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lines 5-104 of file: example/user/subgroup_mulcov.py
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# {xrst_begin user_subgroup_mulcov.py}
# {xrst_comment_ch #}
#
# Example Fitting With Subgroup Covariate Multipliers
# ###################################################
#
# Node Table
# **********
# The following is a diagram of the node tree for this example:
# ::
#
#          p1
#         /  \
#        c1  c2
#
# Subgroup Table
# **************
# The following is a diagram of the subgroup tree for this example:
# ::
#
#            p1
#           /  \
#         g1   none
#        /  \    \
#       s1   s2  none
#
# Model Variables
# ***************
#
# Parent Rates
# ============
# There is an iota
# :ref:`parent rate<model_variables@Fixed Effects, theta@Parent Rates>`
# corresponding to node p1.
# This variable has a uniform prior.
#
# Group Covariate Multiplier
# ==========================
# There is a
# :ref:`group covariate multiplier<model_variables@Fixed Effects, theta@Group Covariate Multipliers>`
# that affects all the data in group g1.
# This variable has a uniform prior.
#
# Child Rate Effects
# ==================
# There are two
# :ref:`model_variables@Random Effects, u@Child Rate Effects`
# one for the data corresponding to child c1,
# the other for child c2.
# These variables have gaussian priors with mean zero and standard deviation
# 100 times the absolute true child rate effect.
#
# Subgroup Covariate Multiplier
# =============================
# There are two
# :ref:`model_variables@Random Effects, u@Subgroup Covariate Multipliers`
# one for the data corresponding to subgroup s1,
# the other for subgroup s2.
# These variables have gaussian priors with mean zero and standard deviation
# 100 times the absolute true subgroup effect.
#
# Rate Table
# **********
# There is one entry in the rate table that
# specifies the iota smoothing for the parent node p1.
# There is another entry that specifies the iota smoothing
# for the child nodes c1, c2.
#
# Mulcov Table
# ************
# There is one entry in the mulcov table for group g1 and
# the two subgroups s1, s1 (that make up g1).
# The group smoothing is used for the fixed effect corresponding to g1
# and the subgroup smoothing is used for the s1, s2 random effects.
#
# Data Table
# **********
# Each child (c1, c2) and each subgroup (s1, s2, none)
# have a corresponding data point that is simulated without any noise.
#
# Problem Parameters
# ******************
# {xrst_spell_off}
# {xrst_code py}
iota_parent_true      = 0.01 # value corresponding to parent with no effects
group_effect_true     = 0.3  # value corresponding to group g1
child_effect_true     = 0.2  # absolute value of child random effects
subgroup_effect_true  = 0.1  # absolute value of subgroup random effects
meas_cv               = 0.1  # coefficient of variation for each data point
# {xrst_code}
# {xrst_spell_on}
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_subgroup_mulcov.py}