Table 3.

Data application: The top five models according to their AIC values for all 12 considered scenarios, where a ✓ denotes that a particular predictor was included in the model. The predictor variables x₁, x₂, and x₃ represent the participant’s age, race, and miscarriage status, respectively. Note, the presence (absence) of “ ^*” indicates that the MCMLE accounted for (ignored) the effect of measurement error.

Model	Data set	x1	x2	x3	$x_1^2$	x1x2	x1x3	x2x3
Log-normal		✓	✓	✓				✓
	ID	✓		✓				✓
		✓	✓	✓
		✓	✓	✓		✓		✓
		✓	✓	✓	✓			✓
		✓		✓				✓
	ID*	✓	✓	✓				✓
		✓		✓			✓	✓
		✓		✓		✓		✓
		✓	✓
				✓				✓
	PD	✓		✓				✓
		✓		✓			✓	✓
		✓		✓		✓		✓
				✓	✓			✓
		✓		✓				✓
	PD*	✓	✓	✓				✓
		✓		✓			✓	✓
		✓	✓	✓			✓	✓
		✓	✓	✓		✓		✓
Gamma(log link)		✓		✓				✓
	ID	✓	✓	✓				✓
		✓		✓			✓	✓
		✓		✓	✓			✓
		✓		✓		✓		✓
		✓		✓				✓
	ID*	✓	✓	✓				✓
		✓		✓			✓	✓
		✓		✓		✓		✓
		✓		✓	✓			✓
		✓	✓	✓				✓
	PD	✓	✓	✓			✓	✓
		✓	✓	✓		✓		✓
		✓	✓	✓	✓			✓
		✓	✓	✓		✓	✓	✓
		✓	✓	✓				✓
	PD*	✓	✓	✓		✓		✓
		✓	✓	✓			✓	✓
			✓	✓		✓		✓
Gamma(inverse link)		✓	✓	✓	✓	✓		✓
		✓		✓				✓
	ID	✓	✓	✓				✓
		✓		✓			✓	✓
		✓		✓		✓		✓
		✓		✓	✓			✓
		✓		✓				✓
	ID*	✓		✓			✓	✓
		✓		✓		✓		✓
		✓	✓	✓				✓
		✓		✓	✓			✓
		✓	✓	✓				✓
	PD	✓	✓	✓			✓	✓
		✓	✓	✓		✓		✓
		✓	✓	✓	✓			✓
			✓	✓		✓	✓	✓
		✓	✓	✓				✓
	PD*	✓	✓	✓			✓	✓
		✓	✓	✓		✓		✓
		✓	✓	✓	✓			✓
			✓	✓		✓	✓	✓