Hello!
I'm trying to work with the metaSEM package for the first time, and I really appreciate it so far!
Why is weighting of the ES by the inverse variance in tssem1 only implemented for fixed effects? Aside from the results of the SEM structure in tssem2, I would like to give readers of my results both FE and RE estimates of the pooled correlation matrix, but I want both to reflect the variance/sample size and they wouldn't be comparable if only one of the methods uses inverse weighting by the variance.
Is there a way to do this for RE, too, or is there a reason why this wouldn't make sense in multivariate RE models?
Thank you!
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Hi,
The multivariate RE model takes the inverse of the sampling covariance matrix of the correlations into account. Besides the sampling covariance matrix of the correlations, it also takes the variance component of the random effects in the estimation. The following is an example:
Fixed-effects model
fixed1 <- tssem1(Digman97$data, Digman97$n, method="REM", RE.type="Zero")
Common correlation matrix
vec2symMat( coef(fixed1), diag=FALSE )
Sampling covariance matrix
vcov(fixed1)
Random-effects model
random1 <- tssem1(Digman97$data, Digman97$n, method="REM", RE.type="Diag")
Average correlation matrix
vec2symMat( coef(random1, select="fixed"), diag=FALSE )
Sampling covariance matrix
vcov(random1, select="fixed")
Mike
Hello,
Thank you very much for your answer!
However, when I experimentally change the weight of an outlier (e.g., one of the Costa & McCrae studies has a correlation of .44 between A and I, but the pooled correlation is only .09), this doesn't affect the pooled estimate, as it should in weighted meta-analysis (and as it does in univariate analysis with metaSEM).
Digman97_edt <- Digman97
Digman97_edt$n[10] <- 100000
Rerunning your code with Digman97_edt with either RE.type="Zero" or "Diag" gives me combined correlation matrices with the same values as using Digman97. The target correlation remains, in all cases, .09.
In contrast, using method = "FEM" seems to take the changed weight into account: With Digman97, the correlation is .09, but with Digman97_edt, it is .43.
fixed1.1 <- tssem1(Digman97$data, Digman97$n, method="FEM")
coef(fixed1.1)
fixed2.1 <- tssem1(Digman97_edt$data, Digman97_edt$n, method="FEM")
coef(fixed2.1)
Is there a way to reflect differences in sample size, such as my extreme example, when using method = "REM"?
Thank you!
Sophie
Hello,
This is a fundamental difference between a fixed- and a random-effects model. In the fixed-effects model, the weights are primarily determined by the inverse of the sampling variances (and covariances), which are a function of N.
In the random-effects model, the weights are determined by both the sampling variances and the between-study heterogeneity variances. Even though the sampling variance is close to 0 in Digman97_edt$n[10] <- 100000, there are still between-study heterogeneity variances. Although the 10th study get a largest weight, it might not be as large as your think in a random-effects model.
If you want your weights to be proportionally related to the sample sizes, you can only do it under the fixed-effects model.
Mike