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.



1 Answer 1


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.

Consider the following example: an experiment to investigate the effect of several drug treatments on a sample of patients. It makes sense to treat the patients as being randomly selected from a larger collection of patients whose characteristics we would like to estimate. A random effects approach attempts to say something about the wider population beyond the particular sample.

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.

You see, it's two different approaches for capturing the dependency across individuals in a group, which is most useful will depend on the data; You can use both, but you should think about the meaning of this first.

  • $\begingroup$ Thank you very much for your answer. My research question is is there a difference between quality of life between 2 groups of patients (exposed group and unexposed group). My outcome variabele is quality of life, measured at equal intervals of time for a time period of 24 months. So I think its appropriate to use AR(1). The reason I added a random intercept is because every individual may have a different baseline quality of life. I'm not sure if that is the correct reason for including a random intercept and using AR(1). $\endgroup$
    – Madeleine
    Commented Nov 23, 2017 at 15:19

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