都可以计算为
p一世j=p一世+p+j=(n一世+n++)(n+jn++).
为了将此预期概率转换为相应的预期频率，我们将概率乘以观察总数：
n一世j=n++p一世j=n++(n一世+n++)(n+jn++)=n一世+n+jn++.

使用我们的选民偏好和性别示例（表 4.1），在独立的零假设下，选民是男性并投票给克林顿的预期（联合）概率可以计算如下：
磷( 选民是男性，投票给克林顿 )=p11 =磷( 选民是男性 )×磷( 投票给克林顿 )=p1+p+1=(n1+n++)(n+1n++) =(606/1442)(618/1442)=(0.42)(0.43)=0.18.
为了将此概率转换为频率，我们将其乘以观察总数（在我们的例子中为 1,442 ）以获得 $\mathrm{n} {11}=\mathrm{n} {++} p_{11}= (1442)(0.18)=259.71.一种一世吨和rn一种吨一世v和一世是,吨H一世s和Xp和C吨和dFr和q你和nC是一种nd一种一世一世这吨H和rsC一种nb和这b吨一种一世n和dd一世r和C吨一世是你s一世nG吨H和和Xp和C吨和dFr和q你和nC一世和sF这r米你一世一种sH这在n一世n和q你一种吨一世这n4.4,一种sF这一世一世这在s:米一种一世和sv这吨一世nGF这rC一世一世n吨这n=n_{11}=\left(n_{1+} n_{+1}\right) / n_{++}=(606)(618) / 1442=259.71;米一种一世和sv这吨一世nGF这r这b一种米一种=n_{12}=\left(n_{1+} n_{+2}\right) / n_{++}=(606)(824) / 1442=346.29;F和米一种一世和sv这吨一世nGF这rC一世一世n吨这n=n_{21}=\left(n_{2+}{ }^{n}{ } {+1}\right) / n {++}=(836)(618) / 1442=358.29;一种ndF和米一种一世和sv这吨一世nGF这r这b一种米一种=n_{22}=\left(n_{2+}{ }^{n}{ } {+2}\right) / n {++}=(836)(824) / 1442=477.71.吨H和s和和Xp和C吨和dFr和q你和nC一世和s一种r和s你米米一种r一世和和d一世n吨一种b一世和4.6(b).ñ这吨和吨H一种吨吨H和和Xp和C吨和d米一种rG一世n一种一世Fr和q你和nC一世和s一种r和一世d和n吨一世C一种一世吨这吨H和这bs和rv和d米一种rG一世n一种一世Fr和q你和nC一世和s,一种nd吨H一世ssH这你一世d一种一世在一种是sb和吨H和C一种s和(s这是这你C一种n你s和吨H一世sF一种C吨吨这CH和C到是这你rC这米p你吨一种吨一世这ns).吨H和j这一世n吨Fr和q你和nC是d一世s吨r一世b你吨一世这n这b吨一种一世n和dFr这米吨H和s一种米p一世和(这bs和rv和d,s和和吨一种b一世和4.6(一种))在一世一世一世b和C这米p一种r和d吨这吨H和d一世s吨r一世b你吨一世这n这b吨一种一世n和d你nd和r吨H和n你一世一世H是p这吨H和s一世s这F一世nd和p和nd和nC和(和Xp和C吨和d,s和和吨一种b一世和4.6(\mathrm{~b})$) 来确定观察到的数据是否与独立性假设一致。

统计代写|属性数据分析作业代写analysis of categorical data代考|Expected Frequencies Under Equal Proportion Distributions

在检验两个分类变量之间是否存在关联的第二种方法下，独立性的零假设表明因变量（例如，改善）的概率分布在自变量的每个类别（例如，治疗组）中是相同的）。在我们之前比较三个治疗组的改善情况的例子中，零假设表明改善结果的分布（是/否）在所有三个治疗组中应该是相同的。因此，改进与组无关（或不相关）。如果是这样的话，那么在

