# Table 1 Average log-binomial method and Robust Poisson method estimates*

Zero Slope Medium Slope High Slope
Prevalence at
X = 5
Intercept (SE) Slope (SE) Intercept (SE) Slope (SE) Intercept (SE) Slope (SE)
0.3 True Parameters -1.2040 0.00 -1.7040 0.10 -2.2040 0.20
(Conv. = 100%) (Conv. = 99.9%) (Conv. = 90.9%)
Log-Binomial -1.2292 (0.3250) 0.0001 (0.0559) -1.7387 (0.3692) 0.1016 (0.0542) -2.2512 (0.3900) 0.2046 (0.0488)
Robust Poisson -1.2291 (0.3247) 0.0001 (0.0558) -1.7426 (0.3692) 0.1023 (0.0544) -2.2634 (0.4027) 0.2064 (0.0520)
0.5 True Parameters -0.6931 0.00 -0.9431 0.05 -1.1931 0.10
(Conv. = 100%) (Conv. = 99.8%) (Conv. = 93.5%)
Log-Binomial -0.7086 (0.2109) 0.0014 (0.0361) -0.9512 (0.2297) 0.0501 (0.0352) -1.2039 (0.2413) 0.1006 (0.0327)
Robust Poisson -0.7088 (0.2112) 0.0015 (0.0362) -0.9517 (0.2311) 0.0502 (0.0356) -1.2058 (0.2477) 0.1009 (0.0345)
0.7 True Parameters -0.3567 0.00 -0.5067 0.03 -0.6567 0.06
(Conv. = 99.0%) (Conv. = 96.1%) (Conv. = 70.3%)
Log-Binomial -.3686 (0.1374) 0.0010 (0.0236) -0.5115 (0.1485) 0.0297 (0.0226) -0.6579 (0.1509) 0.0598 (0.0194)
Robust Poisson -.3680 (0.1383) 0.0009 (0.0237) -0.5139 (0.1513) 0.0301 (0.0234) -0.6669 (0.1621) 0.0614 (0.0225)
1. * Based on 1,000 simulations of the log-binomial model with a sample size of 100 and a single independent variable, X, with uniform distribution [0, 10]. The log-binomial method used the COPY method approximation when needed.
2. Standard Error.
3. Percentage of times the log-binomial model converged on the original data.