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tips:models_with_or_without_intercept [2021/10/29 10:55] – Wolfgang Viechtbauertips:models_with_or_without_intercept [2021/11/10 20:19] – Wolfgang Viechtbauer
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 A different way of conducting the same test is to use the ''L'' argument, which allows us to specify one or more vectors of numbers, which are multiplied with the model coefficients. In particular, we can use: A different way of conducting the same test is to use the ''L'' argument, which allows us to specify one or more vectors of numbers, which are multiplied with the model coefficients. In particular, we can use:
 <code rsplus> <code rsplus>
-anova(res, L=rbind(c(0,1,0),c(0,0,1)))+anova(res, X=rbind(c(0,1,0),c(0,0,1)))
 </code> </code>
 to test the two hypotheses to test the two hypotheses
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 so this contrast reflects how different systematic allocation is compared to random allocation. Using the ''anova()'' function, we can obtain this contrast with so this contrast reflects how different systematic allocation is compared to random allocation. Using the ''anova()'' function, we can obtain this contrast with
 <code rsplus> <code rsplus>
-anova(res, L=c(0,-1,1))+anova(res, X=c(0,-1,1))
 </code> </code>
 <code output> <code output>
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 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 </code> </code>
-(I shortened the names of the coefficients in the output above to make the table under the ''Model Results'' more readable). Now the intercept reflects the estimated (average) log risk ratio for random allocation, while the coefficients for ''alternate'' and ''systematic'' are again contrasts of these two levels compared to random allocation. Note how the coefficient for systematic allocation is the same as we obtained earlier using ''anova(res, L=c(0,-1,1))''. Moreover, as we can see in the output, the results for the omnibus test of these two coefficients is identical to what we obtained earlier.+(I shortened the names of the coefficients in the output above to make the table under the ''Model Results'' more readable). Now the intercept reflects the estimated (average) log risk ratio for random allocation, while the coefficients for ''alternate'' and ''systematic'' are again contrasts of these two levels compared to random allocation. Note how the coefficient for systematic allocation is the same as we obtained earlier using ''anova(res, X=c(0,-1,1))''. Moreover, as we can see in the output, the results for the omnibus test of these two coefficients is identical to what we obtained earlier.
  
 ==== Model Without Intercept ==== ==== Model Without Intercept ====
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 Again, we could use the ''anova()'' function to carry out explicitly the same test with: Again, we could use the ''anova()'' function to carry out explicitly the same test with:
 <code rsplus> <code rsplus>
-anova(res, L=rbind(c(1,0,0),c(0,1,0),c(0,0,1)))+anova(res, X=rbind(c(1,0,0),c(0,1,0),c(0,0,1)))
 </code> </code>
 <code output> <code output>
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 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. Let's test all pairwise differences (i.e., between random and alternating allocation, between systematic and alternating allocation, and between systematic and random allocation): 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. Let's test all pairwise differences (i.e., between random and alternating allocation, between systematic and alternating allocation, and between systematic and random allocation):
 <code rsplus> <code rsplus>
-anova(res, L=rbind(c(-1,1,0),c(-1,0,1), c(0,-1,1)))+anova(res, X=rbind(c(-1,1,0),c(-1,0,1), c(0,-1,1)))
 </code> </code>
 <code output> <code output>
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 Note that the output does not contain an omnibus test for the three contrasts because the matrix with the contrast coefficients (''L'' above) is not of full rank (i.e., one of the three contrasts is redundant). If we only include two of the three contrasts (again, it does not matter which two), then we also get the omnibus test (rest of the output omitted): Note that the output does not contain an omnibus test for the three contrasts because the matrix with the contrast coefficients (''L'' above) is not of full rank (i.e., one of the three contrasts is redundant). If we only include two of the three contrasts (again, it does not matter which two), then we also get the omnibus test (rest of the output omitted):
 <code rsplus> <code rsplus>
-anova(res, L=rbind(c(-1,1,0),c(-1,0,1)))+anova(res, X=rbind(c(-1,1,0),c(-1,0,1)))
 </code> </code>
 <code output> <code output>
tips/models_with_or_without_intercept.txt · Last modified: 2022/08/03 11:34 by Wolfgang Viechtbauer