mxComputeConfidenceInterval: Find likelihood-based confidence intervals

Description

There are various ways to pose an equivalent profile likelihood problem. For good performance, it is essential to tailor the problem to the abilities of the optimizer. The problem can be posed without the use of constraints. This is how the code worked in version 2.1 and prior. Although this way of posing the problem creates an ill-conditioned Hessian, NPSOL is somehow able to isolate the poor conditioning from the rest of the problem and optimize it quickly. However, SLSQP is not so clever and exhibits very poor performance. For SLSQP, good performance is contingent on posing the problem using an inequality constraint on the fit.

Usage

mxComputeConfidenceInterval(plan, ..., freeSet = NA_character_,
  verbose = 0L, engine = NULL, fitfunction = "fitfunction",
  tolerance = NA_real_, constraintType = "ineq")

Arguments

plan

compute plan to optimize the model

...

Not used. Forces remaining arguments to be specified by name.

freeSet

names of matrices containing free variables

verbose

level of debugging output

engine

deprecated

fitfunction

The deviance function to constrain with an inequality constraint.

tolerance

deprecated

constraintType

one of c('ineq', 'eq', 'both', 'none')

Details

Geometrically, SLSQP performs best on smooth likelihood surfaces with smooth derivatives. In the profile CI problem, the distance limit on the deviance is like a wall. Walls do not have smooth derivatives but are more like a step function. The point of mxConstraint is to isolate the parts of a problem that are geometrically non-smooth. Constraints are dealt with specially in SLSQP to best accommodate their sharp geometry.

For the default compute plan, the choice of constraintType is determined by which optimizer is selected.

References

Pek, J. & Wu, H. (in press). Profile likelihood-based confidence intervals and regions for structural equation models. Psychometrica.