information_mat¶

Compute the Observed Information For Fixed Effects¶

Deprecated 2020-03-22¶

Syntax¶

information_rcv = mixed_object . information_mat (
      solution , random_opt
)

Purpose¶

Compute the observed information matrix. We use \(L ( \theta )\) to denote the fixed effects objective . The observed information 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.

solution¶

is the solution for a previous call to optimize_fixed . Only the solution . fixed_opt field is used.

random_opt¶

is the optimal random effects corresponding to the solution; i.e.

      random_opt = mixed_object . optimize_random (
            random_options ,
            solution . fixed_opt ,
            random_lower ,
            random_upper ,
            random_in
      )

random_options , random_lower , random_upper , and random_in , are the same as in the call to optimize_fixed that corresponds to solution .

information_rcv¶

The return value has prototype

CppAD::mixed::d_sparse_rcv information_rcv

see d_sparse_rcv . This is a sparse matrix representation for the lower triangle of the observed information matrix, which 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 information_mat.cpp contains an example and test of this routine. It returns true for success and false for failure.