tips:models_with_or_without_intercept
Differences
This shows you the differences between two versions of the page.
Next revision | Previous revisionNext revisionBoth sides next revision | ||
tips:models_with_or_without_intercept [2019/06/30 11:43] – external edit 127.0.0.1 | tips:models_with_or_without_intercept [2021/02/12 16:09] – Wolfgang Viechtbauer | ||
---|---|---|---|
Line 5: | Line 5: | ||
==== Model With Intercept ==== | ==== Model With Intercept ==== | ||
- | The dataset is called '' | + | The dataset is called '' |
<code rsplus> | <code rsplus> | ||
library(metafor) | library(metafor) | ||
Line 106: | Line 106: | ||
& | & | ||
\end{align} | \end{align} | ||
- | But what about the contrast between | + | But what about the contrast between systematic |
$$ | $$ | ||
\beta_2 - \beta_1 = (\mu_r - \mu_a) - (\mu_s - \mu_a) = \mu_r - \mu_s | \beta_2 - \beta_1 = (\mu_r - \mu_a) - (\mu_s - \mu_a) = \mu_r - \mu_s | ||
$$ | $$ | ||
- | so this difference | + | so this contrast |
<code rsplus> | <code rsplus> | ||
anova(res, L=c(0, | anova(res, L=c(0, | ||
Line 202: | Line 202: | ||
H_0: \mu_a = \mu_r = \mu_s = 0. | H_0: \mu_a = \mu_r = \mu_s = 0. | ||
$$ | $$ | ||
- | This test is clearly significant ($p = .0011), which indicates that we can reject the null hypothesis that the (average) log risk ratio is zero for all three methods of allocation. | + | This test is clearly significant ($p = .0011$), which indicates that we can reject the null hypothesis that the (average) log risk ratio is zero for all three methods of allocation. |
Again, we could use the '' | Again, we could use the '' | ||
Line 224: | Line 224: | ||
</ | </ | ||
- | It is important to realize that this does not test whether there are differences between the different forms of allocation (this is what we tested earlier in the model that included the intercept term). However, we can again use contrasts of the model coefficients to test differences between the levels. | + | It is important to realize that this does not test whether there are differences between the different forms of allocation (this is what we tested earlier in the model that included the intercept term). However, we can again use contrasts of the model coefficients to test differences between the levels. |
<code rsplus> | <code rsplus> | ||
- | anova(res, L=rbind(c(-1, | + | anova(res, L=rbind(c(-1, |
</ | </ | ||
<code output> | <code output> | ||
- | Hypotheses: | + | Hypotheses: |
- | 1: | + | 1: |
- | 2: -factor(alloc)alternate + factor(alloc)systematic = 0 | + | 2: -factor(alloc)alternate |
+ | 3: -factor(alloc)random | ||
Results: | Results: | ||
- | | + | |
- | 1: -0.4478 0.5158 -0.8682 0.3853 | + | 1: -0.4478 0.5158 -0.8682 0.3853 |
- | 2: | + | 2: |
+ | 3: | ||
+ | </ | ||
+ | These are now the exact same results we obtained earlier for the model that included the intercept term. | ||
+ | Note that the output does not contain an omnibus test for the three contrasts because the matrix with the contrast coefficients ('' | ||
+ | <code rsplus> | ||
+ | anova(res, L=rbind(c(-1, | ||
+ | </ | ||
+ | <code output> | ||
Omnibus Test of Hypotheses: | Omnibus Test of Hypotheses: | ||
QM(df = 2) = 1.7675, p-val = 0.4132 | QM(df = 2) = 1.7675, p-val = 0.4132 | ||
</ | </ | ||
- | These are now the exact same results we obtained earlier for the model that included the intercept term. | ||
==== Parameterization ==== | ==== Parameterization ==== | ||
- | What the example above shows is that, whether we remove the intercept or not, we are essentially fitting the same model, but using a different [[wp> | + | What the example above shows is that, whether we remove the intercept or not, we are essentially fitting the same model, but using a different [[wp> |
==== Models with Continuous Moderators ==== | ==== Models with Continuous Moderators ==== | ||
Line 303: | Line 311: | ||
</ | </ | ||
- | When the model only includes continuous (i.e., numeric) predictors/ | + | When the model only includes continuous (i.e., numeric) predictors/ |
==== References ==== | ==== References ==== |
tips/models_with_or_without_intercept.txt · Last modified: 2022/08/03 11:34 by Wolfgang Viechtbauer