Table 2.

Parameter estimates, intervals, and goodness-of-fit measures the CLEAR data. We fit six models, each using the basic Bayesian Poisson regression setup (10) for the true counts. In the model without heaping the reported counts are assumed to be equal to true counts. In the dispersion-only model, the BDP allows misremembering but not heaping. The Wang and Heitjan (2008) model involves deterministic heaping under different regimes (18). The BDP heaping model has global dispersion and heaping parameters, the subject-specific BDP heaping model allows subject-specific effects (15), and the subject-specific model with covariates includes a fixed effect for the influence of gender on heaping behavior. Parameter estimates (posterior means) and 95% posterior quantiles are shown for each parameter. The fixed effects are age, gender, men who have sex with men (MSM), injection drug user, intervention, stimulant use, and trading sex. The random intercept variance ${\sigma }_{\beta }^2$ is also shown. The heaping parameters θ_disp and θ_heap control dispersion and heaping for the BDP models. The heaping regime parameters γ₀, γ₁, γ₂, and γ₃ are shown for the heaping models. The heaping random intercept variance ${\sigma }_{\xi }^2$ and the gender-specific heaping fixed effect ω are also shown. Finally, we provide two measures of goodness-of-fit for each model: deviance information criterion (DIC) and the sum of squared mean prediction errors, and the sum of squared prediction errors (SSPE).

	No heaping	WH08	Dispersion-only	Heaping	Subject-specific heaping	Subject-specific heaping+gender
Age	−0.11 (−0.27,0.08)	−0.07 (−0.25,0.1)	−0.15 (−0.56,0.25)	−0.20 (−0.58,0.14)	−0.12 (−0.55,0.23)	−0.14 (−0.43,0.22)
Male	−0.26 (−0.78,0.25)	−0.24 (−0.74,0.28)	−1.48 (−2.77, −0.27)	−0.85 (−1.81,0.12)	−1.01 (−2.16, −0.01)	−0.98 (−2.05, −0.02)
MSM	0.82 (0.33,1.32)	0.81 (0.3,1.32)	0.57 (−0.59,1.75)	0.89 (−0.06,1.85)	0.99 (0.03,1.99)	0.92 (−0.06,1.95)
Inject	−0.37 (−0.88,0.11)	−0.29 (−0.72,0.18)	−0.38 (−1.45,0.65)	−0.29 (−1.2,0.56)	−0.35 (−1.3,0.55)	−0.38 (−1.54,0.44)
Time	−0.89 (−1.06, −0.72)	−0.85 (−1.03, −0.66)	−1.72 (−2.27, −1.18)	−1.02 (−1.46, −0.6)	−1.09 (−1.51, −0.67)	−1.06 (−1.5, −0.61)
Intv	−0.24 (−0.57,0.05)	−0.18 (−0.5,0.1)	−1.29 (−2.05, −0.6)	−1.07 (−1.76, −0.45)	−1.09 (−1.85, −0.32)	−1.16 (−2.06, −0.47)
Stim	1.00 (0.88,1.12)	0.97 (0.84,1.1)	1.51 (1.14,1.88)	1.09 (0.82,1.39)	1.15 (0.83,1.47)	1.05 (0.77,1.36)
Trade	1.32 (1.2,1.45)	1.21 (1.08,1.35)	2.49 (1.98,3)	1.81 (1.41,2.21)	1.79 (1.44,2.15)	2.00 (1.65,2.34)
${\sigma }_{\beta }^2$	1.15 (0.88,1.48)	1.07 (0.82,1.36)	3.63 (2.2,5.66)	2.77 (1.75,4.47)	2.93 (1.79,4.81)	2.93 (1.93,4.45)
θdisp			1.57 (1.4,1.75)	1.04 (0.86,1.22)	1.08 (0.9,1.27)	1.06 (0.91,1.24)
θheap				0.82 (0.59,1.12)
γ0		0.07 (0.05,0.11)		0.42 (0.26,0.84)	0.29 (0.21,0.4)	0.45 (0.28,0.79)
γ1		−2.37 (−2.86, −1.95)		−4.51 (−6.09, −3.46)	−4.66 (−5.78, −3.68)	−5.50 (−8.43, −4.16)
γ2		−2.90 (−3.47, −2.42)		−5.44 (−8.75, −3.95)	−5.40 (−6.87, −4.21)	−7.23 (−10.11, −5)
γ3		−4.07 (−4.9, −3.39)		−6.81 (−12.47, −4.75)	−6.22 (−7.68, −5.1)	−8.40 (−11.55, −6.36)
${\sigma }_{\xi }^2$					0.74 (0.61,0.98)	0.94 (0.87,1)
ω						−0.03 (−0.69,0.54)
DIC	4585	524	3329	3214	3195	3175
SSPE	47773	55078	28005	25371	25336	24364