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

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

Models can easily be constructed without thought to how well the model actually fits the data. All too often this is seen in publications-logistic regression results with parameter estimates, and standard errors with corresponding $p$-values and without their associated GOF statistics.

Models are simply that: models. They are not aimed at providing a one-toone fit, called overfitting. The problem with overfitting is that the model is difficult to adapt to related data situations outside the actual data modeled. If heart01. dta were overfit, it would have little value in generalizing to other heart patients.
One measure of fit is called the confusion matrix or classification table. The origins of the term may be more confusing than the information provided in the table. The confusion matrix simply classifies the number of instances where

• $y=1$, predicted $y=1$
• $y=1$, predicted $y=0$
• $y=0$, predicted $y=1$
• $y=0$, predicted $y=0$
Predicted values can be calculated by obtaining the linear predictor, $x \boldsymbol{\beta}$, or $\eta$, and converting it by means of the logistic transform, which is the inverse link function. Both of these statistics are available directly after modeling. In Stata, we can obtain the values after modeling by typing
. predict $\mathrm{xb}, \mathrm{xb} / *$ linear predictor */
or
• predict $\mathrm{mu}, \mathrm{mu} / *$ fitted value */
We may also obtain the linear predictor and then compute the fit for them:
• generate $m u=1 /(1+\exp (-x b))$

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

Generally, the models presented throughout this chapter address dichotomous outcomes. In addition, binomial data can be modeled where the user communicates two pieces of information for each row of data. Those information pieces are the number of successes (numerator) and the number of trials (denominator).

In some research trials, an outcome might represent a proportion for which the denominator is unknown or missing from the data. There are a few approaches available to analyze associations with such an outcome measure. Some researchers analyze these outcomes using a linear regression model. The downside is that predicted values could be outside the range of $[0,1]$; certainly extrapolated values would be outside the range.

In GLMS, the approach is to transform the linear predictor (the so-called righthand side of the equation), but we could use the link function to transform the outcome (the left-hand side of the equation)
$$\operatorname{logit}(y)=\ln \left(\frac{y}{1-y}\right)=\eta$$
and then analyze the transformed value with linear regression. This approach works well except when there are values of zero or one in the outcome.

Strictly speaking, there is nothing wrong with fitting these outcomes in a GLM using Bernoulli variance and the logit link. In previous versions of the Stata software, the glm command would not allow noninteger outcomes, but current software will fit this model. As Papke and Wooldridge (1996) suggest, such models should use the sandwich variance estimator for inference on the coefficients.

广义线性模型代考

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

$y=1$预言的 $y=1$

$y=1$预言的 $y=0$

$y=0$预言的 $y=1$

$y=0$预测$y=0$

． 预测$\mathrm{xb}, \mathrm{xb} /$线性预测器/

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

$$\operatorname{logit}(y)=\ln \left(\frac{y}{1-y}\right)=\eta$$

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The links that are associated with members of the continuous family of GLM distributions may be thought of in terms of powers. In fact, except for the standard binomial links and the canonical form of the negative binomial, all links are powers of $\mu$. The relationships are listed in the following table:
\begin{tabular}{lcc}
Link & Function & Power function \
\hline Identity & $\mu$ & $\mu^1$ \
Log & $\ln (\mu)$ & $\mu^0$ \
Reciprocal & $1 / \mu$ & $\mu^{-1}$ \
Inverse quadratic & $1 / \mu^2$ & $\mu^{-2}$
\end{tabular}
A generic power link function can thus be established as
$$\operatorname{Power}(a)= \begin{cases}\mu^a & \text { if } a \neq 0 \ \ln (\mu) & \text { if } a=0\end{cases}$$
The corresponding generic inverse link function is
$$\operatorname{Power}(a)= \begin{cases}\eta^{-a} & \text { if } a \neq 0 \ \exp (\eta) & \text { if } a=0\end{cases}$$
Variance functions for the continuous distributions as well as for the Poisson distribution can also be thought of in terms of powers. The following table displays the relationships:
\begin{tabular}{lll}
Family & Link & Power function \
\hline Gaussian & Identity & $\mu^0=1$ \
Poisson & Log & $\mu^1=\mu$ \
Gamma & Square & $\mu^2$ \
Inverse Gaussian & Cube & $\mu^3$
\end{tabular}

