# (广义）线性模型|STAT3030/STATS5019 /STAT 504/STA600/Stat 539/STAT*6802/ST411/STAT 7430/SS 3860B(Generalized) Linear Models代写

0

$$\mu_{t}=\sum_{i} \beta_{i} x_{i t}$$
However, this yields a conditional model of the form
$$\mu_{t \mid t-1}=\rho\left(y_{t-1}-\sum_{i} \beta_{i} x_{i, t-1}\right)+\sum_{i} \beta_{i} x_{i t}$$
This may also be written
$$\mu_{t \mid t-1}-\sum_{i} \beta_{i} x_{i t}=\rho\left(y_{t-1}-\sum_{i} \beta_{i} x_{i, t-1}\right)$$

## STA 144/STAT 451/STAT 506/STA 317 COURSE NOTES ：

where, again, $K$ is the unknown asymptotic maximum value. And again, we can obtain a linear structure, this time for a complementary log log link:
$$\log \left[-\log \left(\frac{K-y}{K}\right)\right]=\log (\alpha)+\beta t$$
We can use the same iterative procedure as before.

# 广义线性模型 | Generalized Linear Models代写 STAT 504代考

0

$$f(y ; \theta)=\exp [y \theta-b(\theta)+c(y)]$$
the conjugate distribution for the random parameter is
$$p(\theta ; \zeta, \gamma)=\exp [\zeta \theta-\gamma b(\theta)+s(\zeta, \gamma)]$$

where $s(\zeta, \gamma)$ is a term not involving $\theta$. This conjugate is also a member of the exponential family. The resulting compound distribution, for $n$ observations, is
$$f(y ; \zeta, \gamma)=\exp [s(\zeta, \gamma)+c(y)-s(\zeta+y, \gamma+n)]$$
This is not generally a member of the exponential family.

## STAT 504COURSE NOTES ：

$$y=K \frac{\alpha \mathrm{e}^{\beta t}}{1+\alpha \mathrm{e}^{\beta t}}$$
where $K$ is the asymptotic maximum value of the response.
We can transform this to a linear structure by using a logit link:
$$\log \left(\frac{y}{K-y}\right)=\log (\alpha)+\beta t$$