[R-meta] Spatial-temporal meta-analysis

[Viechtbauer Wolfgang (SP)]

Meta-analytic models (like the ones that can be fitted with rma() and rma.mv()) are linear models. So, if you want to examine if the observed outcomes are related to time, then you could examine this by including an appropriate measure of time in your model as a predictors/moderator. Similarly, if you have some information on the location of the measurements and you want to examine if there is some relationship between the location and the size of the outcomes, this can be done via meta-regression. How best to do this in your particular case is a substantive question that I cannot answer.

Alternatively, one could consider modeling space and time via random effects. For time, this might imply assuming an autoregressive structure for the random effects. rma.mv() includes random effects structures for AR1 and (just recently added) continuous-time autoregressive models. See help(rma.mv) and search for "AR" and "CAR" (for the latter, make sure you install the devel version of the metafor package: http://www.metafor-project.org/doku.php/installation#development_version). There are two datasets that illustrate the use of such structures: see help(dat.fine1993) and help(dat.ishak2007). It is useful to closely read the corresponding articles to get a better idea of how this works. There is also:

Musekiwa, A., Manda, S. O., Mwambi, H. G., & Chen, D. G. (2016). Meta-analysis of effect sizes reported at multiple time points using general linear mixed model. PLOS ONE, 11(10), e0164898.

which also illustrates this, using metafor.

For space, you might need to use a spatial random effects structure. At the moment, this could be done by computing a distance matrix (assuming you have information on the location of the measurements) and turning this into a spatial covariance/correlation matrix, for example based on an exponential or Gaussian function; see: https://en.wikipedia.org/wiki/Covariance_function#Parametric_families_of_covariance_functions Then you can include the spatial correlation matrix via the 'R' argument in rma.mv(). Since such spatial structures depend on one (or more) unknown parameters, you would have to do the optimization over that parameter manually (e.g., trying out a bunch of values for the unknown parameters and finding the ones that maximizes the likelihood) or wrap rma.mv() in an extra optimization step. In the future, rma.mv() might include spatial structures directly.

The best illustration of using the 'R' argument in rma.mv() I have at the moment shows how to do a phylogentic meta-analysis:

http://www.metafor-project.org/doku.php/tips:speeding_up_model_fitting#complex_models

That's something different than a spatial structure, but it illustrates how the 'R' argument works.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
>project.org] On Behalf Of Rafael Rios
>Sent: Monday, 13 November, 2017 15:26
>To: Michael Dewey; r-sig-meta-analysis at r-project.org
>Subject: Re: [R-meta] Spatial-temporal meta-analysis
>
>Dear Michael,
>
>Thank you for the reply and assistence. I want to evaluate potential
>spatio-temporal variation in effect size. Thus, I may built a random
>effects meta-analysis to test if effect size changes (or it is
>consistent)
>in space and time. I am having difficulty to choose an appropriate
>approach
>to reach this goal.
>
>Abraço,
>
>Rafael R. Moura.
>*scientia amabilis*
>
>Doutorando da Pós-graduação em Ecologia e Conservação de Recursos
>Naturais
>Universidade Federal de Uberlândia, Uberlândia, MG, Brasil
>
>ORCID: http://orcid.org/0000-0002-7911-4734
>Currículo Lattes:
>http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4244908A8
>Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2
>
><http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4244908A8>
>
>2017-11-13 7:46 GMT-02:00 Michael Dewey <lists at dewey.myzen.co.uk>:
>
>> Dear Rafael
>>
>> It might help to have just a sentence or two about the scientific
>question
>> here as I (and perhaps others) am not quite clear what your phrase
>> "variation in average effect size is greater than zero" means.
>>
>> Michael
>>
>> On 12/11/2017 17:08, Rafael Rios wrote:
>>
>>> Dear Wolfgang,
>>>
>>> Thank you for the attention. My data set follows on attached (CSV
>file).
>>> When we found more than one season (three, for instance), we wrote "3"
>in
>>> the "season" column. Follow, we identified seasons as "1", "2" and "3"
>in
>>> the "class_season" column corresponding to each effect size. When
>there was
>>> only one season, we wrote "1" in the season column and "0" in the
>>> class_season column. We adopted the same procedure for the "pop" and
>>> "pop_class" columns corresponding to data about one or more
>populations. We
>>> also used as random variables "study" and "species". How may I do a
>random
>>> effects model to evaluate if variation in average effect size is
>greater
>>> than zero?
>>>
>>> Abraço,
>>>
>>> Rafael R. Moura.
>>> /scientia amabilis/
>>>
>>> Doutorando da Pós-graduação em Ecologia e Conservação de Recursos
>Naturais
>>> Universidade Federal de Uberlândia, Uberlândia, MG, Brasil
>>>
>>> ORCID: http://orcid.org/0000-0002-7911-4734
>>> Currículo Lattes: http://buscatextual.cnpq.br/bu
>>> scatextual/visualizacv.do?id=K4244908A8
>>> Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2