Table 1.

Summary statistics and recommended empirical prior distributions for Models (1)–(8) developed from QRAD. Model numbers and parameters correspond to those described in the text. For recommended priors: N(μ,σ²) indicates a normal distribution with mean μ and variance σ², LN(μ,σ²) indicates a log-normal distribution with mean $\text{exp}\left\{\text{μ} + \mathrm{½}{\sigma }^2\right\}$ and variance $\left(\text{exp}\left\{{\sigma }^2\right\} – 1\right)\text{exp}\left\{2\text{μ} + {\sigma }^2\right\}$, while Beta(a,b) indicates a Beta distribution with shape parameters a and b.

		sample statistics
Model	parameter	minimum	median	maximum	mean	variance	recommended prior
Quantal linear (1)	γ	0	0.041	1	0.109	0.025	γ~ Beta(0.313, 2.545)
	β1	0	0.583	17.770	−0.470*	1.688*	β1 ~ LN(-0.470, 1.688)
Multi-stage (2)	γ	0	0.041	0.947	0.112	0.025	γ~ Beta(0.326, 2.582)
	β1	0	0.241	11.394	−1.006*	4.949*	β1 ~ LN(-1.006, 4.949)
	β2	0	0.063	15.874	−1.016*	5.013*	β2 ~ LN(-1.016, 5.013)
Weibull (3)	γ	0	0.034	0.947	0.095	0.022	γ~ Beta(0.271, 2.583)
	α	0.20	1.051	17.619	−0.243*	2.467*	α-0.2 ~ LN(-0.243, 2.467)
	β	0	0.706	11.388	−0.464*	1.535*	β ~ LN(-0.464, 1.535)
Gamma (4)	γ	0	0.034	1	0.097	0.023	γ~ Beta(0.276, 2.572)
	α	0.20	1.098	17.799	−0.153*	2.637*	α-0.2 ~ LN(-0.153, 2.637)
	β	0	0.924	16.119	−0.587*	5.659*	β ~ LN(-0.587, 5.659)
Logistic (5)	β0	−16.491	−2.446	2.889	−2.526	3.733	β0 ~ N(-2.526, 3.733)
	β1	0	2.734	16.734	1.018*	0.603*	β1 ~ LN(1.018, 0.603)
Log-Logistic (6)	γ	0	0.031	1	0.097	0.023	γ~ Beta(0.275, 2.571)
	β0	−4.789	0.095	7.353	0.203	4.061	β0 ~ N(0.203, 4.061)
	β1	0.200	1.314	17.760	0.274*	0.960*	β1 ~ LN(0.274, 0.960)
Probit (7)	β0	−11.844	−1.431	1.619	−1.660	3.264	β0 ~ N(-1.66, 3.264)
	β1	0	1.537	13.519	0.473*	0.638*	β1 ~ LN(0.473, 0.638)
Log-Probit (8)	γ	0	0.050	0.947	0.104	0.022	γ~ Beta(0.333, 2.877)
	β0	−17.400	0.047	11.176	−0.514	10.337	β0 ~ N(-0.514,10.337)
	β1	0.200	0.914	5.926	−0.186*	0.579*	β1 ~ LN(-0.186, 0.579)

^*Reported mean and variance based on sample values after logarithmic transformation; values for α component in Models (3) and (4) are based on log(α′) = log(α – 0.2).