如果你也在 怎样代写广义线性模型Generalized linear model 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。广义线性模型Generalized linear model通过允许响应变量具有任意分布(而不是简单的正态分布)，以及响应变量的任意函数(链接函数)随预测器线性变化(而不是假设响应本身必须线性变化)，涵盖了所有这些情况。例如，上面预测海滩出席人数的情况通常会用泊松分布和日志链接来建模，而预测海滩出席率的情况通常会用伯努利分布(或二项分布，取决于问题的确切表达方式)和对数-几率(或logit)链接函数来建模。

广义线性模型Generalized linear model普通线性回归将给定未知量(响应变量，随机变量)的期望值预测为一组观测值(预测因子)的线性组合。这意味着预测器的恒定变化会导致响应变量的恒定变化(即线性响应模型)。当响应变量可以在任意一个方向上以良好的近似值无限变化时，或者更一般地适用于与预测变量(例如人类身高)的变化相比仅变化相对较小的任何数量时，这是适当的。

couryes-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|The probit model

The probit model was first used in bioassay or quantal analysis. Typically, the probability of death was measured against the log of some toxin (for example, an insecticide). Whether death occurred depended on the tolerance the subject had to the toxic agent. Subjects with a lower tolerance were more likely to die. Tolerance was assumed to be distributed normally, hence the use of the probit transform, $\mu=\Phi(x \boldsymbol{\beta})$. Researchers still use probit for bioassay analysis, and they often use it to model other data situations.
The probit link function is the inverse of $\Phi$, the cumulative normal distribution defined as
$$
\mu=\int_{-\infty}^\eta \phi(u) d u
$$
where $\phi(u)$ is the standard normal density function
$$
\frac{1}{\sqrt{2 \pi}} \exp \left(-\frac{1}{2} u^2\right)
$$
Using a probit regression model on binary or grouped binomial data typically results in output similar to that from logistic regression. Logistic regression is usually preferred because of the wide variety of fit statistics associated with the model. Moreover, exponentiated probit coefficients cannot be interpreted as odds ratios, but they can be interpreted as odds ratios in logistic models (see section 10.6.2). However, if normality is involved in the linear relationship, as it often is in bioassay, then probit may be the appropriate model. It may also be used when the researcher is not interested in odds but rather in prediction or classification. Then if the deviance of a probit model is significantly lower than that of the corresponding logit model, the former is preferred. This dictum holds when comparing any of the links within the binomial family.

统计代写|广义线性模型代写generalized linear model代考|The clog-log and log-log models

Clog-log and log-log links are asymmetrically sigmoidal. For clog-log models, the upper part of the sigmoid is more elongated or stretched out than the logit or probit. Log-log models are based on the converse. The bottom of the sigmoid is elongated or skewed to the left.

We provide the link, inverse link, and derivative of the link for both clog-log and log-log models in table 10.2. As we showed for the probit model, we can change logit or probit to clog-log or log-log by replacing the respective functions in the GLM-binomial algorithm.
Figure 10.3 shows the asymmetry of the clog-log and log-log links. We investigate the consequences of this asymmetry on the fitted values and discuss the relationship of the coefficient estimates from models using these links.

We may wish to change the focus of modeling from the positive to the negative outcomes. Assume that we have a binary outcome variable $y$ and the reverse outcome variable $z=1-y$. We have a set of covariates $X$ for our model. If we use a symmetric link, then we can fit a binary model to either
outcome. The resulting coefficients will differ in sign for the two models and the predicted probabilities (fitted values) will be complementary. They are complementary in that the fitted probabilities for the model on $y$ plus the fitted probabilities for the model on $z$ add to one. See our previous warning note on the sign change of the coefficients in section 9.2.

We say that $\operatorname{probit}(y)$ and $\operatorname{probit}(z)$ form a complementary pair and that logit( $y)$ and $\operatorname{logit}(z)$ form a complementary pair. Although the equivalence of the link in the complementary pair is true with symmetric links, it is not true for the asymmetric links. The log-log and clog-log links form a complementary pair. This means that $\log \log (y)$ and $\operatorname{cog} \log (z)$ form a complementary pair and that $\log \log (z)$ and cloglog $(y)$ form a complementary pair.

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 probit model

概率模型首先用于生物测定或定量分析。通常，死亡概率是根据某种毒素(例如杀虫剂)的对数来测量的。是否发生死亡取决于受试者对毒物的耐受性。耐受性较低的受试者更有可能死亡。容差假定为正态分布，因此使用概率变换$\mu=\Phi(x \boldsymbol{\beta})$。研究人员仍然使用probit进行生物测定分析，他们经常使用它来模拟其他数据情况。
probit链接函数是$\Phi$的倒数，累积正态分布定义为
$$
\mu=\int_{-\infty}^\eta \phi(u) d u
$$
其中$\phi(u)$是标准正态密度函数
$$
\frac{1}{\sqrt{2 \pi}} \exp \left(-\frac{1}{2} u^2\right)
$$
对二项或分组二项数据使用概率回归模型通常会得到与逻辑回归相似的输出。逻辑回归通常是首选的，因为各种各样的拟合统计与模型相关。此外，指数概率系数不能解释为比值比，但它们可以解释为逻辑模型中的比值比(见第10.6.2节)。然而，如果正态性涉及到线性关系，就像在生物测定中经常出现的那样，那么probit可能是合适的模型。当研究人员对概率不感兴趣，而是对预测或分类感兴趣时，也可以使用它。然后，如果probit模型的偏差显著低于相应的logit模型的偏差，则首选前者。这句格言适用于比较二项家族中的任何联系。

统计代写|广义线性模型代写generalized linear model代考|The clog-log and log-log models

log-log和log-log链接是非对称的s型。对于log-log模型，s型曲线的上半部分比logit或probit更拉长或伸展。对数-对数模型基于相反的情况。乙状结肠底部拉长或向左倾斜。

我们在表10.2中提供了log-log和log-log模型的链接、反向链接和链接的派生。正如我们在probit模型中所展示的那样，我们可以通过替换glm -二项式算法中的相应函数，将logit或probit更改为log-log或log-log。
图10.3显示了log-log和log-log链路的不对称性。我们研究了这种不对称对拟合值的影响，并讨论了使用这些链接的模型的系数估计的关系。

我们可能希望将建模的重点从积极的结果转向消极的结果。假设我们有一个二元结果变量$y$和一个反向结果变量$z=1-y$。我们的模型有一组协变量$X$。如果我们使用对称链接，那么我们可以将二元模型拟合到两者中
结果。两个模型的所得系数符号不同，预测概率(拟合值)是互补的。它们是互补的，因为$y$上模型的拟合概率加上$z$上模型的拟合概率相加为1。参见我们之前在9.2节中对系数符号变化的警告。

我们说$\operatorname{probit}(y)$和$\operatorname{probit}(z)$形成互补对，logit($y)$和$\operatorname{logit}(z)$)形成互补对。虽然互补对中的链路对于对称链路是等价的，但对于非对称链路则不是等价的。log-log和log-log链接是互补的一对。这意味着$\log \log (y)$和$\operatorname{cog} \log (z)$形成互补对，$\log \log (z)$和cloglog $(y)$形成互补对。

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