of the copula mixed model as long as the univariate margins are correctly specified.

Finally in order to study the relative performance of the one-factor copula mixed model over the quadrivariate vine copula mixed model as the number of quadrature points increase we randomly generated $B = 20$ samples of size $N = 22$ from the D-vine copula mixed model. The model parameters are set as before. The simulations were carried out on a Broadwell E5-2680 v4@2.40GHz. Table \[times\] summarizes the computing times (averaged over 20 replications) in seconds. Clearly the D-vine copula mixed approach requires a much higher computing time. Note in passing that for the estimation of the D-vine copula mixed model we even used parallel programming and 22 (one core for each observation) instead of 1 core that used in the estimation of the one-factor copula mixed model. Hence it is demonstrated that even for the case of $T=2$ tests, the computational improvement of the one-factor copula mixed model is substantial, as one has to calculate numerically bivariate integrals instead of much more difficult quadrivariate integrals.

   $n_q$   factor    vine
  ------- -------- ---------
    15      35.4     799.9
    30      65.7    7355.4
    50     126.2    42997.6

  : \[times\]Small sample of size $N=22$ 