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. Author manuscript; available in PMC: 2019 Dec 3.
Published in final edited form as: Biometrics. 2019 Apr 25;75(3):950–965. doi: 10.1111/biom.13060

TABLE 2.

Performance of JEAIC and JEBIC compared with MLIC and QICWr when the dropout model is misspecified: percentage of selecting six candidate logistic models across 500 Monte Carlo datasets; T = 3, ρ = 0.3

Setups Method C(ρ) x1 x3 x1, x2 x1, x3 x2, x3 x1, x2, x3 Total
n = 100 JEAIC AR1 0.002 0.002 0.092 0 0.012 0.008 0.116
m = 0.2 EXC 0.024 0.01 0.566 0.002 0.191 0.09 0.884
IND 0 0 0 0 0 0 0
Total 0.026 0.012 0.659 0.002 0.203 0.098 1
JEBIC AR1 0.022 0.004 0.084 0 0.012 0 0.122
EXC 0.096 0.022 0.557 0.002 0.195 0.006 0.878
IND 0 0 0 0 0 0 0
Total 0.118 0.026 0.641 0.002 0.207 0.006 1
MLIC AR1 0.006 0.012 0.212 0 0.126 0.054 0.41
EXC 0.012 0.006 0.258 0.006 0.184 0.074 0.54
IND 0 0 0.028 0 0.016 0.006 0.05
Total 0.018 0.018 0.498 0.006 0.326 0.134 1
QICWr AR1 0 0 0.056 0 0.042 0.04 0.138
EXC 0.008 0.004 0.436 0.002 0.232 0.114 0.796
IND 0 0 0.034 0 0.02 0.012 0.066
Total 0.008 0.004 0.526 0.002 0.294 0.166 1
n = 100 JEAIC AR1 0.01 0.002 0.094 0.002 0.032 0.02 0.16
m = 0.3 EXC 0.046 0.026 0.484 0.004 0.194 0.086 0.84
IND 0 0 0 0 0 0 0
Total 0.056 0.028 0.578 0.006 0.226 0.106 1
JEBIC AR1 0.042 0.012 0.078 0 0.028 0.002 0.162
EXC 0.142 0.066 0.436 0 0.184 0.01 0.838
IND 0 0 0 0 0 0 0
Total 0.184 0.078 0.514 0 0.212 0.012 1
MLIC AR1 0.01 0.008 0.154 0.002 0.098 0.046 0.318
EXC 0.038 0.032 0.296 0.002 0.184 0.066 0.618
IND 0.002 0.004 0.028 0 0.016 0.014 0.064
Total 0.05 0.044 0.478 0.004 0.298 0.126 1
QICWr AR1 0.002 0 0.048 0 0.03 0.034 0.114
EXC 0.008 0.004 0.456 0.004 0.232 0.132 0.836
IND 0 0 0.022 0 0.012 0.016 0.05
Total 0.01 0.004 0.526 0.004 0.274 0.182 1
n = 200 JEAIC AR1 0 0 0.036 0 0.008 0.008 0.052
m = 0.2 EXC 0 0 0.726 0 0.092 0.13 0.948
IND 0 0 0 0 0 0 0
Total 0 0 0.762 0 0.1 0.138 1
JEBIC AR1 0 0 0.042 0 0.012 0.002 0.056
EXC 0.01 0 0.806 0 0.11 0.018 0.944
IND 0 0 0 0 0 0 0
Total 0.01 0 0.848 0 0.122 0.02 1
MLIC AR1 0 0 0.216 0 0.05 0.072 0.338
EXC 0 0 0.404 0 0.098 0.098 0.6
IND 0.002 0 0.032 0 0.006 0.022 0.062
Total 0.002 0 0.652 0 0.154 0.192 1
QICWr AR1 0 0 0.056 0 0.01 0.028 0.094
EXC 0 0 0.558 0 0.108 0.168 0.834
IND 0 0 0.04 0 0.002 0.03 0.072
Total 0 0 0.654 0 0.12 0.226 1
n = 200 JEAIC AR1 0 0 0.068 0 0.012 0.008 0.088
m = 0.3 EXC 0.008 0 0.662 0 0.132 0.11 0.912
IND 0 0 0 0 0 0 0
Total 0.008 0 0.73 0 0.144 0.118 1
JEBIC AR1 0.004 0.002 0.078 0 0.012 0 0.096
EXC 0.04 0 0.698 0.002 0.154 0.01 0.904
IND 0 0 0 0 0 0 0
Total 0.044 0.002 0.776 0.002 0.166 0.01 1
MLIC AR1 0.002 0 0.206 0.002 0.054 0.072 0.336
EXC 0.004 0.002 0.374 0 0.13 0.094 0.604
IND 0 0 0.032 0 0.012 0.016 0.06
Total 0.006 0.002 0.612 0.002 0.196 0.182 1
QICWr AR1 0 0 0.064 0 0.004 0.028 0.096
EXC 0 0 0.542 0 0.124 0.192 0.858
IND 0 0 0.018 0 0.004 0.024 0.046
Total 0 0 0.624 0 0.132 0.244 1

The model with {x1, x2} and an EXC correlation structure is the true model. Notations n and m denote the sample size and the missing probability, respectively.

Abbreviations: EXC, exchangeable; IND, independence; JEAIC, joint empirical Akaike information criterion; JEBIC, joint empirical Bayesian information criterion; MLIC, missing longitudinal information criterion; QICW, weighted quasi-likelihood information criterion.

The bold values denote the true mean and correlation structures.