We used a power analysis on claims. dta discussed in chapter $6$ on the gamma family. The canonical reciprocal link was used to model the data. In power link terms, we used power $=-1$. Using power links, we can determine whether the canonical inverse reciprocal link is optimal. We can also ascertain whether another distribution may be preferable for the modeling of the data at hand.
We modeled the main effects for claims.dta as
. glm y i.pa i.cg i.va [fw=number], family(gamma)
The algorithm used the default canonical inverse reciprocal link. Using the power link option, we may obtain the same result by specifying
glm y i.pa i.cg i.va [fw=number], family (gamma) link (power -1)
The following table shows us that the most preferable link for the gamma family is the canonical reciprocal link. If the data are modeled with the inverse Gaussian family, then the most preferable link is the inverse square root. We do not compare deviance values across families. To make comparisons of models across families, we use the BIC or AIC statistics. One must also evaluate the significance of the predictors. Here the significance of predictors is nearly identical.
\begin{tabular}{rrr}
Link & Gamma deviance & Inverse Gaussian deviance \
\hline-2.0 & 130.578 & 0.656 \
-1.5 & 126.826 & 0.638 \
-1.0 & ${ }^* 124.783$ & 0.628 \
-0.5 & 124.801 & $* 0.626$ \
0 & 127.198 & 0.634 \
0.5 & 132.228 & 0.665 \
1.0 & 139.761 & 0.687 \
\hline
\end{tabular}

广义线性模型代考

\begin{tabular}{lcc}
Link & Function & Power function \hline Identity & $\mu$ & $\mu^1$ \Log &$\ln (\mu)$ & $\mu^0$ \Reciprocal &$1 / \mu$ & $\mu^{-1}$ \Inverse quadratic &$1 / \mu^2$ & $\mu^{-2}$
\end{tabular}

$$\operatorname{Power}(a)= \begin{cases}\mu^a & \text { if } a \neq 0 \ \ln (\mu) & \text { if } a=0\end{cases}$$

$$\operatorname{Power}(a)= \begin{cases}\eta^{-a} & \text { if } a \neq 0 \ \exp (\eta) & \text { if } a=0\end{cases}$$

\begin{tabular}{lll}
Family & Link & Power function \hline Gaussian & Identity & $\mu^0=1$ \Poisson & Log &$\mu^1=\mu$ \Gamma & Square &$\mu^2$ \Inverse Gaussian & Cube &$\mu^3$
\end{tabular}

． [fw=number]， family(γ)

GLM y .pa .cg .va [fw=number]， family (gamma) link (power -1)

\begin{tabular}{rrr}
Link & Gamma deviance & Inverse Gaussian deviance \hline-2.0 & 130.578 & 0.656 -1.5 & 126.826 & 0.638-1.0 &${ }^* 124.783$ & 0.628 -0.5 & 124.801 &$* 0.626$ \0 & 127.198 & 0.634\0.5 & 132.228 & 0.665\1.0 & 139.761 & 0.687\hline
\end{tabular}

统计代写|广义线性模型代写generalized linear model代考|Derivation of the gamma model

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

统计代写|广义线性模型代写generalized linear model代考|Derivation of the gamma model

The base density function for the gamma distribution is
$$f(y ; \mu, \phi)=\frac{1}{y \Gamma(1 / \phi)}\left(\frac{y}{\mu \phi}\right)^{1 / \phi} \exp \left(-\frac{y}{\mu \phi}\right)$$
In exponential-family form, the above probability density appears as
$$f(y ; \mu, \phi)=\exp \left{\frac{y / \mu-(-\ln \mu)}{-\phi}+\frac{1-\phi}{\phi} \ln y-\frac{\ln \phi}{\phi}-\ln \Gamma\left(\frac{1}{\phi}\right)\right}$$
This equation provides us with the link and the cumulant given by
\begin{aligned} \theta & =1 / \mu \ b(\theta) & =-\ln (\mu) \end{aligned}
From this, we may derive the mean and the variance
\begin{aligned} b^{\prime}(\theta) & =\frac{\partial b}{\partial \mu} \frac{\partial \mu}{\partial \theta} \ & =\left(-\frac{1}{\mu}\right)\left(-\mu^2\right) \ & =\mu \ b^{\prime \prime}(\theta) & =\frac{\partial^2 b}{\partial \mu^2}\left(\frac{\partial \mu}{\partial \theta}\right)+\frac{\partial b}{\partial \mu} \frac{\partial^2 \mu}{\partial \theta^2} \ & =(1)\left(-\mu^2\right) \ & =-\mu^2 \end{aligned}
The variance here is an ingredient of the variance of $y$, which is found using $b^{\prime \prime}(\theta) a(\phi)=-\mu^2(-\phi)=\phi \mu^2$.

