three MSEs corresponding to $(\gamma,\lambda_0,\lambda_1)$ to obtain a global measure of MSE. Four equal sample size scenarios are chosen: $m_{+0}=m_{+1}=m=10, 25, 50, 100$ to reflect small, moderate and large sample size situations. For symmetry, we only consider cases where $\Delta$ is non-negative. More specifically, we examine cases with $\Delta=\Delta_h=h/10, \,h \in\{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Each choice of $\Delta$ implies the constraint: $0<\gamma<\gamma_{h,\max}=\min(1,1/\Delta_h-1)$. We then choose a grid of $\gamma$ points: $\gamma_{hj}=j\gamma_{h, \max}/10$ with $j=1,2,\dots,9$. These values are meant to capture a wide range of behaviours of the conditional probability of an occurrence of a particular characteristic at one site given an occurrence of that characteristic at the other site in the range $(1-\gamma_{h,\max},1)$. Then, set $\lambda_{hj, \max}=\dfrac{1}{1+\gamma_{hj}}-\Delta_h$. For the pair $(\lambda_0,\lambda_1)$, we select the values: $\lambda
_{0hjk} = k\lambda_{hj,\max}/10$ with $k=1,2,\dots,9$ and $\lambda
_{1hjk} =
\lambda_{0hjk}+\Delta_h$. Hence, for each sample size and $\Delta_h$, we compute the three criterion functions for 81 combinations of the triplets $(\gamma, \lambda_0, \lambda_1)$. In the Bayesian framework, we examine HPD intervals under the uniform, Jeffreys’, and reference priors.

The probability of obtaining degenerate results in the frequentist framework (non-estimable model parameters or model parameters on the boundary of 