spaMM (version 4.7.0)

optimBounds: Optimization bounds

Description

Higher-level fitting functions (fitme, its derived function fitmv and pois4mlogit, and the older function corrHLfit), perform box-constrained numerical optimization of the likelihood objective function. The constraints can be specified in calls of these functions by the lower and upper arguments.

Specifying upper bounds for variances of random effects, and lower and upper bounds for the correlation parameters of random-coefficient covariance matrices, may be useful to prevent divergence of their estimates. Such divergence may otherwise occur notably in REML or ML fits of binary-response models, and more broadly of count-response data with low count values.

The experimental optimBounds function may be used to extract information from a fit object about the lower and upper bounds used in optimization.

Usage

optimBounds(x, transf, ...)

Value

A structured list, with elements lower and upper and themselves being lists.

Arguments

x

Fit object produced by fitme or related higher-level fitting functions.

transf

boolean; whether to report transformed values of (co-)variance parameters or not. Random-coefficients parameter bounds are always returned in transformed space, for reasons given in Details.

...

For development purposes.

Details

Optimization of random-coefficient parameters is performed in a transformed parameter space. Box constraints on the elements of the ranCoefs vectors (i.e., variances and correlations), do not translate into box constraints in the transformed space, and vice versa. For this reason, simple transformation of lower or upper bounds from ranCoefs space to transformed space is generally inadequate, and optimBounds will not provide random-coefficient bounds untransformed as ranCoefs, even when transf=FALSE. It will instead keep any transformed values trRanCoefs in the result, with a message. Such trRanCoefs do not take into account optional box constraints declared by the user as ranCoefs elements of the lower or upper arguments of the fitting function that returned the fit object. Yet, since version 4.6.36, the fit object does satisfy such constraints correctly.

Examples

# Example from VarCorr() documentation in 'nlme' package:
data("Orthodont",package = "nlme")
sp1 <- fitme(distance ~ age+(age|Subject), data = Orthodont, method="REML")
optimBounds(sp1, transf=TRUE) # showing transformed values 'trRanCoefs'

# Constrained fit (here with clear effect on first variance):
sp2 <- fitme(distance ~ age+(age|Subject), data = Orthodont, method="REML",
             upper=list(ranCoefs=list("1"=c(1,0.999,1))))
optimBounds(sp2, transf=TRUE) # showing transformed values 'trRanCoefs' 

# Specifying bounds on transformed parameters is possible:
sp3 <- fitme(distance ~ age+(age|Subject), data = Orthodont, method="REML",
             upper=list(trRanCoefs=list("1"=c(1,0.999,0.0447))))
optimBounds(sp3, transf=TRUE)