Sometimes estimation of the model parameters is difficult,
always check the convergence of the optimisation algorithm. The
asymmetric Laplace model, effect.family="alaplace", is often more
difficult to optimise than effect.family="gaussian".If data are standardised (having general mean zero and general variance one) the
log likelihood function is usually maximised over values between -5 and 5.
The transformed.par is a vector of transformed model parameters
having length 5 up to 7 depending on the chosen model.
The transformed.par is $log s2, log s2_h, log s2_t, m, logit p, logit q$ a vector of length 6 when using effect.family = "gaussian" and var.select=TRUE,
and is $log s2, log s2_h, log s2_tL, log s2_tR, m, logit p, logit q$ a vector of length 7
for effect.family="alaplace" and var.select=TRUE.
When var.select=FALSE the $q$ parameter is dropped, yielding a vector
of length 5 for
effect.family="gaussian" and a vector of length 6
for effect.family="alaplace".
We assumed a Bayesian linear model being $$y_{vctr}=\mu+\eta_{vct}+\delta_v \gamma_{vc}\theta_{vc}+\varepsilon_{vctr}$$ where $y_{vctr}$ is the available data on variable $v$,
cluster(or class) $c$, type $t$, and replicate $r$; $h_{vct}$
is the between-type error, $t_{vc}$ is the disappearing random component controlled by the Bernoulli variables $d_{v}$ with success probability $q$ and $g_{vc}$ with
success probability $p$; and $e_{vctr}$ is the between-replicate error. The types inside a cluster (or class) share the same $t_{vc}$, but may arise with a different $h_{vct}$.
The model parameters has natural interpretations, $s2$ is the
between replicate error variance; $s2_h$ is the variance of
between-type error; $s2_t$ is the variance of
the disappearing random component which is decomposed to
$s2_tL$, $s2_tR$ the left and the right tail
variances if the model is asymmetric Laplace; $m$ is the general
level; $p$ is the proportion of active variable-cluster (or variable-class) combinations, and
$q$ is the proportion of the active variables. For more details see Vahid Partovi Nia and Anthony C. Davison (2012)