random_diff#

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Random Effects Differences Density Function#

k, K#

For each rate_id and each child there is a smoothing and corresponding set of model variables. In addition, for each mulcov_id and each subgroup_id corresponding to the group_id for this mulcov_id , there is a smoothing and a corresponding set of model variables. We use \(k\) to index these smoothings \(s_k\) and \(K\) for the number of these smoothings. We use \(u^k\) to denote the subvector of the random effects \(u\) that corresponds to the k-th smoothing.

A^u#

The random effects age difference function is

\[A^u ( u | \theta ) = \prod_{k=0}^{K-1} A^s ( s_k , u^k, \theta )\]

see definition of A^s .

T^u#

The random effects time difference function is

\[T^u ( u | \theta ) = \prod_{k=0}^{K-1} T^s ( s_k , u^k, \theta )\]

see definition of T^s .