$\omega_1^\circ$ and $\omega_2^\circ$ to handle the positive and negative dependencies, respectively.

Conclusions from the values in the table and the Tables 1 and 2 in the Supplementary material are the following:

-   ML with the true one-factor copula mixed model is highly efficient according to the simulated biases, SDs and RMSEs.

-   The MLEs of $\bfpi_1,\bfpi_2$ are not robust to margin misspecification, e.g., in Table \[sim1\] where the true univariate margins are normal (beta) the scaled biases for the MLEs of $\pi_{02}$ for the various one-factor copula mixed models with beta (normal) margins range from $-4.16$ ($3.21$) to $-1.86$ (4.70).

-   The SDs of $\bfpi_1,\bfpi_2$ are not robust to margin misspecification, e.g., in Table \[sim1\] where the true univariate margins are normal the scaled SDs for the MLEs of $\pi_{01}$ for the various one-factor copula mixed models with normal margins range from $3.13$ to $3.61$, while for the various one-factor copula mixed models with beta margins range from $2.77$ to $3.10$.

-   The MLEs of $\bfpi_1,\bfpi_2$ are rather robust to bivariate copula misspecification, but their biases increase when the assumed bivariate copulas have different tail dependence behaviour. For example, in Table \[sim1\] the scaled biases for the MLEs of $\pi_{11}$ 