Post model fitting checks in Metafor (rma.mv)

Regarding the profile plot for sigma2: I am not quite sure I understand. Does it 'peak' at zero? So, is the estimate (essentially) zero then? That would be okay (essentially means that the variability due to 'Study' is no larger than what would be expected due to the other variance components and/or sampling variability). The issue of zero variance components was also recently (and also in past) discussed on this list (not with respect to meta-analysis, but it's the same issue).

Regarding the resid-fitted plot: So, looks like you have some missings, so the two vectors end up being of different length. This should do it:

options(na.action = "na.pass")
plot(fitted(res), rstandard(res)$z, pch=19)

Also explained here: http://www.metafor-project.org/doku.php/tips:handling_missing_data

Regarding overall effects: I personally don't think an 'overall' effect makes much sense when the effect size appears to be related to a number of moderators/covariates. Take the simplest situation, where the true effect is of size theta_1 for level 1 of a dichotomous covariate and theta_2 for level 2. Now suppose we ignore that covariate and fit a random-effects model. Essentially, that is a misfitted model, because the model assumes normally distributed true effects (and not two point massess). Also, where the 'average' effect then falls depends on how many studies in the sample are at level 1 and at level 2 of that covariate. That doesn't seem that sensible to me. So, instead, we can fit the model with the covariate and then compute predicted values, for example, for level 1 or level 2. Or, if you really want an 'overall' effect, we could use a sort of 'lsmeans' approach and say: Let's assume that in the population of studies, 50% are at level 1 and 50% at level 2, so let's compute the predicted effect for such a population (essentially fill in 0.5 for the 'dummy' variable when computing the predicted value). But I would then describe explicitly that this is what was done (as it makes clear what the assumption is about the population of studies).

I discuss this issue a bit in this article:

Viechtbauer, W. (2007). Accounting for heterogeneity via random-effects models and moderator analyses in meta-analysis. Zeitschrift f?r Psychologie / Journal of Psychology, 215(2), 104-121.

(not the 'lsmeans' idea, but the problem of fitting random-effects models when there is a relevant moderators/covariate). If you can't access the article, let me know and I'll send you a copy if you are interested.

