Sabre

Simulation study [s3bb1.dat-s3bb25.dat]
----------------
Univariate multilevel binary logit model
2449 observations, 1558 level-2 cases, 161 level-3 cases, 4+2 (fixed+random)
parameters (true values: beta_0 = 0.665267, all other parameters equal to 1)

SABRE: 24-point quadrature
STATA: model cannot be fitted
GLLAMM: 24-point non-adaptive quadrature
IGLS: 2nd order PQL
MCMC: default settings (Gamma priors), 25000 iterations;
      approximate timing due to running in interactive mode
      (time quoted is that for a single dataset [3'40"] multiplied by 25)

Sample means and standard deviations over the 25 replications.

         SABRE           STATA          GLLAMM            IGLS            MCMC
beta_0   0.642 (0.037)   na             as SABRE         0.615 (0.035)   0.636 (0.037)
beta_1   0.995 (0.046)                                   0.948 (0.043)   0.984 (0.047)
beta_2   1.000 (0.020)                                   0.951 (0.019)   0.992 (0.021)
beta_3   0.996 (0.045)                                   0.951 (0.043)   0.987 (0.046)
sigma_v  0.957 (0.020)                                   0.909 (0.019)   0.973 (0.023)
sigma_u  0.950 (0.026)                                   0.704 (0.025)   0.881 (0.055)

time    01'52"                          4h'00'          01'27"          91'40"

Mean square errors over the 25 replications.

         SABRE           STATA          GLLAMM            IGLS            MCMC
beta_0   0.034           na             as SABRE         0.034           0.035
beta_1   0.052                                           0.049           0.056
beta_2   0.010                                           0.011           0.011
beta_3   0.050                                           0.049           0.053
sigma_v  0.012                                           0.018           0.014
sigma_u  0.020                                           0.104           0.090

Coverage over the 25 replications (95% confidence intervals).

         SABRE           STATA          GLLAMM            IGLS            MCMC
beta_0     96%           na             as SABRE           92%             96%
beta_1     96%                                             96%             92%
beta_2     96%                                             88%             96%
beta_3    100%                                             96%            100%
sigma_v    96%                                             84%             96%
sigma_u    96%                                             24%             92%