\(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\R}[1]{ {\rm #1} }\)
mixed_fix_constraint_xam.py#
View page sourcefix_constraint: Example and Test#
Random Effects#
For this example there is no random effects.
fix_likelihood#
For this example, the fixed likelihood is
\[f( \theta ) = ( \theta - 1 )^2\]
fix_constraint#
For this example, the fixed constraint is
\[g( \theta ) = ( \theta + 2)^2\]
Fixed Constraint Bounds#
For this example, there is no fixed constraint upper bound and the lower bound is \(g^L \leq g(\theta)\)
Optimal Fixed Effects#
If \(g^L \leq g(1) = 9\), the optimal value for the fixed effects is \(\hat{\theta} = 1\). Otherwise, the optimal value satisfies the equation \(c ( \hat{\theta} ) = g^L\); i.e, \(\hat{\theta} = \sqrt{g^L} - 2\).