The metafor Package

A Meta-Analysis Package for R

User Tools

Site Tools

analyses:konstantopoulos2011

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revisionBoth sides next revision
analyses:konstantopoulos2011 [2020/05/01 14:01] – Wolfgang Viechtbaueranalyses:konstantopoulos2011 [2021/10/20 18:55] – Wolfgang Viechtbauer
Line 260: Line 260:
 We can fit the same model using a multivariate parameterization, which directly provides us with the ICC. For this, we use the syntax: We can fit the same model using a multivariate parameterization, which directly provides us with the ICC. For this, we use the syntax:
 <code rsplus> <code rsplus>
-res.mv <- rma.mv(yi, vi, random = ~ factor(study) | district, data=dat)+res.mv <- rma.mv(yi, vi, random = ~ study | district, data=dat)
 print(res.mv, digits=3) print(res.mv, digits=3)
 </code> </code>
Line 286: Line 286:
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 </code> </code>
-The ''random = ~ factor(study) | district'' argument adds correlated random effects for the different studies within districts to the model, where the variance-covariance matrix of the random effects takes on a compound symmetric structure (''struct="CS"'' is the default). Note that the estimate of $\rho$ that is obtained is exactly the same as the ICC value we computed earlier based on the multilevel model. Also, the estimate of $\tau^2$ obtained from the multivariate parameterization is the same as the total amount of heterogeneity computed earlier based on the multilevel model. Note that ''random = ~ factor(school) | district'' would again yield the same results.+The ''random = ~ study | district'' argument adds correlated random effects for the different studies within districts to the model, where the variance-covariance matrix of the random effects takes on a compound symmetric structure (''struct="CS"'' is the default). Note that the estimate of $\rho$ that is obtained is exactly the same as the ICC value we computed earlier based on the multilevel model. Also, the estimate of $\tau^2$ obtained from the multivariate parameterization is the same as the total amount of heterogeneity computed earlier based on the multilevel model. Note that ''random = ~ school | district'' would again yield the same results.
  
 As long as $\rho$ is estimated to be positive, the multilevel and multivariate parametrizations are in essence identical. In fact, the log likelihoods of the two models should be identical, which we can confirm with: As long as $\rho$ is estimated to be positive, the multilevel and multivariate parametrizations are in essence identical. In fact, the log likelihoods of the two models should be identical, which we can confirm with:
Line 348: Line 348:
 Finally, for illustration purposes, it is instructive to examine what can happen when we fit an overparameterized model. For example, suppose we combine the multilevel and multivariate structures above in a single model: Finally, for illustration purposes, it is instructive to examine what can happen when we fit an overparameterized model. For example, suppose we combine the multilevel and multivariate structures above in a single model:
 <code rsplus> <code rsplus>
-res.op <- rma.mv(yi, vi, random = list(~ factor(study) | district, ~ 1 | district, ~ 1 | study), data=dat)+res.op <- rma.mv(yi, vi, random = list(~ study | district, ~ 1 | district, ~ 1 | study), data=dat)
 print(res.op, digits=3) print(res.op, digits=3)
 </code> </code>
analyses/konstantopoulos2011.txt · Last modified: 2022/08/22 16:00 by Wolfgang Viechtbauer