[R-meta] Meta-analyzing studies that failed to account for their nested data

[Mikkel Vembye]

When I have relevant F-values from ANCOVA and related models, I calculate
vg_corrected = omega^2 * [(g_corrected^2/F-value) * eta +
g_corrected^2/(2*h)]

Have a nice weekend.

Best,
Mikkel

Den fre. 1. okt. 2021 kl. 21.41 skrev Mikkel Vembye <mikkel.vembye using gmail.com
>:

> Sorry. I referred to an older version of the Appendix. I usually just
> follow WWC's recommendation when I cannot obtain R2. This is
>
> "if R2 is not available, then WWC will take a cautious approach to
> calculating the
> standard error and assume a value of zero for R2. This cautious approach
> will overestimate the
> magnitude of the standard error but protects against type I error." (See
> the WWC Procedure Handbook, p. E-5)
>
> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Procedures-Handbook-v4-1-508.pdf
>
>
> Whether this approach is better, is more a James question.
>
> Mikkel
>
> Den fre. 1. okt. 2021 kl. 19.44 skrev Timothy MacKenzie <fswfswt using gmail.com
> >:
>
>> Much appreciated, Mikkel. I saw that. BTW, there is no Table 5, it's a
>> typo in the WWC document (I found other typos as well).
>>
>> But I have both ANOVAs and a few ANCOVAs from primary studies that did
>> cluster assignment but ignored nesting structure, with barely any R^2
>> reported in them.
>>
>> My understanding is that I should find a more general SE[g] that only
>> requires icc, am I correct in thinking this way?
>>
>> Thanks,
>> Tim M
>>
>> On Fri, Oct 1, 2021 at 12:32 PM Mikkel Vembye <mikkel.vembye using gmail.com>
>> wrote:
>>
>>> Hi Tim,
>>>
>>> Glad that I/we can help. You find the ANCOVA examples (both uncorrected
>>> and corrected) in Table 3.
>>>
>>> [image: image.png]
>>>
>>> I forgot to mention that you also can find some corrections to Hedges
>>> (2007) in Table 5.
>>>
>>> All the best,
>>> Mikkel
>>>
>>> Den fre. 1. okt. 2021 kl. 19.21 skrev Timothy MacKenzie <
>>> fswfswt using gmail.com>:
>>>
>>>> Dear James and Mikkel,
>>>>
>>>> Thank you both. In my case, the primary studies have used AN(C)OVAs
>>>> with (non-)random assignment of classes to conditions. I have the
>>>> Means and SDs of student-level data for conditions.
>>>>
>>>> Based on:
>>>> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf
>>>> , I should use the unbiased version of equation E.5.1 to compute the
>>>> SMD effect size (g):
>>>>
>>>> g = wb / s * sqrt(  1 - (2*(n-1)*icc / N - 2)  ) ; s = pooled standard
>>>> deviation; n = ave. cluster size; N = n_t + n_c;  w = hedges'
>>>> correction factor
>>>>
>>>> Based on the same document, the standard error of g (SE[g]) for
>>>> cluster-assignment studies is (equation E.7.1 under "Cluster
>>>> assignment"):
>>>>
>>>> SE[g] = w * sqrt(  (SE_uc / s )^2 * eta + (g^2 / (2*h))  ); eta =  1 +
>>>> (n - 1)*icc; h = ( [(N-2)-2*(n-1)*icc ]^2 ) / ((N-2)*(1-icc)^2 +
>>>> 2*(N-2*n)*icc*(1-icc)  )
>>>>
>>>> where SE_uc = regression coefficient standard errors uncorrected for
>>>> clustering in the primary studies.
>>>>
>>>> Am I pointing to the correct formulas? If yes, I don't have SE_uc in
>>>> my primary studies, what should I do?
>>>>
>>>> Thanks,
>>>> Tim M
>>>>
>>>>
>>>> ------ Forwarded Message ------
>>>> From: Mikkel Vembye <mikkel.vembye using gmail.com>
>>>> Date: Fri, Oct 1, 2021 at 6:54 AM
>>>> Subject: Re-re: [R-meta] Meta-analyzing studies that failed to account
>>>> for their nested data
>>>> To: <fswfswt using gmail.com>, <r-sig-meta-analysis using r-project.org>
>>>>
>>>>
>>>> Hi Tim,
>>>>
>>>> Just to follow up on James, WWC do also have a nice description of how
>>>> they handle cluster trials and quasi-experiments:
>>>>
>>>> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf
>>>>
>>>> Mikkel
>>>>
>>>>
>>>> On Thu, Sep 30, 2021 at 11:09 PM James Pustejovsky <jepusto using gmail.com>
>>>> wrote:
>>>> >
>>>> > For studies that claim to find negligible ICCs, I would guess that
