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\title{

  List of responses to the comments for the author of:
  A multinomial generalized linear mixed model for clustered competing
  risks data

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\section*{Co-Editor}

Based on the advice received, I have decided that your manuscript can be
accepted for publication after you have carried out the corrections as
suggested by the reviewer(s).

\subsection*{Author's response}

We thanks the positive evaluation and we addressed in the paper the
corrections and suggestions of the reviewers.

\section*{Reviewer #1}

The authors have positively answered to all the issues arisen.

\section*{Reviewer #2}

1. Please incorporate the comparison with He et al. (2022) discussed in
the author's response into the paper (Introduction/Discussion).

\subsection*{Author's response}

We thanks for the literature recommendation. The robust approach
proposed by \cite{ahnetal22} has been incorporated into the paper.

\subsection*{Reviewer #2}

2. The authors mentioned that the Laplace-approximated MLE converges
faster than the EM (which has a linear convergence rate), do we know at
what rate it converges, e.g., approximately quadratic?

\subsection*{Author's response}

We thanks fot the insightful comment. The Laplace approximation for the
latent effects of a mixed model consists of two optimizations, an inner
and an outer optimization. The inner one is made through a
Newton-Raphson algorithm, Newton´s method with a quadratic convergence
rate. The external optimization is made through a Quasi-Newton Method,
the BFGS for instance, which in our class of models has a superlinear
convergence rate.

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