mixed_hes_random_obj#

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Hessian of Random Effects Objective#

Syntax#

   # mixed_obj.hes_random_obj(
      hes_random_obj_rcv   = None ,
      fixed_vec            = None ,
      random_vec           = None ,
   # )

Purpose#

We are given a value for the fixed effects \(\theta\), and the corresponding random effects \(u\) . This routine the hessian, with respect to the random effects, of the negative log of random effects objective; i.e., ran_likelihood

\[\B{p} ( y | \theta , u ) \B{p}( u | \theta ) \B{d} u\]

If there is no data, the return value is the Hessian of \(- \log [ \B{p} ( u | \theta ) ]\) w.r.t \(u\) .

hes_random_obj_rcv#

The argument hes_random_obj_rcv is a py_sparse_rcv matrix. The input value of this argument does not matter. Upon return it contains the lower triangle of the Hessian (the Hessian is symmetric).

fixed_vec#

The argument fixed_vec is a numpy vector with float elements and length n_fixed. It contains the value of the fixed effects \(\theta\) at which the Hessian is evaluated. This vector can’t be None.

random_vec#

The argument random_vec is a numpy vector with float elements and length n_random. It contains the value for the random effects at which the Hessian is evaluated., This vector can’t be None.

Examples#