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tips:multiple_factors_interactions [2021/10/22 14:44] Wolfgang Viechtbauertips:multiple_factors_interactions [2022/08/03 11:35] (current) Wolfgang Viechtbauer
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 R^2 (amount of heterogeneity accounted for):            49.85% R^2 (amount of heterogeneity accounted for):            49.85%
  
-Test for Residual Heterogeneity: +Test for Residual Heterogeneity:
 QE(df = 15) = 24.1362, p-val = 0.0628 QE(df = 15) = 24.1362, p-val = 0.0628
  
-Test of Moderators (coefficient(s) 2,3,4): +Test of Moderators (coefficient(s) 2,3,4):
 QM(df = 3) = 9.9698, p-val = 0.0188 QM(df = 3) = 9.9698, p-val = 0.0188
  
 Model Results: Model Results:
  
-             estimate      se     zval    pval    ci.lb    ci.ub    +             estimate      se     zval    pval    ci.lb    ci.ub
 intrcpt        0.4020  0.1300   3.0924  0.0020   0.1472   0.6567  ** intrcpt        0.4020  0.1300   3.0924  0.0020   0.1472   0.6567  **
 weekssome     -0.2893  0.1360  -2.1271  0.0334  -0.5558  -0.0227   * weekssome     -0.2893  0.1360  -2.1271  0.0334  -0.5558  -0.0227   *
 weekshigh     -0.4422  0.1464  -3.0205  0.0025  -0.7291  -0.1552  ** weekshigh     -0.4422  0.1464  -3.0205  0.0025  -0.7291  -0.1552  **
-testeraware   -0.0511  0.0927  -0.5512  0.5815  -0.2327   0.1305    +testeraware   -0.0511  0.0927  -0.5512  0.5815  -0.2327   0.1305
  
 --- ---
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 We have also not yet tested whether there is a difference between levels ''some'' and ''high'' of this factor. One could change the reference level of the ''weeks'' factor and refit the model to obtain this test. Alternatively, and more elegantly, we can just test the difference between these two coefficients directly. We can do this with: We have also not yet tested whether there is a difference between levels ''some'' and ''high'' of this factor. One could change the reference level of the ''weeks'' factor and refit the model to obtain this test. Alternatively, and more elegantly, we can just test the difference between these two coefficients directly. We can do this with:
 <code rsplus> <code rsplus>
-anova(res.a1, L=c(0,1,-1,0))+anova(res.a1, X=c(0,1,-1,0))
 </code> </code>
 <code output> <code output>
-Hypothesis:                            +Hypothesis:
 1: weekssome - weekshigh = 0 1: weekssome - weekshigh = 0
  
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 H^2 (unaccounted variability / sampling variability):   1.33 H^2 (unaccounted variability / sampling variability):   1.33
  
-Test for Residual Heterogeneity: +Test for Residual Heterogeneity:
 QE(df = 15) = 24.1362, p-val = 0.0628 QE(df = 15) = 24.1362, p-val = 0.0628
  
-Test of Moderators (coefficient(s) 1,2,3,4): +Test of Moderators (coefficient(s) 1,2,3,4):
 QM(df = 4) = 12.6719, p-val = 0.0130 QM(df = 4) = 12.6719, p-val = 0.0130
  
 Model Results: Model Results:
  
-             estimate      se     zval    pval    ci.lb   ci.ub    +             estimate      se     zval    pval    ci.lb   ci.ub
 weeksnone      0.4020  0.1300   3.0924  0.0020   0.1472  0.6567  ** weeksnone      0.4020  0.1300   3.0924  0.0020   0.1472  0.6567  **
-weekssome      0.1127  0.0804   1.4021  0.1609  -0.0448  0.2702     +weekssome      0.1127  0.0804   1.4021  0.1609  -0.0448  0.2702 
-weekshigh     -0.0402  0.1020  -0.3941  0.6935  -0.2401  0.1597     +weekshigh     -0.0402  0.1020  -0.3941  0.6935  -0.2401  0.1597 
-testeraware   -0.0511  0.0927  -0.5512  0.5815  -0.2327  0.1305    +testeraware   -0.0511  0.0927  -0.5512  0.5815  -0.2327  0.1305
  
 --- ---
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 R^2 (amount of heterogeneity accounted for):            0.00% R^2 (amount of heterogeneity accounted for):            0.00%
  