我们期望每个治疗组的结果具有相同的概率分布，这也将反映在结果的边际概率分布中。

表 4.7(a) 给出了我们示例的假设观测频率。从观察到的频率，结果的边际概率分布如下：
磷( 改进 = 是的 )=p+1=3375=0.44; 磷( 改进 =ñ这)=p+2=4275=0.56.
这表明结果（改进）的概率分布是44%是的和56%不。在独立的情况下，这个概率分布应该适用于每个治疗组。例如，在接受新药的 25 人中，44%预计会显示出改善和56%如果治疗和结果是独立的，预计不会出现改善。因此，该组（或表格的该行）的预期频率分布将是：
抑郁症状减少的预期频率=(0.44)(25)=11;
抑郁症状没有减少的预期频率=(0.56)(25)=14.
此外，假设原假设为真，则0.44和0.56（对于患者是否分别报告改善）将适用于所有三个治疗组。也就是说，在三组中的每一组（或每一行内），我们期望44%组中的那些在“是”列中，并且56%在“否”栏中。因为我们碰巧每组有 25 个人，所以这些预期概率导致每组中的频率分别为 11 和 14；表 4.7(b) 总结了这些预期频率。再次注意观察到的和预期的边际频率是相同的。为了检验假设，我们现在需要比较从样本中获得的细胞频率（观察到的）和在零假设下获得的细胞频率（预期的），以确定观察到的数据是否与独立性假设一致。

统计代写|属性数据分析作业代写analysis of categorical data代考|Test Statistics

为了计算任一方法的检验统计量，使用第 3 章（第 3.4 节）中讨论的拟合优度检验统计量比较观察到的和预期的频率。具体来说，Pearson 卡方检验统计量是
X2=∑一世=1一世∑j=1Ĵ(这一世j−和一世j)2和一世j

和似然比检验统计量是
G2=2∑一世=1一世∑j=1Ĵ这一世jln⁡(这一世j和一世j),
在哪里这一世j和和一世j指观察到的和预期的联合频率（即，对于一世th 行和jth 列），分别在一个双向列联表中。

列联表的 Pearson 卡方检验统计量由所有单元格的总和组成，并导致检验统计量为(一世−1)(Ĵ−1)自由程度。可以使用第 3 章中提供的相同推理来确定自由度；也就是说，给定边缘频率，只有(一世−1)(Ĵ−1)小区频率是“自由”变化的，而剩余的小区频率是根据边缘频率确定的。（自己尝试一下：在保持表 4.7 中提供的边际频率的同时，您可以“自由”选择多少个细胞频率？）对于我们的药物治疗示例（表 4.7），一世=3和Ĵ=2, 所以自由度是(3−1)(2−1)=2, 检验统计量为
X2=∑一世=13∑j=12(这一世j−和一世j)2和一世j =(这11−和11)2和11+(这12−和12)2和12+(这21−和21)2和21+(这22−和22)2和22+(这31−和31)2和31+(这32−和32)2和32 =(16−11)211+(9−14)214+(12−11)211+(13−14)214+(5−11)211+(20−14)214=10.065.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|属性数据分析作业代写analysis of categorical data代考|Odds Ratio

Posted on 2022年4月13日2022年4月13日 by statistics-lab

如果你也在怎样代写属性数据分析analysis of categorical data这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的属性数据分析analysis of categorical data及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
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

Association Between Two Categorical Variables: Contingency Analysis with Chi Square | SpringerLink — 统计代写|属性数据分析作业代写analysis of categorical data代考|Odds Ratio

