longitudinal data

Dear experts,

I would like to measure change of performance over time in a longitudinal data set. Each participant was tested at 1 day, 1 week, and 3 months. How do I look at change over time treating time as a continuous measure rather than 3 categorical timepoints? I have been using linear mixed effects models to date and it just treats time as categorical, but surely this isn't the correct approach for these timepoints with differing time intervals in between. Any help is greatly appreciated.

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TS Contributor
surely this isn't the correct approach for these timepoints with differing time intervals in between.
Why should that be incorrect?
With just 2 intervals, you do not have
enough data to model the influence
of interval width, and interval width
is confounded with number of performance

With kind regards

I'm just worried that the decline in performance would not be linear, especially when considering the final timepoint at 3mths.


TS Contributor
Why should you be worried about linear/noinlinear decline?
You can compare the time points, and you can maybe discuss
whether the difference between t1 and t2 looks different
(or not) compared with difference between t2 and t3.
But regardless of whether you are worried or not,
or whether there's something linear or nonlinear going on
- you cannot model it (as far as I can see), and interval
width ist totally confounded with number of measurement.

With kind regards



Omega Contributor
Putting this data into a multilevel model is probably fine. However, treating time as continuous has a little hiccup in that your time intervals are not equally spaced. I ran something comparable last year (treating time as continuous), but included a spatial time power structure in the random effects line of my code, since contiguous measurements can have covariance, but the covariance structure is unique between values because of the spacing. So T1 and T2 should be more similar than T2 and T3.

Moreover, a different structure may better explain data than say a traditional autoregressive (AR1).