We now present a rather famous example of a reciprocal-linked gamma dataset. The example first gained notoriety in McCullagh and Nelder (1989) and later was given a full examination in Hilbe and Turlach (1995). The example deals with car insurance claims (claims . dta) and models average claims for damage to an owner’s car on the basis of the policy holder’s age group (PA 1-8), the vehicle age group (VA 1-4), and the car group (CG 1-4). A frequency weight is given, called number, which represents the number of identical covariate patterns related to a particular outcome.
The criterion of coefficient of variation constancy across cell groups is assumed and has been validated in previous studies. Again, the gamma model is robust to deviation from this criterion, but not so much that it should not be assessed. This is particularly the case with the canonical link model.
A schema of the model given the reciprocal link is
$$\eta=\left(\beta_0+\beta_1 \mathrm{PA}+\beta_2 \mathrm{CG}+\beta_3 \mathrm{VA}\right)^{-1}$$
The main-effects model is displayed below. The levels for the age group, vehicle age group, and car group are included in the model through automated production of indicator variables by using Stata’s glm command with factor variables.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Derivation of the gamma model

$$f(y ; \mu, \phi)=\frac{1}{y \Gamma(1 / \phi)}\left(\frac{y}{\mu \phi}\right)^{1 / \phi} \exp \left(-\frac{y}{\mu \phi}\right)$$

$$f(y ; \mu, \phi)=\exp \left{\frac{y / \mu-(-\ln \mu)}{-\phi}+\frac{1-\phi}{\phi} \ln y-\frac{\ln \phi}{\phi}-\ln \Gamma\left(\frac{1}{\phi}\right)\right}$$

\begin{aligned} \theta & =1 / \mu \ b(\theta) & =-\ln (\mu) \end{aligned}

\begin{aligned} b^{\prime}(\theta) & =\frac{\partial b}{\partial \mu} \frac{\partial \mu}{\partial \theta} \ & =\left(-\frac{1}{\mu}\right)\left(-\mu^2\right) \ & =\mu \ b^{\prime \prime}(\theta) & =\frac{\partial^2 b}{\partial \mu^2}\left(\frac{\partial \mu}{\partial \theta}\right)+\frac{\partial b}{\partial \mu} \frac{\partial^2 \mu}{\partial \theta^2} \ & =(1)\left(-\mu^2\right) \ & =-\mu^2 \end{aligned}

$$\eta=\left(\beta_0+\beta_1 \mathrm{PA}+\beta_2 \mathrm{CG}+\beta_3 \mathrm{VA}\right)^{-1}$$

统计代写|广义线性模型代写generalized linear model代考|The Gaussian family

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统计代写|广义线性模型代写generalized linear model代考|The Gaussian family

In the 1800 s, Johann Carl Friedrich Gauss, the eponymous prince of mathematics, described the least-squares fitting method and the distribution that bears his name. Having a symmetric bell shape, the Gaussian density function is often referred to as the normal density. The normal cumulative distribution function is a member of the exponential family of distributions and so may be used as a basis for a GLM. Moreover, because the theory of GLMS was first conceived to be an extension to the normal ordinary least-squares (OLS) model, we will begin with an exposition of how OLS fits into the GLM framework. Understanding how other GLM models generalize this basic form should then be easier.
Regression models based on the Gaussian or normal distribution are commonly referred to as oLs models. This standard regression model is typically the first model taught in beginning statistics courses.

The Gaussian distribution is a continuous distribution of real numbers with support over the real line $\Re=(-\infty,+\infty)$. A model based on this distribution assumes that the response variable, called the dependent variable in the social sciences, takes the shape of the Gaussian distribution. Equivalently, we consider that the error term in the equation
$$y=x \beta+\epsilon$$
is normally or Gaussian distributed. Generalized linear interactive modeling (GLIM), the original GLM software program, uses the term ERROR to designate the family or distribution of a model. Regardless, we may think of the underlying distribution as that of either the response variable or the error term.

统计代写|广义线性模型代写generalized linear model代考|Derivation of the GLM Gaussian family

The various components of a particular GLM can be obtained from the base probability function. The manner in which the probability function is parameterized relates directly to the algorithm used for estimation, that is, iteratively reweighted least squares (IRLS) or Newton-Raphson (N-R). If we intend to estimate parameters by using the standard or traditional IRLS algorithm, then the probability function is parameterized in terms of the mean $\mu$ (estimated fitted value). On the other hand, if the estimation is to be performed in terms of $\mathrm{N}-\mathrm{R}$, parameterization is in terms of $x \beta$ (the linear predictor). To clarify, the IRLS algorithm considers maximizing a function in terms of the mean where the introduction of covariates is delayed until specification of the link function. On the other hand, N-R typically writes the function to be maximized in terms of the specific link function so that derivatives may be clearly seen.

For the Gaussian distribution, $\mu$ is the same as $x \beta$ in its canonical form. We say that the canonical link is the identity link ; that is, there is a straightforward identity between the fitted value and the linear predictor. The canonical-link Gaussian regression model is the paradigm instance of a model with an identity $\operatorname{link}$.

