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Table 5 Percentages of selecting \(\mathcal {M}_{2}\) according to the BIC on N=500 datasets, given t v =(0,1,2,4,6,8,10,12) and \(\sigma _{0}^{2}=1.5\)

From: Item response models for the longitudinal analysis of health-related quality of life in cancer clinical trials

Parameter Scenarios  
Values AM using δ ne CM using δ fa CM using δ ne AM using δ fa
β 1 \(\sigma _{1}^{2}\) LMM AM CM LMM AM CM LMM AM CM LMM AM CM
1 0.01 0 2.3 24.9 0 5.0 6.9 0 2.7 3.7 0.3 6.4 24.8
  0.02 0 21.4 54.7 0 37.6 44.1 0 17.7 18.1 0 50.0 77.0
  0.03 0 61.0 91.0 0 75.7 80.0 0 41.3 45.6 0 86.3 98.3
  0.05 0 97.7 99.7 0 100 100 0.3 89.0 90.0 0 99.3 100
  0.2 39.3 100 100 40.7 100 100 10.7 100 100 57.7 100 100
  0.5 100 100 100 100 100 100 100 100 100 100 100 100
0.5 0.005 0.2 25.5 56.4 0 41.2 25.7 0 14.9 11.0 0 41.2 53.6
  0.008 0.8 73.8 89.4 0 85.8 73.4 0 42.9 38.8 0.2 91.6 93.6
  0.01 2.0 91.2 97.0 0 97.0 91.6 0 66.6 63.4 0.6 99.2 99.2
  0.02 26.4 100 100 4.8 100 100 0 100 100 51.8 100 100
  0.03 77.0 100 100 64.8 100 100 0.8 100 100 96.6 100 100
  0.05 99.8 100 100 100 100 100 62.3 100 100 100 100 100
0.3 0.002 16.7 6.3 21.4 0 2.1 4.0 0 3.1 3.9 11.0 11.0 15.3
  0.005 72.3 86.3 92.7 30.7 55.3 59.0 0 32.3 46.0 85.7 87.3 91.7
  0.008 97.7 100 100 86.0 97.3 98.0 4.0 76.3 88.3 99.3 99.7 100
  0.01 100 100 100 96.3 99.7 99.3 17.3 94.0 97.0 100 100 100
  0.02 100 100 100 100 100 100 96.7 100 100 100 100 100
0 0.001 24.8 2.8 5.7 6.8 0.4 1.6 4.8 0.6 1.9 15.2 1.4 3.7
  0.002 70.2 32.0 37.3 26.4 6.6 8.2 20.6 2.4 5.1 47.6 15.2 21.4
  0.005 99.8 99.4 99.6 92.2 70.4 77.2 88.2 61.8 72.4 99.6 97.8 97.8
  0.008 100 100 100 99.8 98.0 98.8 99.8 98.4 99.2 100 100 100
  0.01 100 100 100 100 100 100 100 100 100 100 100 100
  0.02 100 100 100 100 100 100 100 100 100 100 100 100
−0.3 0.002 0.7 4.4 61.4 0 54.0 5.1 0 93.3 1.8 0 2.1 18.6
  0.005 5.7 62.3 79.0 0 95.7 40.4 0 99.7 33.2 0 56.0 48.3
  0.008 23.7 96.3 97.3 0 100 86.7 0 100 82.7 1.7 96.3 86.3
  0.01 45.2 100 99.6 0 100 98.2 0 100 92.3 6.8 99.8 98.4
  0.02 98.8 100 100 61.4 100 100 26.6 100 100 96.0 100 100
−0.5 0.005 2.6 12.1 48.6 0 57.6 13.2 0 84.8 9.8 0 41.2 53.6
  0.008 3.8 43.5 70.7 0 85.8 41.6 0 96.1 33.5 0.2 91.6 93.6
  0.01 5.6 70.0 84.8 0 95.6 61.5 0 98.4 49.6 0.6 99.2 99.2
  0.02 12.8 100 100 0 100 100 0 100 97.8 51.8 100 100
  0.03 36.8 100 100 0 100 100 0 100 100 96.6 100 100
  0.05 93.0 100 100 43.4 100 100 17.6 100 100 100 100 100
−1 0.01 0 0.6 34.5 0 5.8 5.2 0 8.4 6.3 0 1.6 15.1
  0.02 0 5.8 46.6 0 21.2 18.4 0 20.8 11.0 0 8.8 34.3
  0.03 0 30.4 73.2 0 50.4 44.8 0 50.0 37.4 0 36.4 58.0
  0.05 0 83.6 95.2 0 92.6 91.4 0 85.6 80.1 0 90.0 96.0
  0.2 46.4 100 100 21.4 100 100 12.0 100 100 41.8 100 100
  0.5 100 100 100 100 100 100 100 100 100 100 100 100
  1. For the (adjacent,logistic, Z 1,U a ) a=1,2 models and the (cumulative,logistic, Z 1,U a ) a=1,2 models are denoted by AM and CM, respectively. For the random component, U 1 if \(\sigma _{1}^{2}=0\) and U 2 if \(\sigma _{1}^{2}>0\)