统计代写|属性数据分析作业代写analysis of categorical data代考|Odds

As usual, these population parameters can be estimated using sample data. From Table $4.1$, we can say that the probability of voting for Clinton in the Wisconsin Primary was
$$
P(\text { voted for Clinton })=\frac{618}{1442}=0.43,
$$
Association, Tuo Categorical Variables 51
so the odds of voting for Clinton were
$$
\text { Odds }=\frac{0.43}{1-0.43}=\frac{0.43}{0.57}=0.75 \text {. }
$$
This means that the probability of voting for Clinton was $0.75$ times the probability of not voting for Clinton and, because the odds are less than 1 , the probability of voting for Clinton was lower than the probability of not voting for her (i.e., voting for Obama). Another way to say this is that the probability of a vote for Clinton was $75 \%$ of the probability of a vote for Obama. Additionally, because there are only two outcomes (candidates), the odds of voting for Obama can be computed as the reciprocal of the odds of voting for Clinton, or $1 / 0.75=1.33$. To show this, note that because the probability of voting for Clinton is $0.43$ (and there are only two candidates), the probability of voting for Obama must be $(1-0.43)=0.57$; thus, the odds of voting for Obama are $0.57 /(1-0.57)=0.57 / 0.43=1.33$, which is indeed the reciprocal of the odds of voting for Clinton. So, while the probability of a Clinton vote was $0.75$ times the probability of an Obama vote, the probability of an Obama vote was $1.33$ times the probability of a Clinton vote. In general, when the odds equal 1, the probability of the event occurring is $50 \%$, so it is just as likely to occur as not; when the odds are greater than 1 , the event is more likely to occur than not, and when the odds are less than 1 , the event is less likely to occur than not occur.

统计代写|属性数据分析作业代写analysis of categorical data代考|Odds Ratio

The odds ratio is simply defined as the ratio of two odds. Although the definition seems simple enough, interpreting the odds ratio can be tricky (and easily confused with the interpretation of the odds). Each of the individual odds in the ratio is obtained from comparing the probabilities of one variable (e.g., candidate choice), and each is computed for a given category of another variable (e.g., gender). Using our example, suppose that we want to compare the odds of voting for Clinton across the genders: males (group 1) and females (group 2). This is achieved through the odds ratio:
$$
\text { Odds ratio }=\theta=\frac{\text { odds for group } 1}{\text { odds for group } 2}
$$
It is important to note that the interpretation of the odds ratio requires two components: (1) the category or event of interest (i.e., “success”) that defines the computation of the odds, and (2) the categories that define “group 1 ” (numerator) and “group 2 ” (denominator) in the computation of the odds ratio. In our example, we need to define whether the odds of voting for Clinton or for Obama are being examined (as the event or category of interest), as well as whether males or females are considered as the first comparison group (in the numerator). If we consider the odds of voting for Clinton and use males as “group 1 “, then within the male group the probability of voting for Clinton is
$$
P(\text { voting for Clinton if male })=\frac{n_{11}}{n_{1+}}=\frac{200}{606}=0.33 \text {, }
$$
and the odds of voting for Clinton are
$$
\text { Odds for males }=\frac{0.33}{1-0.33}=\frac{0.33}{0.67}=0.49
$$

统计代写|属性数据分析作业代写analysis of categorical data代考|Relative Risk and Odds Ratios

The relative risk is a measure that might be confused with the odds ratio because it also compares two groups, but it compares the probability of success (rather than the odds of success) between the two groups:
Relative risk $=\frac{\text { Probability for Group1 }}{\text { Probability for Group2 }} .$
For example, consider the hypothetical rates of depression for males and females as summarized in Table 4.5. If we wish to compare the probability of having depression for males (group 1) and females (group 2), we can obtain the probability for males as
$$
P(\text { depression }=\text { yes if male })=\frac{n_{11}}{n_{1+}}=\frac{6}{100}=0.06,
$$
the probability for females as
$$
P(\text { depression }=\text { yes if female })=\frac{n_{21}}{n_{2+}}=\frac{12}{100}=0.12,
$$
Association, Tuo Categorical Variables 55 and the relative risk would be
Relative risk $=\frac{\text { Probability for males }}{\text { Probability for females }}=\frac{0.06}{0.12}=0.5$

