Daily Diary Data - control for DV at t-1?

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Marissa4usa

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Hi all,
I'm hoping some of you have some advice regarding a (admittedly somewhat convoluted) stats question.

I have a dataset that consists of daily observations (21 days) of people's daily general mood and daily life satisfaction . I am interested in understanding the extent to which these two variables fluctuate with one another, so if one day my mood is low, am I also more dissatisfied with my life, and vice versa.

Specifically, I am interested whether the association holds using lagged variables, e.g., does mood on day t-1 predict life satisfaction on day t and vice versa. It seems to be common practice to add the DV at day t-1 as a covariate. Although this makes sense to me to some extent, I also have some concerns about this practice, but I'm unable to find any literature that supports my concern.

Obviously, the DV at time t and t-1 are going to be strongly correlated, especially when we talk about daily data. Clearly, it should be this way, otherwise the measure used to assess the construct (e.g., mood) would not be reliable. It's an established fact that mood and life satisfaction are very strongly correlated, and I want to understand what gives rise to the strong association of these phenomena, particularly, I want to understand: does being in a bad mood make me dissatisfied with my life, or does being dissatisfied make me be in a bad mood? Again, if I controlled for the DV at t-1, I would test extent to which the IV predicts the DV at time t above and beyond the correlation of the IV and DV at time t-1. However, my goal is to identify the processes that give rise to the co-occurance of these two phenomena.

To give another descriptive example to explain what I mea: The weather: Obviously, we all know that the weather fluctuates throughout the day, the week, month, the year, etc. However, over very short periods of time, it's very reliable. If I collect daily weather data over 365 days, and try to predict the weather on day t, but control for the weather on day t-1, I will end up with a horizontal line that'll say that there are no fluctuations in weather over 365 days. Clearly, we know that is not correct.

I'm not trying to convince others of this and I'm open to feedback, but I do think that this perspective has merit, but I can't locate any scholarly writings on this topic that either confirm or disprove my logic. Alternatively, I'm looking for something that provides information on the extent to which one should control for DV on the previous time-point given the frequency of assessments (e.g., should I control for DV at the previous time point when I collect daily data, but not weekly, monthly, yearly?)

I am familiar with the Bolger and Lauenceau book, but I don't seem to find an answer in there, either.

Thanks!
 
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What you are wrote makes sense to me - I think it just depends what argument you want to make. If you want a strong causal argument that mood day 1 predicts life satisfaction day 2, excluding the life satisfaction day 1 covariate won't achieve that. You can argue they are correlated...but I'm not sure the lagging tells you anything at that point. If you are assuming they are too stable over the short-term for that to be meaningful...it makes little sense to be testing it at all - yes? If the argument is strictly for lagged effects of mood, you could try covarying for both same-day IV (vs previous day DV) and see what pops out. Seems like this would still sort of get at the issue, though the two are likely so highly correlated that this may be meaningless too. Are you person-centering or grand-mean centering?

May want to rethink the whole approach though. I'm reading between the lines a bit here, but it sounds like your argument is more for trajectory (i.e. previous mood "sets you on a path to life satisfaction" over the short term). I'd consider chopping it up and looking at say...week 1 mood as a predictor of week 2-4 slope (just as an example). Look into ARMA models if you haven't yet, though you might not have enough data (I assume you are using HLM). We're afraid of ARMA in behavioral sciences for reasons that were always unclear to me, but economists have been dealing with these kinds of issues for years and have tackled similar issues using ARMA and related techniques.
 
Hmm I'm not sure if this will answer your question, but food for thought if you haven't given this thought yet. My lab does a lot of mood variability research - I myself am not familiar with MLM but use it to detrend my data and then (generally) use SEM to test out major models. You may consider looking at any time-dependent trends in your data (unless its a topic of interest); so, for example, making sure that trends aren't contingent on time of day only (which for my study wouldn't be true variability). Also, we always control for the absolute mean levels of whatever variability data we're looking at. For my dissertation I looked at positive and negative affect variability so I examined any trends in the data (there were none) and when I ran my analyses I used overall mean of positive affect and negative affect as a covariate. You're question is a little beyond my expertise but since I have a teeny bit of knowledge on variability data I thought I'd throw my two cents in! Sorry if it's not what you're looking for 🙂
 
What you are wrote makes sense to me - I think it just depends what argument you want to make. If you want a strong causal argument that mood day 1 predicts life satisfaction day 2, excluding the life satisfaction day 1 covariate won't achieve that. You can argue they are correlated...but I'm not sure the lagging tells you anything at that point.
As I said, the processes that give rise to the association of two variables is what I'm primarily interested in. Yes, I do want to establish some directionality, but by controlling for everything could explain the directionality, I'm effectively left with zero.For example, if I want to understand why two people are friends, it's silly to control for the fact that they were friends the day before, since them being friends the previous day is the reason they're friends today.

If you are assuming they are too stable over the short-term for that to be meaningful...it makes little sense to be testing it at all - yes?
It's not about how much either variable changes in a very short-period time. You're right in that over the course of 21 days I will not observe any major fluctuations.
I am interested in the extent to which mood and satisfaction change together. So, even very small fluctuations occuring in both variables at the same time can be meaningful. This is precisely my dilemma. When is a measure "too reliable" to detect any true changes?


If the argument is strictly for lagged effects of mood, you could try covarying for both same-day IV (vs previous day DV) and see what pops out. Seems like this would still sort of get at the issue, though the two are likely so highly correlated that this may be meaningless too. Are you person-centering or grand-mean centering?
I actually do co-varying for same-day IV, and that's another issue, but not one I'm too concerned about at this point.

Are you person-centering or grand-mean centering?
Person-mean centering.

May want to rethink the whole approach though. I'm reading between the lines a bit here, but it sounds like your argument is more for trajectory (i.e. previous mood "sets you on a path to life satisfaction" over the short term). I'd consider chopping it up and looking at say...week 1 mood as a predictor of week 2-4 slope (just as an example). Look into ARMA models if you haven't yet, though you might not have enough data (I assume you are using HLM). We're afraid of ARMA in behavioral sciences for reasons that were always unclear to me, but economists have been dealing with these kinds of issues for years and have tackled similar issues using ARMA and related techniques.
I am using HLM, and at this point, I am not sure your suggestion would answer my research question, but I will look into it.

Hmm I'm not sure if this will answer your question, but food for thought if you haven't given this thought yet. My lab does a lot of mood variability research - I myself am not familiar with MLM but use it to detrend my data and then (generally) use SEM to test out major models. You may consider looking at any time-dependent trends in your data (unless its a topic of interest); so, for example, making sure that trends aren't contingent on time of day only (which for my study wouldn't be true variability).
I couldn't test for time dependent trends as these are paper surveys and we have to take people's word that they completed them every evening at the time we told them to (yes, I know...it's a drawback).

Also, we always control for the absolute mean levels of whatever variability data we're looking at. For my dissertation I looked at positive and negative affect variability so I examined any trends in the data (there were none) and when I ran my analyses I used overall mean of positive affect and negative affect as a covariate. You're question is a little beyond my expertise but since I have a teeny bit of knowledge on variability data I thought I'd throw my two cents in! Sorry if it's not what you're looking for 🙂
I am controlling for the mean level of the predictor variable.

I really welcome any thoughts, ideas, etc., especially any pointers towards literature that addresses this.
 
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