[R-meta] Meta - Bug with REML or small N?

[Viechtbauer, Wolfgang (NP)]

So the REML estimate is correct:

dat <- structure(list(study = c("AA", "BB", "CC",
"EE", "DDD"), en = c(9, 41, 29, 8, 13
), em = c(32, 27.5, 28.7, 22.8, 30.5), esd = c(1.9, 3.8, 5.2,
3.8, 4.9), cn = c(8, 26, 28, 10, 14), cm = c(30.1, 24.9, 26.9,
24.7, 30.2), csd = c(2.4, 3.6, 3, 4.3, 5.1)), row.names = c(NA,
-5L), class = c("tbl_df", "tbl", "data.frame"))

dat <- escalc(measure="MD", m1i=em, sd1i=esd, n1i=en, m2i=cm, sd2i=csd, n2i=cn, data=dat)

res <- rma(dat)
res
profile(res, steps=100)

Rather different tau^2 estimates depending on the estimator:

methods <- c("ML","REML","EB","PM","HS","HSk","HE","DL","SJ")
data.frame(tau2=sapply(methods, \(x) round(rma(dat, method=x)$tau2, 4)))

Sometimes life is difficult.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Jorge Teixeira via R-sig-meta-analysis
>Sent: Tuesday, 21 March, 2023 17:56
>To: Michael Dewey
>Cc: Jorge Teixeira; R Special Interest Group for Meta-Analysis
>Subject: Re: [R-meta] Meta - Bug with REML or small N?
>
>Thanks Michael and Wolfgang.
>
>Here goes the df:
>
>structure(list(study = c("AA", "BB", "CC",
>"EE", "DDD"), en = c(9, 41, 29, 8, 13
>), em = c(32, 27.5, 28.7, 22.8, 30.5), esd = c(1.9, 3.8, 5.2,
>3.8, 4.9), cn = c(8, 26, 28, 10, 14), cm = c(30.1, 24.9, 26.9,
>24.7, 30.2), csd = c(2.4, 3.6, 3, 4.3, 5.1)), row.names = c(NA,
>-5L), class = c("tbl_df", "tbl", "data.frame"))
>
>Thanks
>
>Michael Dewey <lists using dewey.myzen.co.uk> escreveu no dia terça, 21/03/2023
>à(s) 16:36:
>
>> Dear Jorge
>>
>> It looks as though the issue is that REML estimates tau^2 to be
>> effectively zero whereas DL has a positive estimate. The different ways
>> of estimating tau^2 do often differ, sometimes by quite surprising
>> amounts. Whether that is related to the smallish number of studies I
>> could not say but, at the moment, there does not seem to be evicence of
>> anything wrong with the implementation of REML.
>>
>> Michael
>>
>> On 21/03/2023 14:57, Jorge Teixeira via R-sig-meta-analysis wrote:
>> > Hi.
>> >
>> > Let me know if you need me to provide the data for this example.
>> > Screenshots in the bottom.
>> >
>> > I ran this MA with REML, and the weight for random and common effects
>> > are exactly the same! Never saw anything like this. t2values also don’t
>> > look plausible.
>> >
>> > *_#1_*
>> > vo2 <- metacont(en  , em, esd, cn, cm, csd, study, method.tau = "REML",
>> > prediction = TRUE, data = dat_vo2, sm = "MD")
>> > vo2
>> >
>> > Is this a bug or a particular issue of low number of studies and low
>> > sample size?
>> >
>> > *_#2_*
>> > vo2 <- metacont(en  , em, esd, cn, cm, csd, study, method.tau = "DL",
>> > prediction = TRUE, data = dat_vo2, sm = "MD")
>> > vo2
>> >
>> > I ran this with DL estimator and weights and t2are plausible. I also ran
>> > other similar MA using REML and this was all okay.
>> >
>> > #1 using SMD instead of MD also looks fine.
>> >
>> >
>> > Thanks,
>> > Jorge
>> >
>> >
>> > *_REML:_*
>> >
>> > image.png
>> >
>> >
>> > *_DL:_*
>> > image.png