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fixed_value#
View page sourceThe Fixed Effects Value Density Function#
theta_j#
We use \(\theta_j\) to denote one component of the fixed effects vector.
prior_id#
We use prior_id for the prior that is attached to the j-th fixed effect; see Prior for a Variable .
lambda_j#
If \(\theta_j\) is a smoothing standard deviation multiplier then \(\lambda_j = 1\). Otherwise \(\lambda_j\) is the mulstd_value_prior_id multiplier for the smooth_id corresponding to \(\theta_j\).
mu_j#
We use \(\mu_j\) to denote the mean corresponding to prior_id .
sigma_j#
We use \(\sigma_j\) to denote the std corresponding to prior_id .
eta_j#
We use \(\eta_j\) to denote the eta corresponding to prior_id .
d_j#
We use \(d_j\) to denote the density_id corresponding to prior_id . In an abuse of notation, we include eta and eta in d_j ; see d .
delta_j#
We use \(\delta_j\) to denote the transformed standard deviation corresponding to prior_id
V_j^theta#
The value density for the j-th component of \(\theta\) is
where \(D\) is the log-density function .
V^theta#
Let \(n\) be the number of fixed effects. The value density for all the fixed effects \(\theta\) is defined by