### 统计代写|广义线性模型代写generalized linear model代考|ST411

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
• Advanced Probability Theory 高等概率论
• 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|广义线性模型代写generalized linear model代考|Diagnostics

Regression diagnostics are useful in checking the assumptions of the model and in identifying any unusual points. As with linear models, residuals are the most important means of determining how well the data fits the model and where any changes or

improvements might be advisable. We can compute residuals as a difference between observed and fitted values. There are two kinds of fitted (or predicted) values:
linpred <- prediet (lmod)
predprob <- predict (lmod, type=” response”)
The former is the predicted value in the linear predictor scale, $\eta$, while the latter is the
predicted probability $p=\operatorname{logit}^{-1}(\eta)$. Here are the first few values and a confirmation
of the relationship between them:
These can also be obtained as residuals (lmod, type $=$ “response”). Following
the standard practice for diagnostics in linear models, we plot the residuals against
the fitted values:

plot (rawres linpred, xlab” “linear predictor”, ylab=” residuals”)
The plot, as seen in the first panel of Figure 2.6, is not very helpful. Because $y=0$ or 1 , the residual can take only two values given a fixed linear predictor. The upper line in the plot corresponds to $y=1$ and the lower line to $y=0$. We gain no insight into the fit of the model. We have chosen to plot the linear predictor rather than the predicted probability on the horizontal axis because the former provides a better spacing of the points in this direction.

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

The analysis thus far has used only two of the predictors available but we might construct a better model for the response if we used some of the other predictors. We might find that not all these predictors are helpful in explaining the response. We would like to identify a subset of the predictors that model the response well without including any superfluous predictors.

We could use the inferential methods to construct hypothesis tests to compare various candidate models and use this as a mechanism for choosing a model. Back-

ward elimination is one such method which is relatively easy to implement. The method proceeds sequentially:

1. Start with the full model including all the available predictors. We can add derived predictors formed from transformations or interactions between two or more predictors.
2. Compare this model with all the models consisting of one less predictor. Compute the $p$-value corresponding to each dropped predictor. The dropl function in $\mathrm{R}$ can be used for this purpose.
3. Eliminate the term with largest $p$-value that is greater than some preset critical value, say $0.05$. Return to the previous step. If no such term meets this criterion, stop and use the current model.

Thus predictors are sequentially eliminated until a final model is settled upon. Unfortunately, this is an inferior procedure. Although the algorithm is simple to use, it is hard to identify the problem to which it provides a solution. It does not identify the best set of predictors for predicting future responses. It is not a reliable indication of which predictors are the best explanation for the response. Even if one believes the fiction that there is a true model, this procedure would not be best for identifying such a model.

The Akaike information criterion (AIC) is a popular way of choosing a model see Section A.3 for more. The criterion for a model with likelihood $L$ and number of parameters $q$ is defined by
$$A I C=-2 \log L+2 q$$
We select the model with the smallest value of AIC among those under consideration. Any constant terms in the definition of log-likelihood can be ignored when comparing different models that will have the same constants. For this reason we can use $\mathrm{AIC}=$ deviance $+2 q$

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

As mentioned earlier, we cannot use the deviance for a binary response GLM as a measure of fit. We can use diagnostic plots of the binned residuals to help us identify inadequacies in the model but these cannot tell us whether the model fits or not. Even so the process of binning can help us develop a test for this purpose. We divide the observations up into $J$ bins based on the linear predictor. Let the mean response in the $j^{t h}$ bin be $y_{j}$ and the mean predicted probability be $\hat{p}{j}$ with $m{j}$ observations within the bin. We compute these values:
wogsm $<-$ na.omit (wogs)
wegsm \&- mutate (wcgsm, predprob”predict (lmod, type=” response”))
gdf <- group by (wcgsm, cut (linpred, breaksmunique (quantile (linpred,
$\hookrightarrow(1: 100) / 101))))$
hldf <- summarise (gde, y=sum (y), ppredmean (predprob), count=n()) There are a few missing values in the data. The default method is to ignore these cases. The na. omit command drops these cases from the data frame for the purposes of this calculation. We use the same method of binning the data as for the residuals but now we need to compute the number of observed cases of heart disease and total observations within each bin. We also need the mean predicted probability within
each bin. When we make a prediction with probability $p$, we would hope that the event oc-
When we make a prediction with probability $p$, we would hope that the event occurs in practice with that proportion. We can check that by plotting the observed proportions against the predicted probabilities as seen in Figure 2.9. For a wellcalibrated prediction model, the observed proportions and predicted probabilities should be close.

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

linpred <- prediet (lmod)
predprob <- predict (lmod, type=”response”)

plot (rawres linpred, xlab” “linear predictor”, ylab=”residuals”)

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

1. 从包含所有可用预测变量的完整模型开始。我们可以添加由两个或多个预测变量之间的转换或交互形成的派生预测变量。
2. 将此模型与包含一个较少预测变量的所有模型进行比较。计算p- 对应于每个丢弃的预测器的值。中的 dropl 函数R可用于此目的。
3. 消除最大的项p- 大于某个预设临界值的值，例如0.05. 返回上一步。如果没有此类术语符合此标准，请停止并使用当前模型。

Akaike 信息标准 (AIC) 是一种流行的选择模型的方法，请参阅第 A.3 节了解更多信息。具有似然性的模型的标准大号和参数数量q定义为

## 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。