tips:comp_two_independent_estimates
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tips:comp_two_independent_estimates [2020/07/03 10:23] – Wolfgang Viechtbauer | tips:comp_two_independent_estimates [2021/11/08 15:49] – Wolfgang Viechtbauer | ||
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</ | </ | ||
- | We can now compare the two estimates (i.e., the estimated average log risk ratios) by feeding them back to the '' | + | We can now compare the two estimates (i.e., the estimated average log risk ratios) by feeding them back to the '' |
<code rsplus> | <code rsplus> | ||
rma(estimate, | rma(estimate, | ||
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While we find that studies using random assignment obtain on average larger (i.e., more negative) effects than studies not using random assignment ($b_1 = -0.490$, $SE = 0.351$), the difference between the two estimates is not significant ($z = -1.395$, $p = .163$). | While we find that studies using random assignment obtain on average larger (i.e., more negative) effects than studies not using random assignment ($b_1 = -0.490$, $SE = 0.351$), the difference between the two estimates is not significant ($z = -1.395$, $p = .163$). | ||
- | The test of the difference between the two estimates is really just a Wald-type test, given by the equation $$z = \frac{\hat{\mu}_1 - \hat{\mu}_2}{\sqrt{SE[\hat{\mu}_1]^2 + SE[\hat{\mu}_2]^2}}, | + | The test of the difference between the two estimates is really just a [[https:// |
<code rsplus> | <code rsplus> | ||
with(dat.comp, | with(dat.comp, | ||
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Signif. codes: | Signif. codes: | ||
</ | </ | ||
- | The result is very similar to what we saw earlier: The coefficient | + | The result is very similar to what we saw earlier: The coefficient |
However, the results are not exactly identical. The reason for this is as follows. When we fit separate random-effects models in the two subsets, we are allowing the amount of heterogeneity within each set to be different (as shown earlier, the estimates were $\hat{\tau}^2 = 0.393$ and $\hat{\tau}^2 = 0.212$ for studies using and not using random assignment, respectively). On the other hand, the mixed-effects meta-regression model fitted above has a single variance component for the amount of residual heterogeneity, | However, the results are not exactly identical. The reason for this is as follows. When we fit separate random-effects models in the two subsets, we are allowing the amount of heterogeneity within each set to be different (as shown earlier, the estimates were $\hat{\tau}^2 = 0.393$ and $\hat{\tau}^2 = 0.212$ for studies using and not using random assignment, respectively). On the other hand, the mixed-effects meta-regression model fitted above has a single variance component for the amount of residual heterogeneity, | ||
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A discussion/ | A discussion/ | ||
- | Rubio-Aparicio, | + | Rubio-Aparicio, |
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 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: |
tips/comp_two_independent_estimates.txt · Last modified: 2024/04/18 11:36 by Wolfgang Viechtbauer