The Gaussian probability density function , parameterized in terms of $\mu$, is expressed as
$$f\left(y ; \mu, \sigma^2\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left{-\frac{(y-\mu)^2}{2 \sigma^2}\right}$$
where $f(\cdot)$ is the generic form of the density function of $y$, given parameters $\mu$ and $\sigma^2 ; y$ is the response variable; $\mu$ is the mean parameter; and $\sigma^2$ is the scale parameter.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|The Gaussian family

19世纪19年代，数学王子约翰·卡尔·弗里德里希·高斯(john Carl Friedrich Gauss)描述了最小二乘拟合方法和以他的名字命名的分布。高斯密度函数具有对称的钟形，通常被称为正态密度。正态累积分布函数是指数分布族的一员，因此可以用作GLM的基础。此外，由于GLMS理论最初被认为是普通最小二乘(OLS)模型的扩展，我们将首先阐述OLS如何适应GLM框架。理解其他GLM模型是如何概括这种基本形式的应该会更容易。

$$y=x \beta+\epsilon$$

统计代写|广义线性模型代写generalized linear model代考|Derivation of the GLM Gaussian family

$$f\left(y ; \mu, \sigma^2\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left{-\frac{(y-\mu)^2}{2 \sigma^2}\right}$$

有限元方法代写

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MATLAB代写

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

统计代写|广义线性模型代写generalized linear model代考|Generalizations of linear regression $R_2$ interpretations

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统计代写|广义线性模型代写generalized linear model代考|Generalizations of linear regression $R_2$ interpretations

Starting from each of the interpretations in the preceding section, one may generalize the associated formula for use with models other than linear regression.
The most important fact to remember is that a generalized version of the $R^2$ statistic extends the formula associated with the particular interpretation that served as its genesis. As generalizations, these statistics are sometimes called pseudo- $R^2$ statistics. However, this name makes it too easy to forget which original formula was used in the derivation. Many people make the mistake that the use of any pseudo- $R^2$ statistic can be interpreted in the familiar and popular “percentage variance explained” manner. Although the various interpretations in linear regression result in the same calculated value, the pseudo- $R^2$ scalar criteria generalized from different definitions do not result in the same value.
Just as there are adjusted $R^2$ measures for linear regression, there is current research in adjusting pseudo- $R^2$ criterion measures. We list only a few of the proposed adjusted measures.
Efron’s pseudo-R’2
Efron (1978) defines the following measure as an extension to the regression model’s “percentage variance explained” interpretation:
$$R_{\text {Efron }}^2=1-\frac{\sum_{i=1}^n\left(y_i-\widehat{y}i\right)^2}{\sum{i=1}^n\left(y_i-\bar{y}\right)^2}$$
Efron’s presentation was directed at binary outcome models and listed $\widehat{\pi}i$ for $\widehat{y}_i$. The measure could be used for continuous models. The equation is the same as given in (4.44), and the measure is sometimes called the sum of squares $R^2$ or $R{\mathrm{SS}^*}^2$

统计代写|广义线性模型代写generalized linear model代考|Ben-Akiva and Lerman adjusted likelihood-ratio index

Ben-Akiva and Lerman (1985) extended McFadden’s pseudo- $R^2$ measure to include an adjustment. Their adjustment is in the spirit of the adjusted $R^2$ measure in linear regression, and the formula is given by
$$R_{\text {Ben-Akiva\&Lerman }}^2=1-\frac{\mathcal{L}\left(M_\beta\right)-p}{\mathcal{L}\left(M_\alpha\right)}$$
where $p$ is the number of parameters in the $M_\beta$ model. Adjusted $R^2$ measures have been proposed in several forms. The aim of adjusting the calculation of the criterion is to address the fact that $R^2$ monotonically increases as terms are added to the model. Adjusted $R^2$ measures include penalty or shrinkage terms so that noncontributory terms will not significantly increase the criterion measure.
Note that this equation can be used for any model fit by ML.
McKelvey and Zavoina ratio of variances
McKelvey and Zavoina (1975) define the following measure as an extension of the “ratio of variances” interpretation:
\begin{aligned} & R_{\text {McKelvey\&Zavoina }}^2=\frac{\widehat{V}(\widehat{y} )}{\widehat{V}\left(y^\right)} \ & =\frac{\widehat{V}\left(\widehat{y}^\right)}{\widehat{V}\left(\widehat{y}^\right)+V(\epsilon)} \ & V(\epsilon)= \begin{cases}1 & \text { probit } \ \pi^2 / 3 & \text { logit }\end{cases} \ & \widehat{V}\left(\widehat{y}^*\right)=\widehat{\boldsymbol{\beta}}^{\prime} \widehat{V} \widehat{\boldsymbol{\beta}} \ & \widehat{V}=\text { variance-covariance matrix of } \boldsymbol{\beta} \ & \end{aligned}
Note that this equation can be used for ordinal , binary , or censored outcomes.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Generalizations of linear regression $R_2$ interpretations

