[R-meta] Time as indicator vs time as meaning

[Viechtbauer, Wolfgang (SP)]

I don't really know how to respond to that, except to repeat what I said in my previous mail. Or do this:

Draw two lines with different intercepts and slopes. ~ time_wthn | study with struct="GEN" is using random effects to account for differences in intercepts and slopes of those lines.

Now add a bunch of points around those two lines. Those are the true effects for those two studies. Those points could be autocorrelated -- that's captured by phi. Also, they differ from the lines. That source of heterogeneity is captured by gamma^2.

That is what is happening here and it is conceptually analogous to what is happening in lme() (except that in a meta-analysis model, there is the further differentiation between the observed and true effects and the sampling errors could also exhibit autocorrelation, but let's leave this complication aside).

Another way to put this: The error term of a model is also a random effect. It's not typically denoted this way, but such semantic differences can be misleading. Or put differently: What you put in 'random' and what you put in 'correlation' in lme() is still about the same data. What these things do (i.e., what they account for in the data) in the context of a model is different, but again, it's all about modeling the data.

Not sure if this helps.

Best,
Wolfgang

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Tuesday, 12 October, 2021 17:51
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Time as indicator vs time as meaning
>
>Sure, but in the lme(), "correlation=" has to do with the structure of
>V matrix (i.e., e_ij), not random-effects, no?
>
>Say, I had used the categorical "time" (measurement occasions) with
>struct = "HAR", then would it have made sense to add a "UN" on top of
>that?
>
>yi ~ time, random = list(~ time | study, ~ time | study), struct =
>c("HAR", "UN")
>
>Best of all,
>Stefanou
>
>On Tue, Oct 12, 2021 at 10:34 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>
>> Yes, I discovered this bug while working with your data. So thank you - you
>brought something to my attention that requires fixing.
>>
>> And here we go with the modeling questions :)
>>
>> The two structures are doing rather different things. One is modeling
>differences in intercepts and slopes of the regression lines, the other
>accounting for autocorrelation in the data (to be precise, in the deviations
>around the study-specific regression lines).
>>
>> If you look at the literature on longitudinal data analysis, you will find that
>things like this are done commonly also with raw data. For example, I quite
>frequently work with data collected in diary studies (i.e., ecological momentary
>assessment / experience sampling studies). A model like:
>>
>> lme(outcome ~ between.x + within.x, random = ~ within.x | subject/day,
>>     correlation=corCAR1(form = ~ hour | subject/day)
>>
>> is quite standard there. So I am applying the same idea to the meta-analytic
>context.
>>
>> Best,
>> Wolfgang
>>
>> >-----Original Message-----
>> >From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>> >Sent: Tuesday, 12 October, 2021 17:21
>> >To: Viechtbauer, Wolfgang (SP)
>> >Cc: R meta
>> >Subject: Re: [R-meta] Time as indicator vs time as meaning
>> >
>> >Dear Wolfgang,
>> >
>> >Thank you very much! In your answer, you also demystified the problem
>> >of why model2 crashes, if I don't round the "time_wthn" up to 8
>> >decimal places (that had me thinking the whole day yesterday).
>> >
>> >I'm all good. But I wonder what made you add two
>> >differently-structured ("GEN" and "CAR") set of random-effects to the
>> >**same ID variable** (i.e., study)?
>> >
>> >In other words, when such a strategy is warranted?
>> >
>> >Best of all,
>> >Stefanou