I have a data set from a diary study in which daily stress during the current pandemic was assessed for 30 days. However, participants began their diary period at different time points, leading to an overall data collection period of 60 days. I want to build multilevel regressions to investigate the effect of different predictors on stress. However, due to the way the data was collected I am unsure of whether it makes sense to include time as a predictor: Day X/30 should be meaningless regarding stress, whereas day X/60 may be relevant due to the ongoing pandemic/lockdown. However, the sample is very unbalanced in this regard: Only about a fifth of participants answered the questionnaire in the last two weeks of the 60 days, with the numbers declining even more towards the very end. I know that multilevel models can handle unbalanced data to some regard, but I am wondering whether this is too extreme and would be problematic. Does anyone have any insights? Thank you in advance!
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1$\begingroup$ If I was doing this analysis then I would include two types of time: 1) objective time (i.e. which day of the year it is, and 2) a time index for number of days since the diary started. The first one is necessary since it proxies for the severity of the COVID outbreak. The second is probably necessary since it models subjective assessment of stress over time (eg if someone has been stressed for 5 days in a row then it may become the 'new normal' for them, so they stop explicitly mentioning it). $\endgroup$– JamesCommented Jul 7, 2020 at 9:27
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$\begingroup$ Thank you for your input! So the fact that the sample is so strongly unbalanced over the 60 days doesn't mean I shouldn't include that time in my model? And a follow-up question: would including both types of time not cause any issues, given that for each 1 day increase in objective time, time in the diary period also increases by 1 day? $\endgroup$– carlottalilCommented Jul 7, 2020 at 9:49
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1$\begingroup$ "It depends" on the structure of your data but in general the imbalance will probably just mean you have wider credible/confidence intervals for the most recent days and narrower ones for the earlier days. But the lack of data towards the end may make it more difficult to justify strong structural assumptions (eg linear time trend) since there may not be enough data to verify them. $\endgroup$– JamesCommented Jul 7, 2020 at 12:45
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1$\begingroup$ Regarding your second question it really depends on the structure of your data/model, but having two time trends should give an identifiable model if one of the coefficients (corresponding to objective time) is common across all diaries. But you probably wouldn't be able to identify a model where each diary had its own objective time trend coefficient and one for 'number of days' (but you could probably make such a model identifiable using an informative prior, which would be learned from the hierarchical model) $\endgroup$– JamesCommented Jul 7, 2020 at 12:48
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