mxFitFunctionGREML: Create MxFitFunctionGREML Object
In OpenMx: Extended Structural Equation Modelling

mxFitFunctionGREML

R Documentation

Create MxFitFunctionGREML Object

Description

This function creates a new MxFitFunctionGREML object.

Usage

mxFitFunctionGREML(dV=character(0), aug=character(0),
   augGrad=character(0), augHess=character(0), 
   autoDerivType=c("semiAnalyt","numeric"),infoMatType=c("average","expected"))

Arguments

`dV`	Vector of character strings; defaults to a character vector of length zero. If a value of non-zero length is provided, it must be a named character vector. This vector's names must be the labels of each free parameter in the model. The vector's elements (i.e., the character strings themselves) must be the names of `MxAlgebra` or `MxMatrix` object(s), each of which equals the first partial derivative of the 'V' matrix with respect to the corresponding free parameter.
`aug`	Character string; defaults to a character vector of length zero. Any elements after the first are ignored. The string should name a 1x1 `MxMatrix` or an `MxAlgebra` that evaluates to a 1x1 matrix. The named object will be used as an "augmentation" to the GREML fitfunction–specifically, the [1,1] value of the object named by `aug` will be added to the GREML fitfunction value at each function evaluation during optimization. The augmentation can be used to regularize estimation with a prior likelihood, or to use penalty functions to approximate constraints.
`augGrad`	Character string; defaults to a character vector of length zero. Any elements after the first are ignored. The string should name a `MxMatrix` or an `MxAlgebra` that evaluates to the gradient of `aug` with respect to free parameters. The gradient can be either a column or row vector. The free parameters corresponding to the elements of the gradient vector are taken from the names of argument `dV`, e.g. if the third name of `dV` is `'va'`, then the third element of the gradient vector should be the first partial derivative of the augmentation function with respect to `'va'`. Ignored unless both `dV` and `aug` have nonzero length.
`augHess`	Character string; defaults to a character vector of length zero. Any elements after the first are ignored. The string should name a `MxMatrix` or an `MxAlgebra` that evaluates to the Hessian of `aug` with respect to free parameters. The free parameters corresponding to each row and column of this matrix are dictated by the names of argument `dV`, in the same manner as for the elements of `augGrad`. Ignored unless both `dV` and `aug` have nonzero length. Providing a nonzero-length value for `augHess` but not `augGrad` will result in an error at runtime.
`autoDerivType`	"Automatic derivative type." Character string, either "semiAnalyt" (default) or "numeric". See details below.
`infoMatType`	"Information matrix type." Character string, either "average" (default) or "expected". See details below.

Details

Making effective use of arguments dV, augGrad, and augHess will usually require a custom mxComputeSequence(). The derivatives of the REML loglikelihood function with respect to parameters can be internally computed from the derivatives of the 'V' matrix supplied via dV. The loglikelihood's first derivatives thus computed will always be exact, but its matrix of second partial derivatives (i.e., its Hessian matrix) will be approximated by either the average or expected information matrix, per the value of argument infoMatType. The average information matrix is faster to compute, but may not provide a good approximation to the Hessian if 'V' is not linear in the model's free parameters. The expected information matrix is slower to compute, but does not assume that 'V' is linear in the free parameters. Neither information matrix will be a good approximation to the Hessian unless the derivatives of 'V' evaluate to symmetric matrices the same size as 'V'. Note also that these loglikelihood derivatives do not reflect the influence of any parameter bounds or MxConstraints. Internally, the derivatives of the 'V' matrix are assumed to be symmetric, and the elements above their main diagonals are ignored.

Formerly, if any derivatives were provided via dV, then derivatives had to be provided for every free parameter in the MxModel. Currently, users may provide derivatives of 'V' via dV with respect to some or all free parameters. Note that the gradient and Hessian of the augmentation must be complete, i.e. contain derivatives of the augmentation with respect to every parameter or pair of parameters respectively.

If there are any free parameters with respect to which the user did not provide an analytic derivative of 'V', OpenMx will automatically calculate the necessary loglikelihood derivatives according to autoDerivType. If autoDerivType="semiAnalyt", the GREML fitfunction backend will calculate the missing derivatives in a "semi-analytic" fashion. Specifically, the backend will numerically differentiate 'V' with respect to the relevant parameter(s), and use those numeric matrix derivatives to analytically calculate the needed loglikelihood derivatives. If autoDerivType="numeric", the needed loglikelihood derivatives will be calculated numerically, via finite-differences.

Argument aug is intended to allow users to provide penalty functions or prior likelihoods in order to approximate constraints or to regularize optimization. The user is warned that careless use of this augmentation feature may undermine the validity of his/her statistical inferences.