Efron的伪r ‘2
Efron(1978)将以下度量定义为回归模型“百分比方差解释”解释的延伸:
$$R_{\text {Efron }}^2=1-\frac{\sum_{i=1}^n\left(y_i-\widehat{y}i\right)^2}{\sum{i=1}^n\left(y_i-\bar{y}\right)^2}$$
Efron的演讲针对的是二元结果模型，并列出了$\widehat{y}_i$的$\widehat{\pi}i$。该方法可用于连续模型。方程与式(4.44)中给出的相同，度量有时被称为平方和$R^2$或 $R{\mathrm{SS}^*}^2$

统计代写|广义线性模型代写generalized linear model代考|Ben-Akiva and Lerman adjusted likelihood-ratio index

Ben-Akiva和Lerman(1985)扩展了McFadden的伪$R^2$措施，以包括调整。它们的调整本着线性回归中调整$R^2$测度的精神，其公式由
$$R_{\text {Ben-Akiva\&Lerman }}^2=1-\frac{\mathcal{L}\left(M_\beta\right)-p}{\mathcal{L}\left(M_\alpha\right)}$$

McKelvey和Zavoina方差比
McKelvey和Zavoina(1975)将以下度量定义为“方差比”解释的延伸:
\begin{aligned} & R_{\text {McKelvey\&Zavoina }}^2=\frac{\widehat{V}(\widehat{y} )}{\widehat{V}\left(y^\right)} \ & =\frac{\widehat{V}\left(\widehat{y}^\right)}{\widehat{V}\left(\widehat{y}^\right)+V(\epsilon)} \ & V(\epsilon)= \begin{cases}1 & \text { probit } \ \pi^2 / 3 & \text { logit }\end{cases} \ & \widehat{V}\left(\widehat{y}^*\right)=\widehat{\boldsymbol{\beta}}^{\prime} \widehat{V} \widehat{\boldsymbol{\beta}} \ & \widehat{V}=\text { variance-covariance matrix of } \boldsymbol{\beta} \ & \end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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

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

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

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

In assessing the model, residuals measure the discrepancy between our observed and fitted values for each observation. The degree to which one observation affects the estimated coefficients is a measure of influence.

Pierce and Schafer (1986) and Cox and Snell (1968) provide excellent surveys of various definitions for residuals in GLMs. In the following sections, we present the definitions of several residuals that have been proposed for GLMS.
Discussions on residuals are hampered by a lack of uniform terminology throughout the literature, so we will expand our descriptions to facilitate comparison with other books and papers.

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

The jackknife estimate of variance estimates variability in fitted parameters by comparing results from leaving out one observation at a time in repeated estimations. Jackknifing is based on a data resampling procedure in which the variability of an estimator is investigated by repeating an estimation with a subsample of the data. Subsample estimates are collected and compared with the full sample estimate to assess variability. Introduced by Quenouille (1949) , an excellent review of this technique and extensions is available in Miller (1974).
The sandwich estimate of variance is related to the jackknife. Asymptotically, it is equivalent to the one-step and iterated jackknife estimates, and as shown in Efron (1981), the sandwich estimate of variance is equal to the infinitesimal jackknife.
There are two general methods for calculating jackknife estimates of variance. One approach is to calculate the variability of the individual estimates from the full sample estimate. We supply formulas for this approach. A less conservative approach is to calculate the variability of the individual estimates from the average of the individual estimates. You may see references to this approach in other sources. Generally, we prefer the approach outlined here because of its more conservative nature.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

Newey和West(1987)讨论了一种综合考虑每个滞后的贡献的一般方法。然后，具体的实现为每个滞后的分数贡献分配一个权重。在相关章节中，我们将介绍与这种通用方法一起使用的各种权重函数。

\begin{aligned} \widehat{V}{\mathrm{NW}} & =\widehat{V}_H^{-1} \widehat{B}{\mathrm{NW}} \widehat{V}H^{-1} \ \widehat{B}{\mathrm{NW}} & =C\left{\widehat{\Omega}0+\sum{j=1}^G \omega\left(\frac{j}{q+1}\right)\left(\widehat{\Omega}j+\widehat{\Omega}_j^{\prime}\right)\right} \ \widehat{\Omega}_j & =\sum{i=j+1}^n x_i \widehat{r}i^S \widehat{T}{i-j}^S x_i^T \ \omega(z) & =\text { sandwich weights } \ \widehat{r}_i^S & =\text { score residuals (see section 4.4.9) }=\nabla_i\left(y_i-\mu_i\right) / v_i\end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

