for the various one-factor copula mixed models with normal (beta) margins increase to $-1.38$ (-0.92) and $-3.71$ (-2.27) when rotated Clayton copulas with opposite direction tail dependence and Frank copulas with tail independence, respectively, are called.

-   The SDs of $\bfpi_1,\bfpi_2$ are rather robust to bivariate copula misspecification, but increase when the assumed bivariate copulas have different tail dependence behaviour, e.g., in Table \[sim1\] the scaled SDs for the MLEs of $\pi_{11}$ for the various one-factor copula mixed models with normal (beta) margins increase to $2.90$ (2.34) and $3.58$ (2.79) when rotated Clayton copulas with opposite direction tail dependence and Frank copulas with tail independence, respectively, are called.

\[miss\]Misspecification of the copula-mixed model
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We randomly generate 10,000 samples from the D-vine copula mixed model with both normal and beta margins using the algorithm in [@nikoloulopoulos-2018-smmr]. We set the sample size $N$, the study size $n$, the true univariate and Kendall’s $\tau$ parameters, and the disease prevalence to mimic the rheumatoid arthritis data in [@Nishimura-etal2007]. The true (simulated) D-vine copula mixed model uses a Clayton rotated by 270$^\circ$ and Clayton copula to join the (latent) sensitivity and specificity of the first and second test, respectively.

Table \[sim2\] contains the resultant 