# 纵向数据分析|BSTT537/ BST 5441/STAT 6289/STAT 36900/Stat 771/STATS 768Longitudinal Data Analysis代写

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$$\ell\left(\boldsymbol{Y}{i} \mid \boldsymbol{\theta}\right)=\prod{j=1}^{n_{i}} \prod_{c=1}^{C}\left(p_{i j c}\right)^{\boldsymbol{y}{\mathrm{v} c}}$$ where $\mathrm{y}{i j e}=1$ if $Y_{i j}=c$, and 0 otherwise. The marginal log-likelihood from the $N$ level-2 units,
$$\log L=\sum_{i}^{N} \log h\left(\boldsymbol{Y}{i}\right)=\sum{i}^{N} \int_{\theta} \ell\left(\boldsymbol{Y}_{i} \mid \theta\right) g(\boldsymbol{\theta}) d \theta$$

## CS 57800/ 3860/COMP 540 001/COMP_SCI 396/STAT3888/YCBS 255COURSE NOTES ：

$$\mathrm{E}\left(y_{i}\right)=\operatorname{Var}\left(y_{i}\right)=\lambda_{i}$$
The likelihood for $N$ independent observations from ( $12.1$ ) is
$$L=\prod_{i=1}^{N} \frac{\exp \left(-\lambda_{i}\right)\left(\lambda_{i}^{y_{i}}\right)}{y_{i} !}$$
and the corresponding log-likelihood function is
$$\log L=-\sum_{i}^{N}\left[\lambda_{i}+y_{i} \log \lambda_{i}-\log \left(y_{i} !\right)\right]$$