. Author manuscript; available in PMC: 2014 Dec 26.

Published in final edited form as: Stat Methods Med Res. 2013 Jun 26;25(4):1596–1619. doi: 10.1177/0962280213492588

Table 6.

Pap test example – model selection procedure

Models	Random effects	-2logL	AIC	BIC
I	NA	45277	45287	45297

IIa	ε	41882	41894	41906
IIb	μ_A	43329	43341	43353
IIc	μ_B	43398	43410	43423
IId	ν_A	43520	43532	43544
IIe	ν_B	42838	42850	42863

IIIa	ε & μ_A	40510	40524	40539
IIIb	ε & μ_B	40888	40902	40917
IIIc	ε & ν_A	40894	40908	40922
IIId	ε & ν_B	40520	40534	40548

IVa	ε, μ_A & μ_B	39777	39793	39810
IVb	ε, μ_A & ν_A	39762	39778	39795
IVc	ε, μ_A & ν_B	40506	40522	40539
IVd	ε, μ_A, μ_B & ρ_{μ_Aμ_B}	39777	39795	39814
IVe	*ε, μ_A,* ν_A & ρ_{μ_Aμ_B}	39752	39770	39789
IVf	ε, μ_A, ν_B & _{ρμ_Aν_B}	40503	40521	40540

Models in level I–IV include random effects and possible correlations denoted in the corresponding ‘random effects’ column. The procedure starts from the fixed effects model I. In Level 2, five possible random effects are added one at a time. Model IIa with random effect ε (prevalence) has smallest AIC, thus ε is carried to models in level 3. The same process continued until level IV because model fitting became unstable with more random effects than level IV and AIC was not significantly reduced anymore. The bold faced estimates represents the best model with smallest AIC in each level.