>>>> they base this judgement either on a) failing to reject a test of ICC = 0
>>>> or b) a rule of thumb. a) is not a good justification because with few
>>>> classes, the test will have little power. b) is arbitrary and even small
>>>> ICCs (of say 0.02 or 0.04) can be consequential for estimating the variance
>>>> of the effect size estimate. I would use the ICC adjustment regardless.
>>>> >
>>>> > To your second question, yes these adjustments are also important for
>>>> quasi-experiments.
>>>> >
>>>> > James
>>>> >
>>>> > On Thu, Sep 30, 2021 at 10:53 PM Timothy MacKenzie <fswfswt using gmail.com>
>>>> wrote:
>>>> >>
>>>> >> Dear James,
>>>> >>
>>>> >> Many thanks for this information. Certainly this is serious.
>>>> >>
>>>> >> I should add that a few of the (newer) studies in my pool say that
>>>> >> they found their ICCs to be negligible and opted for the single-level
>>>> >> analyses (maybe I should not adjust the sampling variances in these
>>>> >> cases, correct?).
>>>> >>
>>>> >> Also, I'm assuming that I can use these sampling variance adjustments
>>>> >> for quasi-experiments where schools/centers themselves haven't been
>>>> >> randomly recruited as well?
>>>> >>
>>>> >> Thanks,
>>>> >> Tim M
>>>> >>
>>>> >> On Thu, Sep 30, 2021 at 9:40 PM James Pustejovsky <jepusto using gmail.com>
>>>> wrote:
>>>> >> >
>>>> >> > Hi Tim,
>>>> >> >
>>>> >> > One important issue here is that the sampling variance of the
>>>> effect size estimate calculated from such a study will be
>>>> inaccurate---possibly even an order of magnitude smaller than it should be.
>>>> If you ignore this, the consequence will be to make the effect size
>>>> estimates appear far more precise than they actually are.
>>>> >> >
>>>> >> > To properly correct the sampling variance estimate, you would need
>>>> to know the intra-class correlation describing the proportion of the total
>>>> variation in the outcome that is at the cluster level (in this case, what
>>>> fraction of the total variance is between classes?). If this isn't
>>>> reported, then it may be possible to develop a reasonable estimate based on
>>>> external information. The Cochrane Handbook describes how to correct the
>>>> sampling variance based on an imputed intra-class correlation:
>>>> >> >
>>>> https://training.cochrane.org/handbook/current/chapter-23#section-23-1
>>>> >> > Hedges (2007; https://doi.org/10.3102/1076998606298043) and
>>>> (2011; https://doi.org/10.3102/1076998610376617) provides slightly
>>>> more elaborate methods that can be used if you have more details about the
>>>> study designs. Hedges and Hedberg's Variance Almanac (
>>>> http://stateva.ci.northwestern.edu/) is a helpful source for
>>>> developing estimates of ICCs for educational outcomes.
>>>> >> >
>>>> >> > James
>>>> >> >
>>>> >> > On Thu, Sep 30, 2021 at 4:58 PM Timothy MacKenzie <
>>>> fswfswt using gmail.com> wrote:
>>>> >> >>
>>>> >> >> Hello All,
>>>> >> >>
>>>> >> >> I've noticed almost all the studies I have selected for
>>>> meta-analysis
>>>> >> >> have ignored the nested structure of their data (subjects nested
>>>> in
>>>> >> >> classrooms) and have conducted only single-level analyses.
>>>> >> >>
>>>> >> >> I've extracted the condition-level summaries from those studies
>>>> (i.e.,
>>>> >> >> Means and SDs for C vs. T groups).
>>>> >> >>
>>>> >> >> But I'm wondering if I can/should make any adjustment to my
>>>> >> >> meta-regression model to account for the nested structure of the
>>>> data
>>>> >> >> in those studies AND if not, whether such a situation poses a
>>>> >> >> limitation to my meta-analysis?
>>>> >> >>
>>>> >> >> Thank you very much for your assistance,
>>>> >> >> Tim M
>>>> >> >>
>>>> >> >> _______________________________________________
>>>> >> >> R-sig-meta-analysis mailing list
>>>> >> >> R-sig-meta-analysis using r-project.org
>>>> >> >> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>>
>>>

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