-Test for Residual Heterogeneity: +Test for Residual Heterogeneity:
 QE(df = 13) = 23.4646, p-val = 0.0364 QE(df = 13) = 23.4646, p-val = 0.0364
  
-Test of Moderators (coefficient(s) 2,3,4,5,6): +Test of Moderators (coefficient(s) 2,3,4,5,6):
 QM(df = 5) = 9.3154, p-val = 0.0971 QM(df = 5) = 9.3154, p-val = 0.0971
  
 Model Results: Model Results:
  
-                       estimate      se     zval    pval    ci.lb   ci.ub   +                       estimate      se     zval    pval    ci.lb   ci.ub
 intrcpt                  0.3067  0.1857   1.6518  0.0986  -0.0572  0.6707  . intrcpt                  0.3067  0.1857   1.6518  0.0986  -0.0572  0.6707  .
-weekssome               -0.1566  0.2159  -0.7255  0.4682  -0.5797  0.2665    +weekssome               -0.1566  0.2159  -0.7255  0.4682  -0.5797  0.2665 
-weekshigh               -0.3267  0.2597  -1.2584  0.2082  -0.8357  0.1822    +weekshigh               -0.3267  0.2597  -1.2584  0.2082  -0.8357  0.1822 
-testeraware              0.1759  0.2687   0.6547  0.5127  -0.3508  0.7026    +testeraware              0.1759  0.2687   0.6547  0.5127  -0.3508  0.7026 
-weekssome:testeraware   -0.2775  0.3072  -0.9034  0.3663  -0.8795  0.3245    +weekssome:testeraware   -0.2775  0.3072  -0.9034  0.3663  -0.8795  0.3245 
-weekshigh:testeraware   -0.2634  0.3435  -0.7667  0.4433  -0.9366  0.4099   +weekshigh:testeraware   -0.2634  0.3435  -0.7667  0.4433  -0.9366  0.4099
  
 --- ---
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 </code> </code>
 <code output> <code output>
-Test of Moderators (coefficient(s) 5,6): +Test of Moderators (coefficient(s) 5,6):
 QM(df = 2) = 0.8576, p-val = 0.6513 QM(df = 2) = 0.8576, p-val = 0.6513
 </code> </code>
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 H^2 (unaccounted variability / sampling variability):   1.73 H^2 (unaccounted variability / sampling variability):   1.73
  
-Test for Residual Heterogeneity: +Test for Residual Heterogeneity:
 QE(df = 13) = 23.4646, p-val = 0.0364 QE(df = 13) = 23.4646, p-val = 0.0364
  
-Test of Moderators (coefficient(s) 1,2,3,4,5,6): +Test of Moderators (coefficient(s) 1,2,3,4,5,6):
 QM(df = 6) = 11.9111, p-val = 0.0640 QM(df = 6) = 11.9111, p-val = 0.0640
  
 Model Results: Model Results:
  
-                       estimate      se     zval    pval    ci.lb   ci.ub   +                       estimate      se     zval    pval    ci.lb   ci.ub
 weeksnone:testerblind    0.3067  0.1857   1.6518  0.0986  -0.0572  0.6707  . weeksnone:testerblind    0.3067  0.1857   1.6518  0.0986  -0.0572  0.6707  .
-weekssome:testerblind    0.1502  0.1100   1.3646  0.1724  -0.0655  0.3658    +weekssome:testerblind    0.1502  0.1100   1.3646  0.1724  -0.0655  0.3658 
-weekshigh:testerblind   -0.0200  0.1815  -0.1102  0.9122  -0.3757  0.3357   +weekshigh:testerblind   -0.0200  0.1815  -0.1102  0.9122  -0.3757  0.3357
 weeksnone:testeraware    0.4827  0.1942   2.4850  0.0130   0.1020  0.8634  * weeksnone:testeraware    0.4827  0.1942   2.4850  0.0130   0.1020  0.8634  *
-weekssome:testeraware    0.0486  0.1001   0.4851  0.6276  -0.1477  0.2448    +weekssome:testeraware    0.0486  0.1001   0.4851  0.6276  -0.1477  0.2448 
-weekshigh:testeraware   -0.1074  0.1134  -0.9476  0.3433  -0.3296  0.1148   +weekshigh:testeraware   -0.1074  0.1134  -0.9476  0.3433  -0.3296  0.1148
  
