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lines 5-89 of file: example/user/shock_cov.py
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# {xrst_begin user_shock_cov.py}
# {xrst_spell
#       def
#       exp
# }
# {xrst_comment_ch #}
#
# Example Fitting a Covariate with a Shock
# ########################################
#
# Purpose
# *******
# This example demonstrates fitting a covariate multiplier
# where the covariate has a shock. To be more specific, a spike at
# a certain age, time, node, and sex.
#
# Integrand
# *********
# There is only one integrand in this example,
# :ref:`avg_integrand@Integrand, I_i(a,t)@prevalence` .
#
# Node Tables
# ***********
# The node table for this example is
# ::
#
#                         world
#                        /     \
#       north_america       south_america
#
# Subgroup Table
# **************
# For this example there is only one subgroup (the world).
#
# Covariates
# **********
# There are two covariates in this example, *sex* and *shock* .
# Sex has the following values
# {xrst_code py}
sex_name2value = { 'female' : -0.5, 'both' : 0.0, 'male' : +0.5 }
# {xrst_code}
# Shock is defined by the following function
# {xrst_code py}
def shock_fun(age, time, node_name, sex) :
    shock = 0.0
    if (node_name, sex) == ('north_america', 'male') :
        if 0 <= age and age <= 40 and 1920 <= time and time <= 1960 :
            age_factor  = 1.0 - abs( age - 20.0 ) / 20.0
            time_factor = 1.0 - abs(time - 1940.0 ) / 20.0
            shock       = age_factor * time_factor
    return shock
# {xrst_code}
#
# Covariate Multipliers
# *********************
# There is one covariate multiplier in this example.
# It multiples *shock* and effects the rate iota as follows:
# {xrst_code py}
mulcov_true      = 1.0
iota_no_effect   = 0.01
def iota_true(age, time, node_name, sex) :
    effect = mulcov_true * shock_fun(age, time, node_name, sex)
    return iota_no_effect * math.exp(effect)
# {xrst_code}
#
# Simulated Data
# **************
# The data is simulated using the true value for the variables,
# and the covariate effects mentioned above. No noise is added to the data,
# but it is modeled as having a ten percent coefficient of variation.
#
# Rate Variables
# **************
# There is one non-zero rate for this example iota
# and the no effect model for iota is constant and equal to
# ``iota_no_effect`` .
#
# Source Code
# ***********
# {xrst_literal
#       BEGIN PYTHON
#       END PYTHON
# }
#
# {xrst_end user_shock_cov.py}