Check consistency of various parts of a TMB implementation. Requires that user has implemented simulation code for the data and optionally random effects. (Beta version; may change without notice)
checkConsistency(
obj,
par = NULL,
hessian = FALSE,
estimate = FALSE,
n = 100,
observation.name = NULL
)List with gradient simulations (joint and marginal)
Object from MakeADFun
Parameter vector (\(\theta\)) for simulation. If unspecified use the best encountered parameter of the object.
Calculate the hessian matrix for each replicate ?
Estimate parameters for each replicate ?
Number of simulations
Optional; Name of simulated observation
A full simulation/re-estimation study is performed when estimate=TRUE.
By default nlminb will be used to perform the minimization, and output is stored in a separate list component 'estimate' for each replicate.
Should a custom optimizer be needed, it can be passed as a user function via the same argument (estimate).
The function (estimate) will be called for each simulation as estimate(obj) where obj is the simulated model object.
Current default corresponds to estimate = function(obj) nlminb(obj$par,obj$fn,obj$gr).
This function checks that the simulation code of random effects and data is consistent with the implemented negative log-likelihood function. It also checks whether the approximate marginal score function is central indicating whether the Laplace approximation is suitable for parameter estimation.
Denote by \(u\) the random effects, \(\theta\) the parameters and by \(x\) the data. The main assumption is that the user has implemented the joint negative log likelihood \(f_{\theta}(u,x)\) satisfying $$\int \int \exp( -f_{\theta}(u,x) ) \:du\:dx = 1$$ It follows that the joint and marginal score functions are central:
\(E_{u,x}\left[\nabla_{\theta}f_{\theta}(u,x)\right]=0\)
\(E_{x}\left[\nabla_{\theta}-\log\left( \int \exp(-f_{\theta}(u,x))\:du \right) \right]=0\)
For each replicate of \(u\) and \(x\) joint and marginal
gradients are calculated. Appropriate centrality tests are carried
out by summary.checkConsistency. An asymptotic
\(\chi^2\) test is used to verify the first identity. Power of
this test increases with the number of simulations n. The
second identity holds approximately when replacing the
marginal likelihood with its Laplace approximation. A formal test
would thus fail eventually for large n. Rather, the gradient
bias is transformed to parameter scale (using the estimated
information matrix) to provide an estimate of parameter bias caused
by the Laplace approximation.
summary.checkConsistency, print.checkConsistency