optimize_random¶

Optimize Random Effects¶

Syntax¶

random_out =

mixed_object . optimize_random (
        options , fixed_vec , random_lower , random_upper , random_in
)

Purpose¶

This routine maximizes the random likelihood corresponding to the object mixed_object .

mixed_object¶

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

options¶

This argument has the prototype

const std::string& options

This is the ipopt_options for optimizing the random effects with the following qualifications:

evaluation_method¶

There is an additional String option with name = evaluation_method and value is either ipopt_random or ipopt_solve . The ipopt_random choice uses CppAD::mixed::ipopt_random for optimizing random effects. This special purpose class is expected to eventually be the faster choice. This is the default choice; i.e., ipopt_random will be used if this option is not present. The ipopt_solve choice uses CppAD::ipopt::solve for optimizing random effects. Currently this is sometimes faster and so this choice is still included (but may be removed in the future).

fixed_vec¶

This argument has prototype

const CppAD::vector<double>& fixed_vec

It specifies the value of the fixed effects vector \(\theta\).

random_lower¶

This argument has prototype

const CppAD::vector<double>& random_lower

It must have size equal to n_random and specifies the lower limits for the optimization of the random effects vector \(u\). The value minus infinity can be used to specify no lower limit.

random_upper¶

This argument has prototype

const CppAD::vector<double>& random_upper

It must have size equal to n_random and specifies the upper limits for the optimization of the random effect. The value plus infinity can be used to specify no lower limit.

random_in¶

This argument has prototype

const CppAD::vector<double>& random_in

It must have size equal to n_random and specifies the initial value used for the optimization of the random effects vector \(u\). It must hold that

random_lower [ i ] <= random_in [ i ] <= random_upper [ i ]

for each valid index i .

random_out¶

The return value has prototype

CppAD::vector<double> random_out

It is the final value (obtained by optimization) of the random effects vector \(u\).

Example¶

The file optimize_random.cpp contains an example and test of this procedure. It returns true, if the test passes, and false otherwise.