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. Author manuscript; available in PMC: 2014 Jan 13.
Published in final edited form as: Ann Appl Stat. 2012;6(4):1689–1706. doi: 10.1214/12-AOAS557

Table 3.

Estimated parameters from the Shiffman data under simple models for recall (EMA only) and heaping (remembered count and visit day indicator).

Random Effects Model Independence Model

Parameter Posterior mode 95% CI Posterior mode 95% CI
Latent recall: Poisson model
 Intercept: β0 2.32 [2.24, 2.40] 1.14 [1.09, 1.20]
 ln(EMA): β1 0.27 [0.25, 0.30] 0.68 [0.66, 0.69]
σb2 0.09 [0.08, 0.11]
Heaping behavior: Proportional odds model
 Intercept 1: γ1 −1.50 [−2.17, −0.85] −1.06 [−1.30, −0.84]
 Intercept 2: γ2 −5.21 [−6.14, −4.43] −2.94 [−3.26, −2.65]
 Intercept 3: γ3 −10.15 [−12.49, −8.48] −4.17 [−4.59, −3.82]
 Exact count (latent): w 0.11 [0.09, 0.13] 0.07 [0.06, 0.08]
 Visit day −2.96 [−3.50, −2.50] −1.29 [−1.54, −1.06]
σu2 6.65 [5.12, 9.08]