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

[Viechtbauer, Wolfgang (SP)]

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Sunday, 10 October, 2021 23:03
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Time as indicator vs time as meaning
>
>ATTACHMENT(S) REMOVED: image.png
>
>Thanks! Reporting back the results for two models (note: "time_wk" =
>"time_meaning_wks").
>In model 1,  I used "time_wk" to the left of | for "CAR".
>In model 2, I used "time_whtn" to the left of | for "CAR".
>In both models, rho is estimated to be 1. But the likelihood profile
>for rho seems ok for both models (attached).
>
>However, in model 1, phi is estimated to be 0.1170. In model 2, phi is
>estimated to be 0. In both models, the likelihood profiles for phi
>seem ok.
>Which phi, then, seems appropriate?
>
>Thank you,
>Stefanou
>
>#******************************
>MODEL 1:
>#******************************
>rma.mv(yi ~ time_btw + time_wthn, vi,
>               random =
>         list(~ time_wthn | study, ~time_wk | study), struct =
>c("GEN","CAR"),data=data)
>
>Variance Components:
>
>outer factor: study    (nlvls = 49)
>inner term:   ~time_wk (nlvls = 12)
>
>          estim    sqrt  fixed  rho:    intr  tm_w
>intrcpt  0.1306  0.3614     no             -    no
>time_wk  0.0236  0.1536     no        1.0000     -
>
>outer factor: study   (nlvls = 49)
>inner factor: time_wk (nlvls = 12)
>
>            estim    sqrt  fixed
>gamma^2    0.0703  0.2652     no
>phi        0.0544             no
>
>Model Results:
>
>           estimate      se    zval    pval    ci.lb   ci.ub
>intrcpt      0.0049  0.1816  0.0272  0.9783  -0.3510  0.3608
>time_btw     0.3399  0.2164  1.5708  0.1162  -0.0842  0.7641
>time_wthn    0.2837  0.0708  4.0064  <.0001   0.1449  0.4224  ***

Something doesn't match up here. The first part of the 'random' formula says '~ time_wthn | study' but the output says that the inner term is ~time_wk.

>#******************************
>MODEL 2:
>#******************************
>rma.mv(yi ~ time_btw + time_wthn, vi,
>               random =
>                 list(~ time_wthn | study, ~time_wthn | study), struct
>= c("GEN","CAR"),data=data)
>Variance Components:
>
>outer factor: study      (nlvls = 49)
>inner term:   ~time_wthn (nlvls = 9)
>
>            estim    sqrt  fixed  rho:    intr  tm_w
>intrcpt    0.4034  0.6351     no             -    no
>time_wthn  0.1141  0.3377     no        1.0000     -
>
>outer factor: study     (nlvls = 49)
>inner factor: time_wthn (nlvls = 9)
>
>            estim    sqrt  fixed
>gamma^2    0.0770  0.2775     no
>phi        0.0000             no
>
>Test for Residual Heterogeneity:
>QE(df = 402) = 1450.3879, p-val < .0001
>
>Test of Moderators (coefficients 2:3):
>QM(df = 2) = 24.4255, p-val < .0001
>
>Model Results:
>
>           estimate      se    zval    pval    ci.lb   ci.ub
>intrcpt      0.1155  0.1861  0.6204  0.5350  -0.2493  0.4802
>time_btw     0.3184  0.1815  1.7540  0.0794  -0.0374  0.6741    .
>time_wthn    0.3247  0.0658  4.9344  <.0001   0.1957  0.4536  ***