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lines 5-74 of file: example/user/zsum_mulcov_meas.py
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# {xrst_begin user_zsum_mulcov_meas.py}
# {xrst_comment_ch #}
#
# Constrain Sum of Subgroup Measurement Covariate Multipliers to Zero
# ###################################################################
#
# See Also
# ********
# :ref:`user_zsum_child_rate.py-name` ,
# :ref:`user_zsum_mulcov_rate.py-name`
#
# Purpose
# *******
# This example demonstrates using
# The :ref:`option_table@Zero Sum Constraints@zero_sum_mulcov_group`
# to improve the speed and accuracy of estimation of the fixed effects.
#
# Problem Parameters
# ******************
# {xrst_literal
#     begin problem parameters
#     end problem parameters
# }
# Note that the measurement coefficient of variation *measurement_cv*
# is very small so that a small number of data points can be used.
# You should be able to increase the coefficient of variation by a factor,
# so long as you increase the number of data points by the factor squared.
#
# Data Simulation
# ***************
# The true rate for the parent region ``north_america`` ,
# used for simulating data, are
# *iota_parent* and *rho_parent* problem parameters.
# The
# :ref:`model_variables@Random Effects, u@Subgroup Covariate Multipliers`
# for ``canada`` is *subgroup_mulcov*
# and for the ``united_states`` is ``-`` *subgroup_mulcov* .
# These multipliers effect the rates (not the measurements).
#
# Nodes
# *****
# There are just three nodes for this example,
# The parent node, ``north_america`` , and the two child nodes
# ``united_states`` and ``canada`` .
# The child rate effects are constrained to be zero
# to simplify the example.
#
# Model Variables
# ***************
# The non-zero fixed effects for this example are
# :ref:`rate_table@rate_name@iota` and *rho*
# for the parent node ``north_america`` .
# The non-zero random effects are the subgroup measurement covariate multipliers
# for the ``united_states`` and ``canada`` .
# The parent rates and subgroup covariate multipliers 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
# covariate multipliers.
# The resulting rates will be constant
# in age and constant in time except between the two time grid points
# where it is linear.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_zsum_mulcov_meas.py}