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I have a dataset on two disorders, one measured on a continuous scale, and one with three categories (which can be collapsed into a yes/no variable if necessary). The two disorders have been measured at a maximum of 7 time points per individual, with irregular spacing in between.

I already know the two variables are correlated when you look at them cross-sectionally. But now I would like to know if there is a correlation in time, i.e., are changes in one condition associated with simultaneous changes in the other?

What would be the best way to analyse this? I read somewhere that it might be done with multiple regression, taking subject out as a factor, but with no further explanation, so I'm not sure this is indeed what I'm looking for. Any ideas?

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  • $\begingroup$ What is it you want to know about them? $\endgroup$ – gung - Reinstate Monica Aug 17 '15 at 12:05
  • $\begingroup$ I would like to know whether the two disorders (or maybe I should say symptoms) are only correlated very generally ("people with trait A tend to also develop trait B at some point in their life"), or whether the two symptoms are actually manifestations of one and the same thing, reflected in them occurring and disappearing at the same moment. Does that clarify the question? $\endgroup$ – nopainnogain Aug 18 '15 at 13:17
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Without knowing the details of your experimental design, it's hard to make recommendations. But it sounds like what you need is a multi-level model (i.e., random effects model, hierarchical model, random effects model, and many other names; see Bristol MLM).

Because of the repeated measures within each participant, you can model the covariance structure of your data. Some common structures are: variance components, diagonal, unstructured, and autoregressive (see Wiki page on AR structure).

If you would like to know if changes in one condition are associated with changes with the other, it sounds like you're testing whether some interaction effect is significant, which you can model in any multi-level model really easily (same as linear regression).

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  • $\begingroup$ About the design: it's a population-based survey study with repeated measures of the same traits, no interventions or anything. We just asked the participants to report on two traits repeatedly, with several years in between, just observing the development of the symptoms over time. I would like to know: is improvement in one symptom usually parallelled by an improvement in the other symptom? (without any ambitions at this point to say anything about the direction of causality - just interested in temporal correlations) $\endgroup$ – nopainnogain Aug 18 '15 at 13:31
  • $\begingroup$ You should definitely try fitting a multi-level model because of the nested structure (i.e., repeated measurements for each participant over time; so observations are nested within participants) of your data. Here's one possible model with begin with: Choose an outcome (either of the two traits, depending on your theory); include time as the predictor (to see if outcome significantly changes over time); then include the other trait as a second predictor (to see whether and how it's associated with the outcome); then you can test the interaction effect. $\endgroup$ – hsl Aug 18 '15 at 17:08
  • $\begingroup$ Also, you should probably plot your data first to see what trends are in your data. Usually, you'll have a better idea of what analysis/model to use once you see your data graphically. Depending on what you're trying to do, you might have to fit complicated multi-level models. $\endgroup$ – hsl Aug 18 '15 at 17:10
  • $\begingroup$ I did plot the data, and my conclusion was that the severity of the traits fluctuates quite a bit over time. It comes and goes and doesn't necessarily persist after onset. Initially I was interested in studying the order of onset (does one occur before the other, or do they start at the same time?), but soon found out there wasn't really a clear moment of onset. So now I think maybe I should focus on whether the fluctuations over time are correlated within an individual. $\endgroup$ – nopainnogain Aug 19 '15 at 11:25
  • $\begingroup$ Point biserial correlstion could be calcucated because you have one categorical variable. Three categories can be scored arbitrarily $\endgroup$ – Subhash C. Davar Aug 31 '15 at 12:08

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