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lines 5-78 of file: example/user/zsum_child_rate.py
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# {xrst_begin user_zsum_child_rate.py}
# {xrst_comment_ch #}
#
# Constrain Sum of Child Rate Effect to Zero
# ##########################################
#
# See Also
# ********
# :ref:`user_zsum_mulcov_rate.py-name` ,
# :ref:`user_zsum_mulcov_meas.py-name`
#
# Purpose
# *******
# This example demonstrates using
# The :ref:`option_table@Zero Sum Constraints@zero_sum_child_rate`
# to improve the speed and accuracy of estimation of the fixed effects.
#
# Problem Parameters
# ******************
# {xrst_literal
#     begin problem parameters
#     end problem parameters
# }
#
# Data Simulation
# ***************
#
# north_america
# =============
# The true rates for the parent region ``north_america``
# (used for simulating data) are the
# *iota_parent* and *rho_parent* problem parameters.
#
# canada
# ======
# The true
# :ref:`child rate effect<model_variables@Random Effects, u@Child Rate Effects>`
# for ``canada`` is *rate_effect_child* .
#
# united_states
# =============
# The true child rate effect
# for the ``united_states`` is ``-`` *rate_effect_child* .
#
# mexico
# ======
# No data is included for mexico, hence it is automatically constrained to have
# zero child rate random effects.
#
# Nodes
# *****
# There are just four nodes for this example,
# The parent node, ``north_america`` , and the three child nodes
# ``united_states`` , ``canada`` and ``mexico`` .
#
# Model Variables
# ***************
# The non-zero :ref:`model_variables-name` for this example are
# :ref:`rate_table@rate_name@iota` and *rho* .
# Both the parent and child rates use a grid with one point in age
# and two points in time. Thus there are six model variables for each rate,
# two for the parent rates and four for the child rate effects.
# The resulting rates will be constant
# in age and constant in time except between the two time grid points
# where it is linear with respect to time.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_zsum_child_rate.py}