属性数据分析

统计代写|属性数据分析作业代写analysis of categorical data代考|Odds

像往常一样，可以使用样本数据估计这些总体参数。从表4.1，我们可以说在威斯康星州初选中投票给克林顿的概率是
磷( 投票给克林顿 )=6181442=0.43,
Association, Tuo 分类变量 51
所以投票给克林顿的几率是
赔率 =0.431−0.43=0.430.57=0.75.
这意味着投票给克林顿的概率是0.75乘以不投票给克林顿的概率，并且因为几率小于 1，所以投票给克林顿的概率低于不投票给她的概率（即投票给奥巴马）。另一种说法是，投票给克林顿的概率是75%奥巴马投票的概率。此外，因为只有两个结果（候选人），所以投票给奥巴马的几率可以计算为投票给克林顿的几率的倒数，或者1/0.75=1.33. 为了证明这一点，请注意，因为投票给克林顿的概率是0.43（而且只有两个候选人），投票给奥巴马的概率一定是(1−0.43)=0.57; 因此，投票给奥巴马的几率是0.57/(1−0.57)=0.57/0.43=1.33，这确实是克林顿投票几率的倒数。所以，虽然克林顿投票的概率是0.75乘以奥巴马投票的概率，奥巴马投票的概率是1.33乘以克林顿投票的概率。一般来说，当赔率等于 1 时，事件发生的概率是50%，所以它发生的可能性和不发生的可能性一样；当几率大于 1 时，事件发生的可能性大于不发生的可能性，而当几率小于 1 时，事件发生的可能性小于不发生的可能性。

统计代写|属性数据分析作业代写analysis of categorical data代考|Odds Ratio

优势比被简单地定义为两个优势的比率。尽管定义看起来很简单，但解释优势比可能很棘手（并且很容易与赔率的解释混淆）。该比率中的每个个体优势都是通过比较一个变量（例如，候选选择）的概率获得的，并且每个优势都是针对另一个变量（例如，性别）的给定类别计算的。使用我们的示例，假设我们想要比较不同性别的投票给克林顿的几率：男性（第 1 组）和女性（第 2 组）。这是通过优势比实现的：
赔率 =θ= 团体赔率 1 团体赔率 2
重要的是要注意，赔率比的解释需要两个组成部分：（1）定义赔率计算的类别或感兴趣的事件（即“成功”），以及（2）定义“组1”（分子）和“组 2”（分母）计算优势比。在我们的示例中，我们需要定义是否正在检查投票给克林顿或奥巴马的几率（作为感兴趣的事件或类别），以及是否将男性或女性视为第一个比较组（在分子中） . 如果我们考虑投票给克林顿的几率并将男性作为“第一组”，那么在男性组内，投票给克林顿的概率为
磷( 如果是男性，投票给克林顿 )=n11n1+=200606=0.33,
并且投票给克林顿的几率是
男性的赔率 =0.331−0.33=0.330.67=0.49

统计代写|属性数据分析作业代写analysis of categorical data代考|Relative Risk and Odds Ratios

相对风险是一种可能与优势比混淆的度量，因为它也比较两组，但它比较的是两组之间的成功概率（而不是成功几率）：
相对风险= Group1 的概率 Group2 的概率 .
例如，考虑表 4.5 中总结的男性和女性的假设抑郁率。如果我们想比较男性（第 1 组）和女性（第 2 组）患抑郁症的概率，我们可以得到男性的概率为
磷( 沮丧 = 是的，如果是男性 )=n11n1+=6100=0.06,
女性的概率为
磷( 沮丧 = 是的，如果是女性 )=n21n2+=12100=0.12,
关联，Tuo 分类变量 55 和相对风险将是
相对风险= 男性的概率女性的概率 =0.060.12=0.5

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写