coldIntegrate: Auxiliary for controlling "cold" fitting

Description

Auxiliary function as user interface for cold fitting.

Usage

coldIntegrate(li=-4,ls=4, epsabs=.Machine$double.eps^.25, 
epsrel=.Machine$double.eps^.25,limit=100,key=6,lig=-4,lsg=4)

Arguments

lower limit of integration for the log-likelihood.

upper limit of integration for the log-likelihood.

epsabs

absolute accuracy requested.

epsrel

relative accuracy requested.

key

integer from 1 to 6 for choice of local integration rule for number of Gauss-Kronrod quadrature points. A gauss-kronrod pair is used with: 7 - 15 points if key = 1, 10 - 21 points if key = 2, 15 - 31 points if key = 3, 20 - 41 points if key = 4, 25 - 51 points if key = 5 and 30 - 61 points if key = 6.

limit

integer that gives an upperbound on the number of subintervals in the partition of (li,ls), limit.ge.1.

lig

lower limit of integration for the gradient.

lsg

upper limit of integration for the gradient.

Value

A list with the arguments as components.

Details

coldIntegrate returns a list of constants that are used to compute integrals based on a Fortran-77 subroutine dqage from a Fortran-77 subroutine package QUADPACK for the numerical computation of definite one-dimensional integrals. The subroutine dqage is a simple globally adaptive integrator in which it is possible to choose between 6 pairs of Gauss-Kronrod quadrature formulae for the rule evaluation component. The source code dqage was modified and re-named dqager, the change was the introduction of an extra variable that allow, in our Fortran-77 subroutines when have a call to dqager, to control for which parameter the integral is computed.

For given values of li and ls, the above-described numerical integration is performed over the interval (li*\(\sigma\), ls*\(\sigma\)), where \(\sigma=\exp(\omega)/2\) is associated to the current parameter value \(\omega\) examined by the optim function. In some cases, this integration may generate an error, and the user must suitably adjust the values of li and ls. In case different choices of these quantities all lead to a successful run, it is recommended to retain the one with largest value of the log-likelihood. Integration of the gradient is regulated similarly by lig and lsg.

For datasets where the individual profiles have a high number of observed time points (say, more than 30), use coldIntegrate function to set the integration limits for the likelihood and for the gradient to small values than the default ones.

When the fitting procedure is complete but the computation of the information matrix produces NaNs, changing in coldIntegrate function the default values for the gradient integration limits (lig and lsg) might solve this problem.

Examples

Run this code

# NOT RUN {
#####  data= seizure

Integ <- coldIntegrate(li = -3.5, ls = 3.5, lig = -3.5, lsg = 3.5)

### AR1R without patient 207
# }
# NOT RUN {
seizure207 <- seizure[seizure$id != 207, ]

seiz1R1.207 <- cold(y~ lage + lbase + v4 + trt  + trt:lbase, 
random = ~ 1, data = seizure207, dependence = "AR1R", integrate = Integ)
summary (seiz1R1.207)
# }
# NOT RUN {
# }