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lines 5-107 of file: xrst/table/rate_eff_cov_table.xrst
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{xrst_begin rate_eff_cov_table}
{xrst_spell
  attaches
}

The Rate Effect Covariate Table
###############################

Improvements
************
This table is a quick fix for the problem below.
It uses the existing :ref:`weight_table-name` to represent an arbitrary
bilinear function.
A better fix would separate the covariate grid from the covariate
values so that:

#. The grid does not need to be repeated when only values change.
#. weights are not used for purposes other than weighting.

Problem
*******
The data table only assigns one value for each covariate to each data point;
see :ref:`data_table@Covariates` in the data table.
This works fine for most cases.
The problem is when a covariate multiplier affects a
:ref:`mulcov_table@mulcov_type@rate_value` , and
the covariate values changes with age or time , and
the measurement is for an
:ref:`ode integrand <integrand_table@integrand_name@ODE>`.

Solution
********
This table attaches a bilinear function of age and time to
each covariate, node, and :ref:`option_table@splitting_covariate` value.
The covariate values in this table are used,
to compute covariate multiplier effects,
when all the following conditions hold:

#. The covariate appears in this table .
#. The multiplier type is :ref:`mulcov_table@mulcov_type@rate_value` .

If the conditions above do not hold,
the :ref:`data table <data_table@Covariates>` in the data and avgint tables
are used to compute covariate multiplier effects.

Optional
********
This table is optional.
The case where there is not ``rate_eff_cov`` table in the database
is the same as when the table has not entries.

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

covariate_id
************
This column has type ``integer`` and is the
:ref:`covariate_table@covariate_id` corresponding to this row.
The covariate_id corresponding to the splitting covariate
cannot appear in this column; i.e.,
the splitting covariate value is constant with respect to age and time.

node_id
*******
This column has type ``integer`` and is the
:ref:`node_table@node_id` corresponding to this row.

split_value
***********
This column has type ``real`` and is the value of the
splitting corresponding to this row.
This value is not used when the splitting covariate is ``null`` .

weight_id
*********
This column has type ``integer`` and is the
:ref:`weight_table@weight_id` corresponding to this row.
As a quick fix, we use *weight_id* to identify an
arbitrary bilinear functions of age and time.

Rectangular Grid
****************
For each *covariate_id* that appears in this table,
each *node_id* in the node table,
each splitting covariate value in the data table,
and each splitting covariate value in the avgint table,
there must be one an only one row with that
*covariate_id*, *node_id*, and splitting covariate value.

Example
*******
The file :ref:`rate_eff_cov_table.py-name`
contains an example ``rate_eff_cov`` table.

{xrst_toc_hidden
   example/table/rate_eff_cov_table.py
}


{xrst_end rate_eff_cov_table}