ran_likelihood¶

User Defined Random Likelihood Function¶

Syntax¶

vec = mixed_object . ran_likelihood ( fixed_vec , random_vec )

mixed_object¶

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

Virtual Function¶

The following virtual function may be implemented in the derived class:

      virtual CppAD::vector<a1_double> ran_likelihood (
            const CppAD::vector<a1_double>& fixed_vec   ,
            const CppAD::vector<a1_double>& random_vec
      )

fixed_vec¶

This argument has prototype

const CppAD::vector<a1_double>& fixed_vec

It contains a value for the fixed effects vector.

random_vec¶

This argument has prototype

const CppAD::vector<a1_double>& random_vec

It contains a value for the random effects vector.

vec¶

This result has prototype

CppAD::vector<a1_double> vec

It is a Negative Log-Density Vector corresponding to the random likelihood f(theta, u) where

\[f( \theta , u) = - \log [ \B{p}( y | \theta, u) \B{p} ( u | \theta ) ]\]

The Laplace approximation only makes sense if this function is smooth; i.e,

vec . size () == 1

constant¶

Adding or subtracting a constant to vec [0] , that does not depend on the fixed effects \(\theta\) or the random effects \(u\), does not affect the optimal estimates for the fixed and random effects.

Default¶

The base class definition (default) for ran_likelihood returns an empty vector; i.e., vec . size () == 0 . This corresponds to the case where none of the data depends on the random effects; i.e., the data vector y is empty. In this case there random effects vector should also be empty.

Example¶

The file ran_likelihood.cpp contains an example of defining this virtual function.