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\section*{Link adjusted von Mises}

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\subsection*{Parametrisation}

The (circular) von Mises distribution has density
\begin{displaymath}
    p(y_i) =\frac{\exp(s_i\kappa \cos(x-\mu ))}{2\pi I_{0}(s_i\kappa)}
\end{displaymath}
where $s_i>0$ is a fixed scaling, the location is $\mu$
and the precision-parameter is $\kappa$.

\subsection*{Link-function}

The linkfunction is given as 
\begin{displaymath}
    \mu =  2\pi \left(\frac{1}{1+\exp(-\eta)} - 1/2\right)
\end{displaymath}
where $\eta$  is the linear predictor.

\subsection*{Hyperparameters}

The hyperparameter is ${\kappa}=\exp(\theta)$
and prior are given on $\theta$
\subsection*{Specification}

\begin{itemize}
\item \texttt{family="vm"}
\item Required arguments: $y$ (and optional $s$ through option
    \texttt{scale})
\end{itemize}

\subsubsection*{Hyperparameter spesification and default values}
\input{../hyper/likelihood/lavm.tex}

\subsection*{Example}

In the following example we estimate the parameters in a simulated
example.
\verbatiminput{example-lavm.R}

\subsection*{Notes}

This distribution is experimental, and changes will occur.

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