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。
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统计代写|广义线性模型代写generalized linear model代考|Power links
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}
统计代写|广义线性模型代写generalized linear model代考|Example: Power link
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
统计代写|广义线性模型代写generalized linear model代考|Power links
与GLM分布的连续族成员相关联的链接可以用幂来考虑。事实上，除了标准的二项式链接和负二项式的规范形式外，所有链接都是$\mu$的幂。关系如下表所示:
\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}
因此，可以建立一个通用的电源链路函数为
$$
\operatorname{Power}(a)= \begin{cases}\mu^a & \text { if } a \neq 0 \ \ln (\mu) & \text { if } a=0\end{cases}
$$
对应的泛型逆链函数为
$$
\operatorname{Power}(a)= \begin{cases}\eta^{-a} & \text { if } a \neq 0 \ \exp (\eta) & \text { if } a=0\end{cases}
$$
连续分布和泊松分布的方差函数也可以用幂来考虑。关系如下表所示:
\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}
统计代写|广义线性模型代写generalized linear model代考|Example: Power link
我们对索赔进行了功率分析。Dta在$6$章讨论伽玛族。使用规范互反链接对数据进行建模。在power link术语中，我们使用power $=-1$。利用功率链路，我们可以确定正则逆互链路是否最优。我们还可以确定另一种分布是否更适合对手头的数据进行建模。
我们模拟了索赔的主要影响。Dta as
． [fw=number]， family(γ)
该算法使用默认的规范逆互链接。使用power link选项，我们可以通过指定
GLM y .pa .cg .va [fw=number]， family (gamma) link (power -1)
下表告诉我们，伽玛族最理想的链接是标准互易链接。如果数据是用反高斯族建模的，那么最可取的链接是反平方根。我们不会比较不同家庭的偏差值。为了对不同家庭的模型进行比较，我们使用BIC或AIC统计数据。人们还必须评估预测因素的重要性。在这里，预测因子的重要性几乎相同。
\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}
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