[R-meta] Multilevel Meta-regression with Multiple Level Covariates

This is an interesting framework (GEE that is) that I was not previously
familiar with. I appreciate bringing my attention to this. I agree that a
binomial distribution is more intuitive to what I'm trying to answer. If I
had actual, item-level data for a sample (i.e., each participant's
responses -- either 0 or 1 -- to each item), then I would use GLMM assuming
a binomial, though really Bernoulli, distribution to do an item response
theory model. The idea of doing this meta-analysis actually came from
trying to figure out how to do that kind of analysis on summary level data
since I don't have that individual-level data.

For my own edification, is this something that is doable in metafor? I
don't see how to specify a non-gaussian distribution in rma.mv, but I'm
also no expert on the metafor package. Cursory googling brought my
attention to gee and geepack packages for R, but it doesn't seem like it's
possible to include more than one cluster in those packages. I could do
this in lme4, but I believe that their estimation method is still
inappropriate for meta-analysis (though maybe this has been changed? it's
been a while since I looked at multilevel meta-analysis in lme4 since
rma.mv works so well).

Also, is there any guidance on how many studies should be collected for
these kinds of analyses? I suspect that this is a relatively specific
meta-analysis, and it sounds like rules-of-thumbs will be biased if the
distribution of moderators is restricted or sparse. Any good Monte Carlo
simulation methods that could be used to check the extent to which the
model has too few studies to estimate the various moderators?

On Mon, Sep 28, 2020 at 8:17 PM James Pustejovsky <jepusto at gmail.com>
wrote:

Hi Billy,

The approach you describe seems reasonable to me. Whether you've got too
many predictors will depend on how many studies' worth of data you are able
to gather and on the distribution of the item-level, study-level, and
test-level characteristics. Not knowing the correlations between items does
complicate things a bit, but could be handled using robust variance
estimation methods.

One way to set up this problem might be by using proportion of successes
as the effect size metric, modeled by a binomial distribution (where the
number of trials = number of respondents to that item), and where the
probability of success is related to the covariates via a logit (or probit)
link. Combining this with RVE for standard errors gives you something like
a GEE model.

James

On Fri, Sep 25, 2020 at 12:39 PM Billy Goette <billy.goette at gmail.com>
wrote:

Hope this finds everyone well,

I was hoping to get some feedback on addressing some practical concerns
with an idea for a meta-analysis that I have. At the core, I'm concerned
with the interpretability of the data analysis, so I'm trying to check
whether this is even possible before I start the study.

My field commonly administers lists of words that a participant must read
correctly. Item difficulty is often summarized in studies as the
proportion
of respondents who got an item correct over the total sample size.
Studies
use different word-reading tests and lists of varying length (usually
between 20 and 50). Each test differs in how long the words are
presented, how many words are presented at a time, etc. I'm interested in
whether certain word-specific variables (e.g., frequency of word in
English) are related to the item difficulty (i.e., proportion of people
who
answer it correctly).

My current conceptualization of the problem is as a multilevel
meta-regression. The effect size is computed from the proportion of
correct
answers to each word which is nested within study and within tests. I
would
have multiple covariates (i.e., word traits) for each effect size,
covariates at the study level (i.e., average sample demographics), and
covariates at the test level (i.e., administration differences). My
concern
is that these are too many predictors to include in a meta-regression,
and
I also am anticipating that I won't have any information about
the covariance matrix of the effect sizes. Any recommendations, words of
warning, caveats, or suggestions would be incredibly helpful since I'm
early in the process.

Thank you!

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