Table 6.

Large-sample robustness of the assumed Gaussian random effects model (GRE) when the true dependence structure between tests is a finite mixture (FM) model

r	η1	Estimator (misspecified model)			Expected log-likelihood*
		$P_d^{\ast }$	SENS*	SPEC*	EFM[log LFM]	EFM[log LGRE]
0	.2	.41	.45	.92	−2.24106	−2.24106
.02		.22	.70	.90	−2.24359	−2.24319
.2		.20	.73	.90	−2.26357	−2.26241
1		.20	.75	.90	−2.34997	−2.34782
0	.5	.15	.77	.86	−2.10467	−2.10476
.02		.16	.74	.87	−2.10903	−2.10758
.20		.25	.57	.88	−2.13865	−2.13370
1		.26	.57	.89	−2.25944	−2.24983

NOTE: Verification is restricted to those patients who screen positive on at least one test, and r is the proportion of samples who are verified at random from those patients [i.e., $P(V_i=1|{\sum }_{j=1}^J{y}_{ij}=s)=0$ if s = 0 and r otherwise]. The true model is an FM model with η₀ = .2, P_d = .2, SENS = .75 and SPEC = .9 for differing r and η₁ and with J = 5.

^*Expected individual contribution to the log-likelihood.