[100 Multilevel Questions]Modeling Changes in HLM?

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I would like to know whether and how I can model changes in my IVs (and DV) at the level 1 of analysis in HLM. I measured affect and stress (my IVs) and effort (my DV) at four points in time (weekly), and a personality facet (my moderator) at the beginning of the study (level 2 variable). I would like to know whether and how I can examine the relationships between changes in affect/stress and changes in intensity. Do I need to add a time variable to my model? I already unconditional growth models and found a very good amount of within-person variance.

Any information would be greatly appreciated!

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关键词：Multilevel questions question Modeling changes

To model changes over time, I would create a time variable. Use the time  variable to interact with your independent variables (timeX iv). When you run the model, you will see the differences at each time point.

I've used a random-intercept model to measure changes over time and set  time as a fixed effect.

Hope that helps.

I think a trick that will serve you well is group mean centering your time-varying covariates. This will allow you to identify the association between change in x and change in y, and between the invariant component of x and y.

See Enders and Tofighi for a good introduction to the merits of group mean centering. I don't know of a published paper that articulates this simply in the context of panel data, though my recent paper elaborates this where the units observed repeatedly are themselves composed of many members each observed only once:  http://dx.doi.org/10.1017/psrm.2013.24

Hope that helps,
Malcolm Fairbrother

Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey Datasets

Malcolm Fairbrother

Political Science Research and Methods / Volume 2 / Issue 01 / April 2014, pp 119 - 140

DOI: 10.1017/psrm.2013.24, Published online: 14 October 2013

Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey.pdf (717.85 KB, 需要: 1 个论坛币)

2014-3-17 23:08:19 上传

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Dear all,

A difficulty with group mean-centering in longitudinal data is that it may imply an influence of the future on the past.

Best,
Tom

I included a time variable at my level 1 of analysis. I centered my time-varying covariate but left the time variable uncentered. However, I ran into two problems:

• How can I interpret the time x IV (time-varying covariate) in terms of changes? In other words, how can I interpret my HLM coefficient as representing a "change"?
• Also, I have had a hard time interpreting the results of the time x IV (time-varying covariate) x my level 2 moderator interaction (and even plotting them). Would anyone know whether and how it is possible to do so?
  

I read a few papers and book chapters by Patrick Curran and Daniel Bauer on this topic, but am still struggling with the interpretation of my coefficients, certainly when trying to interpret them in light of changes (for both the time x IV and the time x IV x level-2 moderation). I know that many people are using Latent Growth Modeling (and Latent Change Scores) to examine changes in IVs and DVs, but my data fits better an HLM approach.

Thank you once again for your help,

If X_{ti} is the observed value for individual i at time t, and X{.i} is the mean of X_{ti} over i, then
(X_{ti} - X_{.i}) depends on outcomes for time later than t. This applies of course to the dependent as well as explanatory variables.
This is why in the example in Chapter 15 (longitudinal multilevel modeling) of Snijders & Bosker ("Multilevel Analyais", 2nd ed.), we use the initial value of the changing covariate, rather than its person mean, as the level-two variable, to distinguish between within-person and between-person regression coefficients; see page 258-259.


Best,
Tom Snijders

This is awesome information; thank you!

If including the initial value of my time-varying covariate at the level 2 of analysis and not centering the time-varying covariates at the level 1 of analysis, would this be a more accurate examination of changes in my time-varying covariate? Can I still include the initial value at the level 1, or should I instead start with time 2?

Thank you!

Dear Serge and others,

Well, "more accurate" ... that kind of statements is impossible to make in general. It all depends on the design of the study, the purposes of analysis, etc.
The principle to which I referred is that for the variables affecting the dependent variable at time t, you shouldn't use any variables that, perhaps due to transformations, include information about things after time t. This means that if you use the initial ("time 1") value of explanatory variables as the level-2 variable with a fixed effect, replacing effectively the group mean (where group={level 2 unit}=individual in this case), then you can use all the variables starting from time 1 onward just as usual.
The principle seems pretty general to me. The elaboration is not a general rule, it should be considered in each given case whether this meaningful.

Best regards,

Tom Snijders

Thanks for this discussion. You've raised an interesting issue (at least to me), and I'm trying to think this through. But it's making my head spin. I see your point, but I think a lot rides on what you meant (in your previous post) by "depends".

The mean-centring approach yields the "within" estimator, which is precisely equivalent to the output of a "fixed effects" model. Your comment therefore implies a rather fundamental criticism of what is a pretty dominant methodology in some fields. Do you see what I mean?

One concern is that under the mean-centring approach the two resulting components are perfectly uncorrelated by construction, and at least the de-meaned component of X is guaranteed to be uncorrelated with any time-invariant error (i.e., with the unit random intercepts). Using your differenced-from-time-zero approach, on the other hand, the resulting components may be correlated. And it follows that they may *both* be correlated with any time-invariant random error. (In practice, in a given application, this correlation may well be small and unimportant, but I don't believe this can be tested.)

I guess, as you say, it may well depend on the specifics of a given study. I'd be interested to hear any further thoughts.

Malcolm