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fit_var_table

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\W}[1]{ \; #1 \; }@)@ This is dismod_at-20221105 documentation: Here is a link to its current documentation . The Optimization Results for Variables
Discussion
Lagrange Multipliers
fit_var_id
fit_var_value
residual_value
residual_dage
residual_dtime
lagrange_value
lagrange_dage
lagrange_dtime
Example

Discussion
The fit_var table contains the maximum likelihood estimate for the model_variables corresponding to the data table meas_value . A new fit_var table is created each time the fit_command is executed.

Lagrange Multipliers
Setting good upper and lower limits, not zero or infinite, helps dismod_at determine the scale for the constraints and gives better detection of which constraints are active.

fit_var_id
This column has type integer and is the primary key for this table. Its initial value is zero, and it increments by one for each row. The fit_var_id column is also a foreign key for the var_table ; i.e.,
   var_id = fit_var_id
In addition, the size of both tables is the same.

fit_var_value
This column has type real and contains the final model variables determined by the fit. This is an approximations for the fixed effects @(@ ( \theta ) @)@ that maximize the Laplace approximate objective @(@ L( \theta) @)@, and the random effects that maximum the joint likelihood @(@ \hat{u} ( \theta ) @)@; see the cppad_mixed documentation for more details.

residual_value
This column has type real and contains the weighted residual corresponding to the value_prior_id for this variable. If there is no such residual, this column is null. For example, if the corresponding density is uniform.

residual_dage
This column has type real and contains the weighted residual corresponding to the dage_prior_id for this variable. If there is no such residual, this column is null. For example, if the corresponding dage_prior_id is null.

residual_dtime
This column has type real and contains the weighted residual corresponding to the dtime_prior_id for this variable. If there is no such residual, this column is null. For example, if the corresponding dtime_prior_id is null.

lagrange_value
This column has type real and contains the Lagrange multipliers for the lower and upper limits corresponding the value_prior_id for this variable. If it is positive (negative) the upper (lower) limit is active. If neither prior limit is active, this column is zero. The Lagrange multipliers are in the scaled space where the optimization takes place.

lagrange_dage
This column has type real and contains the Lagrange multipliers for the lower and upper limits corresponding the dage_prior_id for this variable. If it is positive (negative) the upper (lower) limit is active. If neither prior limit is active, this column is zero. The Lagrange multipliers are in the scaled space where the optimization takes place.

lagrange_dtime
This column has type real and contains the Lagrange multipliers for the lower and upper limits corresponding the dtime_prior_id for this variable. If it is positive (negative) the upper (lower) limit is active. If neither prior limit is active, this column is zero. The Lagrange multipliers are in the scaled space where the optimization takes place.

Example
See the fit_command.py example and test.

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Input File: omh/table/fit_var_table.omh