# Mixed model analysis and covariance structure

I have a question about including a random intercept per subject in a mixed model and using a autoregressive covariance structure.

I have longitudinal data with repeated measures per subject (observational study). A statistician told me that I should not include a random intercept per subject in a model when I use a autoregressive covariance structure (AR(1)), since using this covariance structure you already account for differences between observations of people. I don't really understand why?

Should I furthermore include baseline outcome in my mixed model to correct for it?

Hopefully someone can help me.

Thanks!

When you put a random effect in the model, it means you're adding a random term that follows a $Normal(0, \sigma^2_\alpha)$ distribution. This is normally done when you want to model a grouping structure.
When using an AR(1) covariance structure, it is assumed that the variance is constant across occasions, say $\sigma^2$, and $Corr(Y_{ij}, Y_{ij + k}) = \rho^k$. This structure is only appropriate when the measurements are made at equal intervals of time. Note that the correlations decline over time as separation between pairs of repeated measures increases.