[R-meta] Moderator analysis test of residual heterogeneity confusion

[James Pustejovsky]

Mia,

To add a little bit to Wolfgang's feedback: Even if you fit the two models
on the same set of observations (say, assuming that you had complete data
for all of the moderators), my understanding is that adding more moderators
will not necessarily explain more of the residual heterogeneity. It is true
that, in regular old linear regression models, adding more predictors will
always increase R-squared, but once we are in the land of multi-level
models, there is no such guarantee (unfortunately!).

To help diagnose what is going on in situations like this, it is useful to
have an understanding of whether the moderators vary at the within-study
level or only at the between-study level.

James

On Wed, Sep 18, 2019 at 3:17 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> The first model has 8 model coefficients with k = 456. The second model
> has 58 model coefficients with k = 389. So, the datasets used in those two
> analyses are not the same (probably because of missing values on some of
> the moderators included in the second model). So, it's a bit difficult to
> compare the results. This aside, including 58 model coefficients with k =
> 389 is not a good idea. This is likely to lead to overfitting.
>
> Also, I notice that the random effect you added is called 'study', while k
> is much larger than the number of studies. This was actually just discussed
> on this mailing list, but to repeat: You really should also include an
> observation-level random effect in the model.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Mia Daucourt [mailto:miadaucourt using gmail.com]
> Sent: Wednesday, 18 September, 2019 19:35
> To: Viechtbauer, Wolfgang (SP)
> Cc: r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] Moderator analysis test of residual heterogeneity
> confusion
>
> Oops, let me try that again...
>
> I am using the metafor package to run a multilevel correlated effects
> model. For moderator analyses, I am running them one at a time, to see how
> much heterogeneity each accounst for, and then I ran model with all mods to
> see how much variance is left to be explained they're combined.
>
> I have an odd a situation where there is no significant residual variance
> with just an individual moderator in the model, but then for a set of
> moderators (that includes that moderator) there is significant residual
> variance. How can this be?
>
> Maybe this output can help...
>
> Single moderator results:
>
> Multivariate Meta-Analysis Model (k = 456; method: REML)
>
>    logLik   Deviance        AIC        BIC       AICc
>  112.1356  -224.2713  -206.2713  -169.3281  -205.8603
>
> Variance Components:
>
>             estim    sqrt  nlvls  fixed  factor
> sigma^2    0.0136  0.1166     51     no   study
>
> Test for Residual Heterogeneity:
> QE(df = 448) = 409.9810, p-val = 0.9007
>
> Test of Moderators (coefficients 1:8):
> F(df1 = 8, df2 = 448) = 6.2947, p-val < .0001
>
> All mods results:
>
> Multivariate Meta-Analysis Model (k = 389; method: REML)
>
>   logLik  Deviance       AIC       BIC      AICc
> -36.0635   72.1270  186.1270  403.1911  210.1707
>
> Variance Components:
>
>             estim    sqrt  nlvls  fixed  factor
> sigma^2    0.0330  0.1818     43     no   study
>
> Test for Residual Heterogeneity:
> QE(df = 333) = 1028.1159, p-val < .0001
>
> Test of Moderators (coefficients 2:56):
> F(df1 = 55, df2 = 333) = 4.0802, p-val < .0001
>
> Thank you for your help!
>
> My best,
>
> Mia
>
> On Sep 18, 2019, at 12:50 PM, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> Dear Mia,
>
> Your screenshots did not come through properly. Note that this a text-only
> mailing list, so please post output, not screenshots. Also, please post in
> plain text -- not rich text format or HTML.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Mia Daucourt
> Sent: Wednesday, 18 September, 2019 18:24
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] Moderator analysis test of residual heterogeneity
> confusion
>
> Good afternoon,
>
> I am using the metafor package to run a multilevel correlated effects
> model. For moderator analyses, I am running them one at a time, to see how
> much heterogeneity each accounst for, and then I ran model with all mods to
> see how much variance is left to be explained they're combined.
>
> I have an odd a situation where there is no significant residual variance
> with just an individual moderator in the model, but then for a set of
> moderators (that includes that moderator) there is significant residual
> variance. How can this be?
>
> Maybe these screenshots can help...
> Single moderator results:
> Moderator analysis test of residual heterogeneity confusion
>
> All mods model results:
>
> Thank you for your help!
>
> My best,
>
> Mia
>
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