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lines 5-78 of file: example/user/fit_random.py
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# {xrst_begin user_fit_random.py}
# {xrst_spell
#     exp
# }
# {xrst_comment_ch #}
#
# Fitting Just Random Effects
# ###########################
#
# Purpose
# *******
# This example demonstrates using the command
#
#     ``dismod_at`` *database* ``fit random``
#
# See the :ref:`fit_command@variables@random` option
# to fit the fit command.
#
# Discussion
# **********
# The following describes the model and data for this example:
#
# #. The :ref:`age_table-name` has values
#    ``0.0`` , ``50.0`` , ``100.0`` .
#    The :ref:`time_table-name` has values
#    ``1995.0`` , ``2005.0`` , ``2015.0`` .
# #. The parent node is North America, the child nodes are
#    Canada and the United States.
# #. The only :ref:`model_variables-name` in this example are
#    :ref:`rate_table@rate_name@iota` for the parent and the
#    corresponding random effects for two children.
#    These rates are modeled as constant with respect to age and
#    linear between time 1995 and 2015.
#    The true iota is
#
#    .. csv-table::
#        :widths: auto
#
#        0.01,North America
#        0.01 * exp(+0.5),United States
#        0.01 * exp(-0.5),Canada
#
#    Note that the random effect for the United States is +0.5
#    and for Canada it is -0.5.
# #. There are three measurements, one for each node.
#    All the measurements are at age 50 and time 2000
#    (there is no age or time interval for the data points).
#    The measurement value is exactly equal to the true value of *iota*
#    for the corresponding node.
#    The measurement noise is modeled to have a 10 percent coefficient
#    of variation (even though there is no noise in the actual measurements).
# #. The prior for North America is a uniform with mean equal to the
#    true value for the United States.
#    The prior for Canada and the United States is a Gaussian with mean zero and
#    standard deviation 100.
#    The large standard deviation is so that it does not have much effect.
# #. The prior for the difference in *iota* between time 1995
#    and time 2015 for the children (parent) is a Gaussian (log Gaussian)
#    with mean zero and standard deviation 0.1.
# #. The init command is used to set the
#    :ref:`init_command@start_var_table` equal to the
#    prior mean.
#    The prior means for North America (the fixed effects) are not their
#    true values and the optimal values for the random effects
#    compensate for this.
#
# Source Code
# ***********
# {xrst_literal
#     BEGIN PYTHON
#     END PYTHON
# }
#
# {xrst_end user_fit_random.py}