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lines 5-88 of file: example/user/bnd_mulcov.py
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# {xrst_begin user_bnd_mulcov.py}
# {xrst_spell
#     diff
# }
# {xrst_comment_ch #}
#
# Bounding Covariate Multipliers Absolute Data Effect
# ###################################################
#
# Purpose
# *******
# This example shows how to use the
# :ref:`bnd_mulcov_command-name` .
#
# Integrands
# **********
# For this example there is only one integrand, ``Sincidence`` .
#
# Nodes
# *****
# There are two nodes, one called ``world`` and the other called
# ``europe`` .
#
# True Iota
# *********
# For this example, the true incidence rates for europe is given by
# {xrst_spell_off}
# {xrst_code py}
import math
mulcov_true      = -3e-3
income_reference = 1e3
def iota_europe_true(income) :
    effect  = mulcov_true * (income - income_reference)
    return 0.01 * math.exp( effect )
# {xrst_code}
# {xrst_spell_on}
# Here *europe_avg* contains the reference value for
# income and weight in europe.
#
# Parent Node
# ***********
# For this example the parent node is europe and hence world data
# is not included in the :ref:`data_subset_table-name` .
# This demonstrates that the world node is not included when
# the bnd_mulcov command computes its limits for the covariate multiplier.
#
# Data
# ****
# There are four data points measuring Sincidence.
# The first point is for the world, has a very large income, and is
# not included when computing the multiplier bounds.
#
# Model
# *****
# There is only one rate *iota* and it is constant as a function
# of age and time. In addition, there is one covariate multiplier
# for income.
#
# bnd_mulcov
# **********
# The maximum absolute effect for the this example are
# {xrst_spell_off}
# {xrst_code py}
max_abs_effect = 1.0
# {xrst_code}
# {xrst_spell_on}
# Note that the bound on the covariate multiplier have units
# while the maximum absolute effect does not.
#
# max_cov_diff
# ************
# The income values in the europe data are
# its reference, its reference divided by two, and its reference times two.
# The corresponding maximum absolute difference from the
# reference is equal to the reference.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_bnd_mulcov.py}