Best,
Wolfgang

> -----Original Message-----
> From: Shona Smith [mailto:s.smith.7 at research.gla.ac.uk]
> Sent: Wednesday, September 03, 2014 13:39
> To: Viechtbauer Wolfgang (STAT); r-sig-mixed-models at r-project.org
> Subject: RE: Post model fitting checks in Metafor (rma.mv)
>
> Hi Wolfgang,
>
> Thanks for such a useful and quick reply.  The sigma2 profile plot does
> not have a peak - but it's not flat, it seems to just decline (even when
> I expand the x axis values) - I wondered what this meant?  The other two
> look fine, although tau2 drops off much more gradually than rho (which is
> quite a steep drop) after the parameter estimate.  What would be the
> ideal plot?
>
> I can now plot the standardised residuals but fitted against residuals
> gives me an error:
>
> plot(fitted(res), rstandard(res)$z, pch=19)
> Error in xy.coords(x, y, xlabel, ylabel, log) :
>   'x' and 'y' lengths differ
>
> The fitted values seem to have the row number alongside each value,
> whiles the standardised residuals don't - so perhaps this is the problem?
>
> Finally, I also wondered if it is possible to get an overall effect size
> estimate for my response variable?  I notice other studies have carried
> out a separate meta-analysis to obtain this, before looking at
> moderators, but I wasn't sure if this was correct.
>
> Thanks again,
> Shona
>
>
> Shona Smith
> PhD Researcher
>
> Room 321
> Institute of Biodiversity, Animal Health and Comparative Medicine
> Graham Kerr Building
> University of Glasgow
> Glasgow G12 8QQ
> ________________________________________
> From: Viechtbauer Wolfgang (STAT)
> [wolfgang.viechtbauer at maastrichtuniversity.nl]
> Sent: 03 September 2014 10:28
> To: Shona Smith; r-sig-mixed-models at r-project.org
> Subject: RE: Post model fitting checks in Metafor (rma.mv)
>
> Dear Shona,
>
> The profile() function in metafor allows you to examine the profiled
> (restricted) log-likelihood for a particular parameter. So, ideally, you
> should do this for each variance component and correlation in the model
> (in your case, sigma2, tau2 and rho). I am not sure what you mean by: "
> how I know which value to specify for each?" After you have fitted your
> model and stored the results in, let's say, 'res', then just do:
>
> par(mfrow=c(3,1))
> profile(res, sigma2=1)
> profile(res, tau2=1)
> profile(res, rho=1)
>
> to get all three profile plots. And yes, the functions should peak at the
> parameter estimates. If a function is flat, then this suggests that the
> model is overparameterized.
>
> You could also look at how quickly the log-likelihood drops off as you
> move away from the parameter estimate. The bounds of a 95% profile
> likelihood CI for a particular parameter would be those two values from
> the x-axis where the log-likelihood has dropped by 3.84/2. You could add
>
> abline(h = logLik(res) - qchisq(.95, df=1)/2, lty="dotted")
>
> to the figures to see that cutoff. Depending on how much data you have,
> you may find that those CIs are quite wide. You may have to increase the
> x-axis range, in case the cutoff isn't reached within the range chosen by
> default by the profile function (use the 'xlim' argument).
>
> Indeed, you could also look at the (standardized) residuals. Use
>
> rstandard(res)$z
>
> to get those values. Or:
>
> plot(fitted(res), rstandard(res)$z, pch=19)
>
> to create a fitted values versus standardized residuals plot.
>
> As for the interpretation of the results when you exclude the intercept
> (i.e., mods = ~ Age + Treatment + Biomarker - 1), you will get the
> estimated (average) effect for each level of 'Age', but the coefficients
> for 'Treatment' and 'Biomarker' are still going to be contrasts that
> indicate how much higher/lower the (average) effect is for the levels
> indicated, relative to the reference level.
>
> I hope this helps!
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-
> > models-bounces at r-project.org] On Behalf Of Shona Smith
> > Sent: Tuesday, September 02, 2014 18:37
> > To: r-sig-mixed-models at r-project.org
> > Subject: [R-sig-ME] Post model fitting checks in Metafor (rma.mv)
> >
> > Hi all,
> >
> > I am currently conducting a meta-analysis using rma.mv in metafor.  My
> > model uses Hedges' d (converted to g) and includes 3 moderators (age-3
> > levels; treatment-5 levels; biomarker-3 levels).  I have included 3
> > random effects: species nested within taxonomic class (since I have
> more
> > than one study for some species, and species are spread over 7
> taxonomic
> > classes) and study separately.  So my code is as follows:
> >
> > rma.mv(yi, vi, mods = ~ Age + Treatment + Biomarker, random = list(~ 1
> |
> > Study, ~ Species | Taxonomic.class), data=mydata)
> >
> > I was wondering what the best method for post model fitting checks was
> in
> > rma.mv?  I know in the reference manual it mentions profile.rma to
> create
> > a plot of the restricted log likelihood and I have done so.  However, I
> > wondered if I need to plot all 3 variables (sigma2, tau2 and rho) and
> > also how I know which value to specify for each?  Am I correct in that
> I
> > should see a clear peak in each graph?  Is there anything else I should
> > be looking for?
> >
> > For post model fitting checks should I also look at residual normality
> > and residual against fitted values, as would be done for a typical
> mixed
> > model?  I think the standardised residuals are best for this - I can
> get
> > them with rstandard.rma.mv, but it does not allow me to plot them.
> >
> > Finally, when I include the intercept in the model, I can see if there
> > are significant differences among moderator levels.  However, I was
> > wondering what the output includes when the intercept is not included:
> is
> > this the overall effect size estimates for each moderator level?
> >
> > Kind regards,
> > Shona
> >
> >
> > Shona Smith
> > PhD Student
> >
> > Room 321
> > Institute of Biodiversity, Animal Health and Comparative Medicine
> > Graham Kerr Building
> > University of Glasgow
> > Glasgow G12 8QQ
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models