These variance estimators are referred to as HAC variance estimators because they are heteroskedasticity- and autocorrelation-consistent estimates of the variances (of parameter estimators). A weighted sandwich estimate of variance calculates a (possibly) different middle of the sandwich. Instead of using only the usual score contributions, a weighted sandwich estimate of variance calculates a weighted mean of score contributions and lagged score contributions.
Newey and West (1987) discuss a general method for combining the contributions for each considered lag. The specific implementation then assigns a weight to each lagged score contribution. In related sections, we present various weight functions for use with this general approach.

In the following, let $n$ be the number of observations, $p$ be the number of predictors, $G$ be the maximum lag, $C$ be an overall scale factor, and $q$ be the prespecified bandwidth (number of lags for which the correlation is nonzero). The overall scale factor is usually defined as one but could be defined as $n /(n-p)$ to serve as a small sample scale factor adjustment.

\begin{aligned} \widehat{V}{\mathrm{NW}} & =\widehat{V}_H^{-1} \widehat{B}{\mathrm{NW}} \widehat{V}H^{-1} \ \widehat{B}{\mathrm{NW}} & =C\left{\widehat{\Omega}0+\sum{j=1}^G \omega\left(\frac{j}{q+1}\right)\left(\widehat{\Omega}j+\widehat{\Omega}_j^{\prime}\right)\right} \ \widehat{\Omega}_j & =\sum{i=j+1}^n x_i \widehat{r}i^S \widehat{T}{i-j}^S x_i^T \ \omega(z) & =\text { sandwich weights } \ \widehat{r}_i^S & =\text { score residuals (see section 4.4.9) }=\nabla_i\left(y_i-\mu_i\right) / v_i\end{aligned}

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

The jackknife estimate of variance estimates variability in fitted parameters by comparing results from leaving out one observation at a time in repeated estimations. Jackknifing is based on a data resampling procedure in which the variability of an estimator is investigated by repeating an estimation with a subsample of the data. Subsample estimates are collected and compared with the full sample estimate to assess variability. Introduced by Quenouille (1949) , an excellent review of this technique and extensions is available in Miller (1974).
The sandwich estimate of variance is related to the jackknife. Asymptotically, it is equivalent to the one-step and iterated jackknife estimates, and as shown in Efron (1981), the sandwich estimate of variance is equal to the infinitesimal jackknife.
There are two general methods for calculating jackknife estimates of variance. One approach is to calculate the variability of the individual estimates from the full sample estimate. We supply formulas for this approach. A less conservative approach is to calculate the variability of the individual estimates from the average of the individual estimates. You may see references to this approach in other sources. Generally, we prefer the approach outlined here because of its more conservative nature.

广义线性模型代考

统计代写|广义线性模型代写generalized linear model代考|Weighted sandwich: Newey–West

Newey和West(1987)讨论了一种综合考虑每个滞后的贡献的一般方法。然后，具体的实现为每个滞后的分数贡献分配一个权重。在相关章节中，我们将介绍与这种通用方法一起使用的各种权重函数。

\begin{aligned} \widehat{V}{\mathrm{NW}} & =\widehat{V}_H^{-1} \widehat{B}{\mathrm{NW}} \widehat{V}H^{-1} \ \widehat{B}{\mathrm{NW}} & =C\left{\widehat{\Omega}0+\sum{j=1}^G \omega\left(\frac{j}{q+1}\right)\left(\widehat{\Omega}j+\widehat{\Omega}_j^{\prime}\right)\right} \ \widehat{\Omega}_j & =\sum{i=j+1}^n x_i \widehat{r}i^S \widehat{T}{i-j}^S x_i^T \ \omega(z) & =\text { sandwich weights } \ \widehat{r}_i^S & =\text { score residuals (see section 4.4.9) }=\nabla_i\left(y_i-\mu_i\right) / v_i\end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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

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

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

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

In developing a model, we hope to generate fitted values $\widehat{\mu}$ that are close to the data $y$. For a dataset with $n$ observations, we may consider candidate models with one to $n$ parameters. The simplest model would include only one parameter. The best one-parameter model would result in $\widehat{\mu}_i=\mu$ (for all $i$ ). Although the model is parsimonious, it does not estimate the variability in the data. The saturated model (with $n$ parameters) would include one parameter for each observation and result in $\widehat{\mu}_i=y_i$. This model exactly reproduces the data but is uninformative because there is no summarization of the data.

