Table 1 Prior distributions for different versions of cumulative proportional odds model

\(\alpha\)

0

0

0

Normal (\(\mu = 0,\ \sigma = 0.1\))

\(\tau _{yk}\)

Normal (\(\mu = 0,\ \sigma = 100\))

Normal (\(\mu = 0,\ \sigma = 100\))

Normal (\(\mu = 0,\ \sigma = 100\))

\(t_{\text {student}} (\mathrm {df} = 3,\ \mu = 0,\ \sigma = 8)\)

\(\boldsymbol{\beta}\)  

Normal (\(\boldsymbol\mu=\mathbf0,\mathrm\Sigma=100^2I_{p\times p}\))

Normal (\(\boldsymbol\mu=\mathbf0,\mathrm\Sigma=100^2I_{p\times p}\))

Normal (\(\boldsymbol\mu=\mathbf0,\mathrm\Sigma=100^2I_{p\times p}\))

Normal (\(\boldsymbol\mu=\mathbf0,\mathrm\Sigma=2.5^2I_{p\times p}\))

\(\delta _{k_{c}}\)

Normal (\(\mu = \delta _{c},\ \sigma = \eta\))

Normal (\(\mu = \delta _{c},\ \sigma = \eta\))

Normal (\(\mu = \delta _{c},\ \sigma = \eta\))

Normal (\(\mu = \delta _{c},\ \sigma = \eta\))

\(\eta\)  

Cauchy (\(\mu = 0,\ \sigma = 100\))

\(t_{\text {student}} (\mu = 0,\ \sigma = 100)\)

\(t_{\text {student}} (\mu = 0,\ \sigma = 100)\)

\(t_{\text {student}} (\mathrm {df} = 3, \mu = 0,\ \sigma = 0.25)\)

\(\delta _{c}\)

Normal (\(\mu=-\triangle_{co},\;\sigma=\eta_0\))

Normal (\(\mu=-\triangle_{co},\;\sigma=\eta_0\))

Normal (\(\mu=-\triangle_{co},\;\sigma=\eta_0\))

Normal (\(\mu=-\triangle_{co},\;\sigma=\eta_0\))

\(\eta_0\)  

Cauchy (\(\mu = 0,\ \sigma = 100\))

\(t_{\text {student}} (\mu = 0,\ \sigma = 100)\)

\(t_{\text {student}} (\mu = 0,\ \sigma = 100)\)

0.1

\(-\triangle _{co}\)

Normal (\(\mu = 0,\ \sigma = 100\))

Normal (\(\mu = 0,\ \sigma = 100\))

Normal (\(\mu = 0,\ \sigma = 0.354\))

Normal (\(\mu = 0,\ \sigma = 0.354\))