 --- ---
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 Now, the table with the model results directly provides the estimated average effect for each factor level combination. It is now also quite easy to test particular factor level combinations against each other. For example, to test the difference between levels ''some'' and ''high'' of the ''weeks'' factor within the ''blind'' level of the ''tester'' factor, we could use: Now, the table with the model results directly provides the estimated average effect for each factor level combination. It is now also quite easy to test particular factor level combinations against each other. For example, to test the difference between levels ''some'' and ''high'' of the ''weeks'' factor within the ''blind'' level of the ''tester'' factor, we could use:
 <code rsplus> <code rsplus>
-anova(res.i2, L=c(0,1,-1,0,0,0))+anova(res.i2, X=c(0,1,-1,0,0,0))
 </code> </code>
 <code output> <code output>
-Hypothesis:                                                    +Hypothesis:
 1: weekssome:testerblind - weekshigh:testerblind = 0 1: weekssome:testerblind - weekshigh:testerblind = 0
  
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 To test the same contrast within the ''aware'' level of the ''tester'' factor, we would use: To test the same contrast within the ''aware'' level of the ''tester'' factor, we would use:
 <code rsplus> <code rsplus>
-anova(res.i2, L=c(0,0,0,0,1,-1))+anova(res.i2, X=c(0,0,0,0,1,-1))
 </code> </code>
 <code output> <code output>
-Hypothesis:                                                    +Hypothesis:
 1: weekssome:testeraware - weekshigh:testeraware = 0 1: weekssome:testeraware - weekshigh:testeraware = 0
  
Line 400: Line 400:
  
 Linear Hypotheses: Linear Hypotheses:
-                             Estimate Std. Error z value Pr(>|z|)    +                             Estimate Std. Error z value Pr(>|z|) 
-some:blind - none:blind == 0 -0.15660    0.21585  -0.725  0.46816    +some:blind - none:blind == 0 -0.15660    0.21585  -0.725  0.46816 
-high:blind - none:blind == 0 -0.32675    0.25965  -1.258  0.20824    +high:blind - none:blind == 0 -0.32675    0.25965  -1.258  0.20824 
-none:aware - none:blind == 0  0.17592    0.26872   0.655  0.51269    +none:aware - none:blind == 0  0.17592    0.26872   0.655  0.51269 
-some:aware - none:blind == 0 -0.25818    0.21098  -1.224  0.22105    +some:aware - none:blind == 0 -0.25818    0.21098  -1.224  0.22105 
-high:aware - none:blind == 0 -0.41418    0.21757  -1.904  0.05696 .  +high:aware - none:blind == 0 -0.41418    0.21757  -1.904  0.05696 . 
-high:blind - some:blind == 0 -0.17015    0.21223  -0.802  0.42271    +high:blind - some:blind == 0 -0.17015    0.21223  -0.802  0.42271 
-none:aware - some:blind == 0  0.33252    0.22324   1.490  0.13635    +none:aware - some:blind == 0  0.33252    0.22324   1.490  0.13635 
-some:aware - some:blind == 0 -0.10158    0.14877  -0.683  0.49475    +some:aware - some:blind == 0 -0.10158    0.14877  -0.683  0.49475 
-high:aware - some:blind == 0 -0.25759    0.15799  -1.630  0.10302    +high:aware - some:blind == 0 -0.25759    0.15799  -1.630  0.10302 
-none:aware - high:blind == 0  0.50267    0.26582   1.891  0.05862 .  +none:aware - high:blind == 0  0.50267    0.26582   1.891  0.05862 . 
-some:aware - high:blind == 0  0.06857    0.20727   0.331  0.74076    +some:aware - high:blind == 0  0.06857    0.20727   0.331  0.74076 
-high:aware - high:blind == 0 -0.08744    0.21398  -0.409  0.68282    +high:aware - high:blind == 0 -0.08744    0.21398  -0.409  0.68282 
-some:aware - none:aware == 0 -0.43410    0.21852  -1.986  0.04698 * +some:aware - none:aware == 0 -0.43410    0.21852  -1.986  0.04698 *
 high:aware - none:aware == 0 -0.59010    0.22490  -2.624  0.00869 ** high:aware - none:aware == 0 -0.59010    0.22490  -2.624  0.00869 **
 high:aware - some:aware == 0 -0.15601    0.15126  -1.031  0.30235 high:aware - some:aware == 0 -0.15601    0.15126  -1.031  0.30235
tips/multiple_factors_interactions.1634913865.txt.gz · Last modified: 2021/10/22 14:44 by Wolfgang Viechtbauer