如何在R中使用AR（1）随机效应相关结构拟合线性混合模型？

Question

I am trying to use R to rerun someone else's project, so we need to use some macros in R.

Here comes a very basic question:

m1.nlme = lme(log.bp.dia ~ M25.9to9.ma5iqr + temp.c.9to9.ma4iqr + o3.ma5iqr + sea_spring + sea_summer + sea_fall + BMI + male + age_ini, data=barbara.1.clean, random = ~ 1|study_id)

Since the model is using AR(1) [autocorrelation 1 covariance model] in SAS for within person variance, I am not sure how to do this in R.

And where I can see the index for different models, like unstructured?

Thanks

Answer 1

我不知道不同模型的“索引”是什么意思，但是要为残差指定AR（1）协方差结构，可以将corr=corAR1()添加到lme调用中。

Answer 2

The correlation at lag $1$ is say $r$, where $-1< r <1$ for a stationary $AR(1)$ model. The correlation at lag $k \\geq 1$ is $r^k$. This gives you the autocovariance matrix by just multiplying by the variance of $X_t$.