We define a measure of fit for the model as twice the difference between the log likelihoods of the model of interest and the saturated model. Because this difference is a measure of the deviation of the model of interest from a perfectly fitting model, the measure is called the deviance. Our competing goals in modeling are to find the simplest model (fewest parameters) that has the smallest deviance (reproduces the data).
The deviance, $D$, is given by
$$D=\sum_{i=1}^n 2\left[y_i\left{\theta\left(y_i\right)-\theta\left(\mu_i\right)\right}-b\left{\theta\left(y_i\right)\right}+b\left{\theta\left(\mu_i\right)\right}\right]$$
where the equation is given in terms of the mean parameter $\mu$ instead of the canonical parameter $\theta$. In fitting a particular model, we seek the values of the parameters that minimize the deviance. Thus, optimization in the IRLS algorithm is achieved when the difference in deviance calculations between successive iterations is small (less than some chosen tolerance). The values of the parameters that minimize the deviance are the same as the values of the parameters that maximize the likelihood.

统计代写|广义线性模型代写generalized linear model代考|Estimated variance matrices

It is natural to ask how the Newton-Raphson (based on the observed Hessian) variance estimates compare with the usual (based on the expected Hessian) variance estimates obtained using the IRLS algorithm outlined in the preceding section. The matrix of second derivatives in the IRLS algorithm is equal to the first term in (3.31). As Newson (1999) points out, the calculation of the expected Hessian is simplified from that of the observed Hessian because we assume that $E(\mu-y)=0$ or, equivalently, the conditional mean of $y$ given $X$ is correct. As such, the IRLS algorithm assumes that the conditional mean is specified correctly. Both approaches result in parameter estimates that differ only because of numeric roundoff or because of differences in optimization criteria.

This distinction is especially important in the calculation of sandwich estimates of variance. The Hessian may be calculated as given above in (3.31) or may be calculated using the more restrictive (naïve) assumptions of the IRLS algorithm as
$$E\left(\frac{\partial^2 \mathcal{L}}{\partial \beta_j \partial \beta_k}\right)=-\sum_{i=1}^n \frac{1}{a(\phi)} \frac{1}{v\left(\mu_i\right)}\left(\frac{\partial \mu}{\partial \eta}\right)i^2 x{j i} x_{k i}$$
occurs because for the canonical link we can make the substitution that $\theta=\eta$ to zero because

\begin{aligned}
\left(\mu_i-y_i\right) & \left{\frac{1}{v\left(\mu_i\right)^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial v\left(\mu_i\right)}{\partial \mu}-\frac{1}{v\left(\mu_i\right)}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}_i \
& =\left(\mu_i-y_i\right)\left{\frac{1}{(\partial \mu / \partial \eta)_i^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\frac{1}{(\partial \mu / \partial \eta)_i}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}(3.52) \
& =\left(\mu_i-y_i\right)\left{\frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\left(\frac{\partial \eta}{\partial \mu}\right)_i\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right} \
& =\left(\mu_i-y_i\right)\left{\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i-\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i\right} \
& =0
\end{aligned}

广义线性模型代考

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

$$D=\sum_{i=1}^n 2\left[y_i\left{\theta\left(y_i\right)-\theta\left(\mu_i\right)\right}-b\left{\theta\left(y_i\right)\right}+b\left{\theta\left(\mu_i\right)\right}\right]$$

统计代写|广义线性模型代写generalized linear model代考|Estimated variance matrices

$$E\left(\frac{\partial^2 \mathcal{L}}{\partial \beta_j \partial \beta_k}\right)=-\sum_{i=1}^n \frac{1}{a(\phi)} \frac{1}{v\left(\mu_i\right)}\left(\frac{\partial \mu}{\partial \eta}\right)i^2 x{j i} x_{k i}$$

\begin{aligned}
\left（\mu＿i-y＿i\right) ＆ \left{\frac{1}{v\left(\mu_i\right)^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial v\left(\mu_i\right)}{\partial \mu}-\frac{1}{v\left(\mu_i\right)}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}＿i \＆ =\left（\mu＿i-y＿i\right）\left{\frac{1}{(\partial \mu / \partial \eta)_i^2}\left(\frac{\partial \mu}{\partial \eta}\right)_i^2 \frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\frac{1}{(\partial \mu / \partial \eta)_i}\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right}(3.52) \＆ =\left（\mu＿i-y＿i\right）\left{\frac{\partial}{\partial \mu_i}\left(\frac{\partial \mu}{\partial \eta}\right)_i-\left(\frac{\partial \eta}{\partial \mu}\right)_i\left(\frac{\partial^2 \mu}{\partial \eta^2}\right)_i\right} \＆ =\left（\mu＿i-y＿i\right）\left{\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i-\left(\frac{\partial^2 \mu}{\partial \mu \partial \eta}\right)_i\right} \＆ =0
\end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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

