Handling EMA data including a mixture of momentary and retrospective items in ctsem #69
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Hi, Thank you for the ctsem package and the detailed tutorials! I’m relatively new to the continuous-time framework and have a question about handling temporally aggregated measurements. In intensive longitudinal (EMA) designs we sometimes collect two types of outcomes at the same prompt: (1) a momentary “right now” state (a point-in-time observation) and (2) a retrospective item referring to the interval since the previous prompt (e.g., “Over the past X hours, how much did you feel/do/etc. Y?”). My question is: What is the most appropriate way to incorporate such an interval-based retrospective outcome into a continuous-time state-space model alongside the momentary measurement, while keeping the implementation parsimonious and avoiding overfitting or non-identifiable latent constructs? In particular, I’m considering the pragmatic compromise of “back-projecting” the interval outcome onto a single reference timepoint (e.g., the interval midpoint or end) and treating it there as an approximate observation of the latent state. How does ctsem handle the bias and temporal imprecision introduced by this approximation? Are there recommended diagnostics or adjustments that make this projection more defensible, or does this strategy tend to induce spurious or misleading inferences? Thanks a lot! |
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Replies: 2 comments
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Hi Steffen, ctsem doesn't do anything with this kind of data explicitly, it doesn't know what kind of question you've asked people and just models it however you request :) but it generally has the flexibility to handle it in a variety of ways. I think there are two broad classes of approach -- the first is quite simple, you just model the latent 'aggregation' process, so you don't try to directly infer the specific state you just do inference on the aggregation state, then your predictions / dynamics are with reference not to the momentary state, but the aggregate. i.e., any forecasts made will reflect your prediction of what the individfual would say about the same question (aggregate mood) at some later time point. Getting at the momentary process based only on the aggregate data is trickier and requires building in your assumptions about how the individuals aggregate such information into the model. There is a range of work on this in the panel data context already, and I know a postdoc working with me, Michael Aristodemou @mearistodemou , has been looking into this a bit more, but the general concept is that you have a latent aggregation process that is observed, and a latent momentary process which is subject to random changes, dynamics etc, and is the sole cause of the aggregation process. |
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Thanks a lot for the quick and helpful explanation. It’s always useful to take a step back and consider what question was actually asked, and then build the statistical model from that perspective, so I really appreciate the idea of modeling the aggregation process! I also appreciate the idea behind the second approach, though that one seems like it could get quite (too) complex at the moment. |
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Hi Steffen, ctsem doesn't do anything with this kind of data explicitly, it doesn't know what kind of question you've asked people and just models it however you request :) but it generally has the flexibility to handle it in a variety of ways.
I think there are two broad classes of approach -- the first is quite simple, you just model the latent 'aggregation' process, so you don't try to directly infer the specific state you just do inference on the aggregation state, then your predictions / dynamics are with reference not to the momentary state, but the aggregate. i.e., any forecasts made will reflect your prediction of what the individfual would say about the same question (aggregate m…