hes_fixed_obj¶

Compute the Hessian of The Fixed Effects Objective¶

Syntax¶

hes_fixed_obj_rcv = mixed_object . hes_fixed_obj (
      fixed_vec , random_opt
)

Prototype¶

CppAD::mixed::d_sparse_rcv cppad_mixed::hes_fixed_obj(
   const d_vector& fixed_vec            ,
   const d_vector& random_opt           )

Purpose¶

Compute the Hessian of the fixed effects objective function \(L ( \theta )\); see fixed effects objective . The Hessian is

\[L^{(2)} ( \hat{\theta} )\]

Absolute value terms in the Negative Log-Density Vector for the fix_likelihood are not include in this Hessian (because they do not have a derivative, let alone Hessian, at zero).

mixed_object¶

We use mixed_object to denote an object of a class that is derived from the cppad_mixed base class.

fixed_vec¶

is the vector of fixed effects \(\theta\) at which the Hessian is evaluated.

random_opt¶

is the optimal random effects corresponding to this value for the fixed effects; i.e., u^(theta) .

hes_fixed_obj_rcv¶

The return value is a d_sparse_rcv representation of the lower triangle of the Hessian. (The Hessian is symmetric and hence determined by its lower triangle.) Absolute value terms in the Negative Log-Density Vector for the fix_likelihood are not include in this Hessian because they do not have a derivative (let alone Hessian) at zero.

Example¶

The file hes_fixed_obj.cpp contains an example and test of this routine. It returns true for success and false for failure.