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lines 5-65 of file: xrst/table/hes_fixed_table.xrst
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{xrst_begin hes_fixed_table}

Hessian of The Fixed Effect Objective Function
##############################################

Creation
********
A new version of this table is created each time the
:ref:`sample_command@asymptotic`
sample command is executed.
The :ref:`density_table@density_name@laplace` densities
are not included in the Hessian
because the Laplace density is not differentiable at zero.
None of the constraints are included in the calculation of this Hessian.

Scaling
*******
The Hessian is in the scaled space for the fixed effects; see
:ref:`prior_table@eta@Scaling Fixed Effects` .

hes_fixed_id
************
This column has type ``integer`` and is the primary key for
the this table.
Its initial value is zero, and it increments by one for each row.

row_var_id
**********
This is the :ref:`var_table@var_id`
for the row of the Hessian that this element corresponds to.

col_var_id
**********
This is the :ref:`var_table@var_id`
for the column of the Hessian that this element corresponds to.

hes_fixed_value
***************
This column has type ``real`` and is the value of the second derivative
of the fixed effects objective w.r.t. the two
:ref:`fixed effects<model_variables@Fixed Effects, theta>`
specified by the row and column indices above.
Note that the row and column indices are equal for the diagonal
elements of the Hessian.

Representation
**************

#. Only the lower triangle of the Hessian is included
   (because the Hessian is symmetric).
#. The matrix is in row major order; i.e. *row_var_id*
   is monotone non-decreasing and for each value of *row_var_id*
   the *col_var_id* is monotone increasing.
#. This is a sparse representation; i.e.,
   if a pair of row and column indices in the lower triangle
   are not present, the Hessian is zero for that row and column pair.
#. The asymptotic statistics require the Hessian to be positive definite
   on the sub-set of variables that have their lower limit less than upper.
   Only these variables are included in the sparse representation of the Hessian.

{xrst_end hes_fixed_table}