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

[Viechtbauer, Wolfgang (SP)]

Actually, if you are really going this route, I would consider:

rma.mv(es ~ time_wks_btw + time_wks_wth, random = list(~ time_wks_wth | study, ~ time_meaning_wks | study, struct = c("GEN","CAR"))

that is, add random intercepts for studies, random slopes for time_wks_wth, and also add a CAR structure on top of that (whether you use time_meaning_wks or time_wks_wth for that does not matter, since it is only the relative distance within studies that matters and that will be the same wehther you do within-study centering or not). Not sure whether this is overparameterized. profile() will tell you.

Note that if 'es' was calculated based on the same group of subjects within studies, then the sampling errors are not independent. One could also assume that the sampling errors are autocorrelated with a CAR structure. You can construct an approximate V matrix using impute_covariance_matrix() from clubSandwich or the new vcalc() function in metafor (in the devel version: https://wviechtb.github.io/metafor/reference/vcalc.html).

Best,
Wolfgang

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Sunday, 10 October, 2021 19:13
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Time as indicator vs time as meaning
>
>Dear Wolfgang,
>
>This was such an important point. I'm highly grateful for this. To
>follow your advice, I'm going to do:
>
>rma.mv(es ~ time_wks_btw + time_wks_wth, random = ~ time_meaning_wks |
>study, struct = "CAR")
>
>But:
>
>1) Can the right side of | in the random part, remain as
>"time_meaning_wks" or it should be "time_wks_wth"?
>
>2) If I want to interact "condition" with time, which time moderator
>should I use: "time_wks_btw" or "time_wks_wth"?
>
>Many thanks,
>Stefanou
>
>On Sun, Oct 10, 2021 at 8:56 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>
>> See below for my responses.
>>
>> Best,
>> Wolfgang
>>
>> >-----Original Message-----
>> >From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>> >Sent: Saturday, 09 October, 2021 19:28
>> >To: Viechtbauer, Wolfgang (SP)
>> >Cc: Michael Dewey; R meta
>> >Subject: Re: [R-meta] Time as indicator vs time as meaning
>> >
>> >Thank you so much, Wolfgang and Michael. So, based on your advice I
>> >will use the following:
>> >
>> >rma.mv(es ~ time_meaning_wks, random = ~ time_meaning_wks | study,
>> >struct = "CAR")
>> >
>> >Then I think, the fixed coef. of "time_meaning_wks" is interpreted as:
>> >The change in true effects for 1 week change in time regardless of the
>> > testing occasions' indicator.
>>
>> Correct. And now comes the part again where I am being pedantic:
>>
>> 1) To be precise: The average change.
>>
>> 2) You could run this model even if not a single study had used two (or more)
>measurement occasions (one could then not estimate rho - so in principle, the
>model is then overparameterized, but this isn't relevant to the point I am trying
>to make here). In this case, the coefficient for time_meaning_wks is estimated
>purely by examining the size of the effect across studies that used different
>measurement weeks. In this case, speaking of 'change' might suggest that the
>studies are actually providing evidence about the change in the effect over time,
>when in fact the evidence is purely cross-sectional (or "cross-studinal" if there
>even is such a word - Google gives me 0 hits for this, so maybe not, but then I
>just invented it). You *do* have studies that used multiple measurement
>occasions, so the coefficient for time_meaning_wks is actually a mixture of
>cross-studinal evidence and actual changes in the effect that occurred within
>studies. To disentangle such between- and within-study evidence, one can apply
>methods that are well-known in the multilevel / longitudinal data analysis
>context, namely by computing the study-level means of time_meaning_wks and the
>deviations from these means within studies and then including both of these
>variables in the model.
>>
>> >One other option that we came up with to keep time_id (as a factor) in
>> >the model was to control for "time_meaning_wks" as in:
>> >
>> >rma.mv(es ~ factor(time_id) + time_meaning_wks, random = ~
>> >factor(time_id) | study, struct = "UN")
>> >
>> >Does this alternative make sense?
>>
>> One can do this, but it's trying to squeeze a lot of information out of your
>data. The factor(time_id) fixed effect is asking about differences in measurement
>occasions irrespective of their actual time values (so the second measurement
>occasions might be at 6 weeks in study 1 and at 24 weeks in study 2 but these are
>both treated identically). The time_meaning_wks effect is asking about (linear)
>changes (or differences -- see above) in the effect over time measured in weeks.
>>
>> And as discussed in a previous post, using something like 'random = ~
>factor(time_id) | study, struct = "UN"' is likely to lead to a rather large
>number of variance components and correlations being estimated.