### 统计代写|广义线性模型代写generalized linear model代考|STAT7608

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|Interpreting Odds

Odds are sometimes a better scale than probability to represent chance. They arose as a way to express the payoffs for bets. An evens bet means that the winner gets paid an equal amount to that staked. A $3-1$ against bet would pay $\$ 3$for every$\$1$ bet while a $3-1$ on bet would pay only $\$ 1$for every$\$3$ bet. If these bets are fair in the sense that a bettor would break even in the long-run average, then we can make a correspondence to probability. Let $p$ be the probability and $o$ be the odds, where we represent $3-1$ against as $1 / 3$ and $3-1$ on as 3 , then the following relationships hold:
$$\frac{p}{1-p}=o \quad p=\frac{o}{1+o}$$
One mathematical advantage of odds is that they are unbounded above which makes them more convenient for some modeling purposes.

Odds also form the basis of a subjective assessment of probability. Some probabilities are determined from considerations of symmetry or long-term frequencies, but such information is often unavailable. Individuals may determine their subjective probability for events by considering what odds they would be prepared to offer on the outcome. Under this theory, other potential persons would be allowed to place bets for or against the event occurring. Thus the individual would be forced to make an honest assessment of probability to avoid financial loss.
If we have two covariates $x_1$ and $x_2$, then the logistic regression model is:
$$\log (o \mathrm{ods})=\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2$$

Now $\beta_1$ can be interpreted as follows: a unit increase in $x_1$ with $x_2$ held fixed increases the log-odds of success by $\beta_1$ or increases the odds of success by a factor of exp $\beta_1$. Of course, the usual interpretational difficulties regarding causation apply as in standard regression. No such simple interpretation exists for other links such as the probit.

An alternative notion to odds-ratio is relative risk. Suppose the probability of “success” in the presence of some condition is $p_1$ and $p_2$ in its absence. The relative risk is $P_1 / P_2$. For rare outcomes, the relative risk and the o dds ratio will be very similar, but for larger probabilities, there may be substantial differences. There is some debate over which is the more intuitive way of expressing the effect of some condition.

## 统计代写|广义线性模型代写generalized linear model代考|Prospective and Retrospective Sampling

In prospective sampling, the predictors are fixed and then the outcome is observed. In other words, in the infant respiratory disease example shown in Table 2.1, we would select a sample of newborn girls and boys whose parents had chosen a particular method of feeding and then monitor them for their first year. This is also called a cohort study.
In retrospective sampling, the outcome is fixed and then the predictors are observed. Typically, we would find infants coming to a doctor with a respiratory disease in the first year and then record their sex and method of feeding. We would also obtain a sample of respiratory disease-free infants and record their information. How these samples are obtained is important-we require that the probability of inclusion in the study is independent of the predictor values. This is also called a case-control study.

Since the question of interest is how the predictors affect the response, prospective sampling seems to be required. Let’s focus on just boys who are breast or bottle fed. The data we need is:

• Given the infant is breast fed, the log-odds of having a respiratory disease are $\log 47 / 447=-2.25$
• Given the infant is bottle fed, the log-odds of having a respiratory disease are log $77 / 381=-1.60$
The difference between these two log-odds, $\Delta=-1.60–2.25=0.65$, represents the increased risk of respiratory disease incurred by bottle feeding relative to breast feeding. This is the log-odds ratio.

# 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|Interpreting Odds

$$\frac{p}{1-p}=o \quad p=\frac{o}{1+o}$$

$$\log (\text { oods })=\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2$$

## 统计代写|广义线性模型代写generalized linear model代考|Prospective and Retrospective Sampling

• 鉴于婴儿是母乳喂养，患呼吸系统疾病的对数几率是 $\log 47 / 447=-2.25$
• 鉴于婴儿是奶瓶喂养，患呼吸系统疾病的对数几率是对数 $77 / 381=-1.60$ 这两个对数赔率之间的差异， $\Delta=-1.60-2.25=0.65$, 表示相对于母乳喂养，奶瓶 喂养引起呼吸道疾病的风险增加。这是对数优势比。

## 有限元方法代写

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## MATLAB代写

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