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

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

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

GLMS are traditionally formulated within the framework of the exponential family of distributions. In the associated representation, we can derive a general model that may be fit using the scoring process (IRLS) detailed in section 3.3 . Many people confuse the estimation method with the class of GLMs. This is a mistake because there are many estimation methods. Some software implementations allow specification of more diverse models than others. We will point this out throughout the text.
The exponential family is usually (there are other algebraically equivalent forms in the literature) written as
$$f_y(y ; \theta, \phi)=\exp \left{\frac{y \theta-b(\theta)}{a(\phi)}+c(y, \phi)\right}$$
where $\theta$ is the canonical (natural) parameter of location and $\phi$ is the parameter of scale. The location parameter (also known as the canonical link function) relates to the means, and the scalar parameter relates to the variances for members of the exponential family of distributions including Gaussian, gamma, inverse Gaussian, and others. Using the notation of the exponential family provides a means to specify models for continuous, discrete, proportional, count, and binary outcomes.

In the exponential family presentation, we construe each of the $y_i$ observations as being defined in terms of the parameters $\theta$. Because the observations are independent, the joint density of the sample of observations $y_i$, given parameters $\theta$ and $\phi$, is defined by the product of the density over the individual observations (review section 2.2). Interested readers can review Barndorff-Nielsen (1976) for the theoretical justification that allows this factorization:
$$f_{y_1, y_2, \ldots, y_n}\left(y_1, y_2, \ldots, y_n ; \theta, \phi\right)=\prod_{i=1}^n \exp \left{\frac{y_i \theta_i-b\left(\theta_i\right)}{a(\phi)}+c\left(y_i, \phi\right)\right}$$

统计代写|广义线性模型代写generalized linear model代考|Example: Using an offset in a GLM

In subsequent chapters (especially chapter $3$ ), we illustrate the two main components of the specification of a GLM. The first component of a GLM specification is a function of the linear predictor, which substitutes for the location (mean) parameter of the exponential family. This function is called the link function because it links the expected value of the outcome to the linear predictor comprising the regression coefficients; we specify this function with the link ( ) option. The second component of a GLM specification is the variance as a scaled function of the mean. In Stata, this function is specified using the name of a particular member distribution of the exponential family; we specify this function with the family ( ) option. The example below highlights a log-link Poisson GLM.
For this example, it is important to note the treatment of the offset in the linear predictor. The particular choices for the link and variance functions are not relevant to the utility of the offset.

Below, we illustrate the use of an offset with Stata’s glm command. From an analysis presented in chapter 12 , consider the output of the following model:

We would like to test whether the coefficient on white is equal to -0.20 . We could use Stata’s test command to obtain a Wald test

test white=-.20
(1) [los] white $=-.2$
\begin{aligned} \operatorname{chi}(1) & = & 2.83 \ \text { Prob }>\operatorname{chi2} & = & 0.0924 \end{aligned}
which indicates that -0.15 (coefficient on white) is not significantly different at a $5 \%$ level from -0.20 . However, we want to use a likelihood-ratio test, which is usually a more reliable test of parameter estimate significance. Stata provides a command that stores the likelihood from the unrestricted model (above) and then compares it with a restricted model. Having fit the unrestricted model, our attention now turns to fitting a model satisfying our specific set of constraints. Our constraint is that the coefficient on white be restricted to the constant value -0.20 .

广义线性模型代考

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

$$f_y(y ; \theta, \phi)=\exp \left{\frac{y \theta-b(\theta)}{a(\phi)}+c(y, \phi)\right}$$

$$f_{y_1, y_2, \ldots, y_n}\left(y_1, y_2, \ldots, y_n ; \theta, \phi\right)=\prod_{i=1}^n \exp \left{\frac{y_i \theta_i-b\left(\theta_i\right)}{a(\phi)}+c\left(y_i, \phi\right)\right}$$

统计代写|广义线性模型代写generalized linear model代考|Example: Using an offset in a GLM

(1) [los] white $=-.2$
\begin{aligned} \operatorname{chi}(1) & = & 2.83 \ \text { Prob }>\operatorname{chi2} & = & 0.0924 \end{aligned}

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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

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

statistics-lab™ 为您的留学生涯保驾护航 在代写广义线性模型generalized linear model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义线性模型generalized linear model代写方面经验极为丰富，各种代写广义线性模型generalized linear model相关的作业也就用不着说。

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

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

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

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

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

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

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

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

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