. Author manuscript; available in PMC: 2009 Oct 1.

Published in final edited form as: J Am Stat Assoc. 2008 Mar 1;103(481):61–73. doi: 10.1198/016214507000000329

Table 3.

Large-sample robustness of the assumed Gaussian random effects (GRE) model to the true dependence structure between tests given by the finite mixture (FM) model

η₁

Estimator (misspecified model)

Expected log-likelihood^*

P_{d}^{*}

SENS^*

SPEC^*

E_FM[log L_FM]

E_FM[log L_GRE]

.41

.45

.92

−2.24106

.02

.21

.71

.90

−2.24327

−2.24374

.20

.74

.90

−2.26317

−2.26454

.20

.75

.90

−2.35160

−2.35410

.15

.77

.86

−2.10467

−2.10476

.02

.16

.75

.87

−2.10796

−2.10973

.20

.18

.76

.89

−2.13749

−2.14648

.20

.76

.90

−2.26875

−2.28668

NOTE: Verification is independent of Y_i, and r denotes the proportion of random samples verified [i.e., P(V_i = 1) = r]. The true model is an FM model with η₀ = .2, P_d = .20, SENS = .75, and SPEC = .9 for differing r and η₁ and with J = 5. Asymptotic bias for sensitivity and specificity is SENS^* ′ SENS and SPEC^* ′ SPEC, respectively.

Expected individual contribution to the log-likelihood.