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--- tips:comp_two_independent_estimates [2023/02/18 17:35] – Wolfgang Viechtbauer
+++ tips:comp_two_independent_estimates [2023/02/18 19:24] – Wolfgang Viechtbauer
@@ Line 169: / Line 169: @@
 Note that the two estimates of $\tau^2$ are now identical to the ones we obtained earlier from the separate random-effects models. Also, the coefficient, standard error, and p-value for the moderator now matches the results obtained earlier.((See also [[tips:different_tau2_across_subgroups|here]] for another example to illustrate various approaches for allowing $\tau^2$ to differ across subgroups.))
-A discussion/comparison of these two approaches (i.e., assuming a single $\tau^2$ value or allowing $\tau^2$ to differ across subsets) can be found in the following article:
+A discussion/comparison of these two approaches (i.e., assuming a single $\tau^2$ value or allowing $\tau^2$ to differ across subsets) can be found in the following articles:
+Rubio-Aparicio, M., Sánchez-Meca, J., López-López, J. A., Botella, J. & Marín-Martínez, F. (2017). Analysis of categorical moderators in mixed-effects meta-analysis: Consequences of using pooled versus separate estimates of the residual between-studies variances. //British Journal of Mathematical and Statistical Psychology, 70//(3), 439-456. [[https://doi.org/https://doi.org/10.1111/bmsp.12092]]
 Rubio-Aparicio, M., López-López, J. A., Viechtbauer, W., Marín-Martínez, F., Botella, J., & Sánchez-Meca, J. (2020). Testing categorical moderators in mixed-effects meta-analysis in the presence of heteroscedasticity. //Journal of Experimental Education, 88//(2), 288-310. [[https://doi.org/10.1080/00220973.2018.1561404]]
-We can also do a likelihood ratio test (LRT) to examine whether there are significant differences in the $\tau^2$ values across subsets. This can be done with:
+We can also conduct a likelihood ratio test (LRT) to examine whether there are significant differences in the $\tau^2$ values across subsets. This can be done with:
 <code rsplus>
@@ Line 188: / Line 190: @@
 So in this example, we would not reject the null hypothesis $H_0: \tau^2_1 = \tau^2_2$ ($p = .58$).
+==== Other Types of Models ====
+The issue discussed above also arises for other types of models (e.g., multilevel meta-analytic models). When fitting a particular model within several subgroups, then the variance components of the model are automatically allowed to differ across the subgroups. On the other hand, when fitting the same type of model to all studies combined (but including a moderator to allow the mean effect size to differ across subgroups), then the variance components are assumed to be the same within each subgroups (unless one takes extra steps as illustrated above to allow the variance components to differ across subgroups). Consequently, the results obtained with these two approaches will not be identical.