Table 2.

Effect of incorporating ${\sigma }_{infl}^2$ for statistical fit to ANC-SS and household survey data with r-trend model, r-spline model, and r-spline model without equilibrium prior.

	r-trend				r-spline				r-spline, no equilibrium prior
	None	Regr.	Unbia.	Estim.	None	Regr.	Unbia.	Estim.	None	Regr.	Unbia.	Estim.
In-sample ANC coverage (%)a	77.8	86.4	95.7	94.9	77.7	85.9	95.2	94.5	78.1	86.9	95.4	94.7
Out-of-sample prediction coverage (%)b	68.6	76.7	89.7	89.2	68.3	76.5	90	89.6	69.2	77.4	89.4	89.6
LPPD for HH survey prevalencec	2.70	2.95	3.24	3.24	2.81	3.13	3.26	3.26	2.66	2.93	3.09	3.08
Change in LPPDd		0.25	0.55	0.55		0.33	0.45	0.45		0.27	0.43	0.43
Median IMIS iterationse	25.5	26.4	28.6	26.9	52.6	53.5	52.7	55.0	56.2	55.5	53.5	56.0
IQR of IMIS iterationsf	7.0	6.9	6.6	6.2	11.5	12.2	11.5	11.8	12.7	12.5	12.2	12.7

Results represent means over 40 regions. ‘None’=no additional variance ( ${\sigma }_{infl}^2=0$); ‘regr’=regression estimator (approach 1); ‘unbia.’=substituting unbiased variance estimator (approach 2); ‘estim.’=full Bayesian inference (approach 3). ANC, antenatal clinic; HH, household; IMIS, Incremental Mixture Importance Sampling; IQR, interquartile range; LPPD, log-posterior predictive density.

^aIn-sample coverage of 95% posterior predictive interval for observed ANC prevalence data points that were included in model fitting.

^bCoverage of 95% posterior predictive intervals for 10% of withheld ANC prevalence data points, averaged over 50 randomly created training / test data splits.

^cLog posterior predictive density (LPPD) for population prevalence in household surveys.

^dChange in LPPD defined as the average difference in LPPD when incorporating ${\sigma }_{infl}^2$ compared to ‘none’.

^eMedian number of IMIS iteration in 50 model fits for out-of-sample prediction test, average over 40 datasets.

^fSpan of the interquartile range of the number of IMIS iterations required for the 50 out-of-sample prediction model fits, averaged over 40 datasets.