I am running a simple random-effects meta-analysis in R using the metafor package, with random intercepts at the study level:
mod1 <- rma.mv(Hedges_g, cov, random = ~ 1 | study, data = rev)
This is the model output:
Multivariate Meta-Analysis Model (k = 90; method: REML) logLik Deviance AIC BIC AICc -170.3401 340.6802 344.6802 349.6575 344.8197 Variance Components: estim sqrt nlvls fixed factor sigma^2 0.5512 0.7424 24 no study Test for Heterogeneity: Q(df = 89) = 1014.3323, p-val < .0001 Model Results: estimate se zval pval ci.lb ci.ub 0.9749 0.1572 6.2018 <.0001 0.6668 1.2830
As I understand, the observation of significant heterogeneity means that the estimate of g = 0.97 cannot be regarded as an estimate of one true effect. Rather, the studies in this data set seem to be estimating different true effects.
Now, I'm comparing my model (mod1) to another model without random intercepts at the study level:
mod0 <- rma.mv(Hedges_g, cov, data = rev, method = "ML") (I have set method = "ML" for mod1 too, to enable the comparison). This is the output for
df AIC BIC AICc logLik LRT pval QE Full 2 347.2963 352.2960 347.4343 -171.6482 1014.3323 Reduced 1 916.1363 918.6361 916.1818 -457.0682 570.8400 <.0001 1014.3323
Thus, mod1 fits the data significantly better than mod0. This means that the estimated between-study variance of sigma^2 = 0.55, is significant. To me, this would also suggest that the studies are estimating significantly different true effects.
My question now is: what is the difference between the test for heterogeneity, and the model comparison? Do they both lead to the exact same conclusion ("There is heterogeneity among the true effects"), or is there more nuance to it?