mixed#

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Laplace Approximation of Mixed Effects Models#

Notation#

theta#

We use \(\theta\) to denote a value for the fixed effects vector.

u#

We use \(u\) to denote a value for the random effects vector.

z#

We use \(z\) to denote the data that does not depend on the random effects.

y#

We use \(y\) to denote the data that depends on the random effects.

p(theta)#

We use \(\B{p} ( \theta )\) to denote the prior density for \(\theta\).

p(z|theta)#

We use \(\B{p} (z | \theta )\) to denote the density of \(z\) given \(\theta\).

p(u|theta)#

We use \(\B{p} (u | \theta )\) to denote the density of \(u\) given \(\theta\).

p(y|theta,u)#

We use \(\B{p} (y | \theta , u)\) to denote the density of \(y\) given \(\theta\) and \(u\).

Fixed Effects Likelihood#

We refer to \(\B{p} (z | \theta ) \B{p} ( \theta )\) as the fixed effects likelihood. The negative log of this, as function of \(\theta\), is computed by fix_likelihood .

Random Effects Likelihood#

We refer to \(\B{p} (y | \theta , u ) \B{p} ( u | \theta )\) as the random effects likelihood. The negative log of this, as function of \(\theta, u\), is computed by ran_likelihood .

Children#

Name	Title
mixed_ctor	Mixed Class Constructor
mixed_warning	Mixed Class Warnings
mixed_fatal_error	Mixed Class Fatal Errors
mixed_fix_likelihood	Fixed Effects Likelihood
mixed_fix_constraint	Fixed Effects Constraint Function
mixed_ran_likelihood	Random Effects Likelihood
mixed_optimize_fixed	Optimize The Fixed Effects
mixed_optimize_random	Optimize The Random Effects
mixed_hes_fixed_obj	Hessian of Fixed Effects Objective
mixed_hes_random_obj	Hessian of Random Effects Objective