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

Tue Oct 5 23:51:37 CEST 2021

Dear All,

I just read a paper (
https://link.springer.com/content/pdf/10.3758/s13428-011-0153-1.pdf) that
made me think whether I understood your advice correctly or not.

My question was what to do with studies that provide "means" and "sds" for
"student-level" data while they ignore their students being nested in
classrooms.

The article linked above says that only if we calculate an SMD based on
"cluster-level" data (d_cluster), then d_cluster is upwardly biased.

But I want to calculate an SMD for studies only based on "student-level"
data (d_individual), so do I need to adjust "d_individual" just like
"d_cluster"?

Thank you for clarifying this confusion for me,
Tim M

On Fri, Oct 1, 2021 at 3:47 PM Mikkel Vembye <mikkel.vembye using gmail.com>
wrote:

> No it isn't. I mainly have it from James and his blog (see link below),
> and then I added the correction from WWC.
> https://www.jepusto.com/alternative-formulas-for-the-smd/
>
> James, please let me/us know if this approach is viable. :)
>
> Mikkel
>
> Den fre. 1. okt. 2021 kl. 22.27 skrev Timothy MacKenzie <fswfswt using gmail.com
> >:
>
>> Mikkel,
>>
>> Thank you. Is this new formula (with F-value) for the sampling variance
>> of g in the WWC procedures handbook? Would you please provide a reference?
>>
>> Best regards,
>> Tim M
>>
>> On Fri, Oct 1, 2021 at 3:22 PM Mikkel Vembye <mikkel.vembye using gmail.com>
>> wrote:
>>
>>> 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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