[R-meta] 3-level meta with robust errors

[Valeria Ivaniushina]

Dear James,
Thank you!

Attached are the code and the database.
And here is some results

> summary(based_inf)
Multivariate Meta-Analysis Model (k = 17; method: REML)
  logLik  Deviance       AIC       BIC      AICc
-14.2991   28.5983   34.5983   36.9161   36.5983

Variance Components:
            estim    sqrt  nlvls  fixed       factor
sigma^2.1  0.0000  0.0000     12     no     ID_study
sigma^2.2  4.1629  2.0403      5     no  ID_database

Test for Heterogeneity:
Q(df = 16) = 48.1411, p-val < .0001

Model Results:
estimate      se    tval    pval   ci.lb   ci.ub
  2.0905  0.9704  2.1542  0.0468  0.0333  4.1478  *


> coef_test(based_inf, vcov = "CR2",
+            cluster = wb$ID_database)
    Coef. Estimate    SE t-stat d.f. p-val (Satt) Sig.
1 intrcpt     2.09 0.954   2.19 3.91       0.0952    .


I think I found out where our mistake was.

The sandwich correction doesn't calculate Conf Intervals, so we calculated
them using formula: SE*1.96
Stupid, I know.
Still, even now I am not sure how to correctly calculate CI here - could
you please explain?

And another question
There are several methods for outliers detection: Cook distance,
residuals, hat values.  Rather often a study is problematic with one method
but OK with others. Are there any guidelines which studies should be
removed   -- i.e., when at least two methods indicate it as outliers?

Best,
Valeria


On Tue, Dec 1, 2020 at 9:10 PM James Pustejovsky <jepusto using gmail.com> wrote:

> Valeria,
>
> These are indeed perplexing results. Based on the information you've
> provided, it's hard to say what could be going on. Could you provide
> examples of the code you're using and the results of your analyses? Doing
> so will help to identify potential problems or coding errors.
>
> Kind Regards,
> James
>
> On Tue, Dec 1, 2020 at 10:45 AM Valeria Ivaniushina <
> v.ivaniushina using gmail.com> wrote:
>
>> Dear list members,
>>
>> We are conducting several meta-analyses using the metafor package in R
>> (Viechtbauer 2010) because of 3-level data structure, followed by
>> sandwich-type estimator with a small-sample adjustment to get cluster
>> robust standard errors.
>>
>> There are some things that puzzle me, and I hope to get answers from the
>> community.
>>
>> 1. We calculate 95% CI for our mean effect size, and p-value is calculated
>> as a part of the output. While CI always indicate significant mean effect
>> size, p-values are often > 0.05
>> - Should I report both CI and p-value?
>> - How to interpret such discrepancy?
>>
>> 2. When I draw a forest plot for a meta-analysis of 8 models, I can see
>> that 95% CIs for every coefficient contain zero (for example, -0.40 -
>> 0.84). However, the 95% CI for the mean coefficient is well above zero
>> (0,28 - 0,45).  How is it possible?
>>
>> 3.  Theoretically, the data has a 3-level structure (model; article;
>> database). But sometimes I see that there is no variance on one or two of
>> the levels. Should I repeat the analysis with only 2 or 1 level, according
>> to the variance distribution?
>>
>> Best, Valeria
>>
>>         [[alternative HTML version deleted]]
>>
>> _______________________________________________
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>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>
>

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