\name{bildIntegrate}
\alias{bildIntegrate}
\title{ Auxiliary for Controlling "bild" Fitting}
\description{Auxiliary function as user interface for \code{bild} fitting }
\usage{bildIntegrate(li=-4,ls=4, epsabs=.Machine$double.eps^.25, 
epsrel=.Machine$double.eps^.25,limit=100,key=6,lig=-4,lsg=4) }
\arguments{ 
  \item{li}{lower limit of integration for the log-likelihood.}                                                                 
  \item{ls}{upper limit of integration for the log-likelihood.}                                                                 
   \item{epsabs}{absolute accuracy requested.}                                                                                  
   \item{epsrel}{relative accuracy requested.}                                                                                 
    \item{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: \cr                                                                                             
    7 - 15 points if key = 1, \cr                                                                                                      
    10 - 21 points if key = 2,\cr                                                                                                      
    15 - 31 points if key = 3,\cr                                                                                                      
    20 - 41 points if key = 4,\cr                                                                                                      
    25 - 51 points if key = 5 and \cr                                                                                                  
    30 - 61 points if key = 6.}                                                                                                        
    \item{limit}{integer that gives an upperbound on the number of subintervals in the partition                                
     of (\code{li},\code{ls}), limit.ge.1.}                                                                                            
    \item{lig}{lower limit of integration for the gradient.}                                                                    
    \item{lsg}{upper limit of integration for the gradient.}                                                                    
   }      
 \details{       
 \code{bildIntegrate} returns a list of constants that are used to compute integrals based on a Fortran-77 subroutine \code{dqage} from a   
 Fortran-77 subroutine package \code{QUADPACK} for the numerical computation of definite one-dimensional integrals.              
 The subroutine \code{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 \code{dqage} was modified and re-named  
 \code{dqager}, the change was the introduction of an extra variable that allow, in our Fortran-77 subroutines when              
 have a call to \code{dqager}, to control for which parameter the integral is computed.
 
For given values of \code{li} and \code{ls}, the above-described
numerical integration is performed over the interval 
(\code{li}*\eqn{\sigma}, \code{ls}*\eqn{\sigma}), where \eqn{\sigma=\exp(\omega)/2}
is  associated to the current parameter value \eqn{\omega} examined by
the \code{optim} function.  In some cases, this integration may
generate an error, and the user must suitably adjust the values of \code{li} 
and \code{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 \code{lig} and \code{lsg}.
                         
For datasets where the individual profiles have a high number of 
observed time points (say, more than 30), 
use \code{bildIntegrate} function to set the integration limits for the 
likelihood and for the gradient to small values 
than the default ones, see the example of \code{\link{locust}} data. 
 
If fitting procedure is complete but when computing the information matrix 
some NaNs are produced, the change in \code{bildIntegrate} function of the default values 
for the gradient integration limits (\code{lig} and \code{lsg}) might solve this problem.
  }    

\value{A list with the arguments as components.}    

\seealso{\code{\link{bild-class}}}

\examples{ \donttest{ 
## It takes a very long time to run

####  data=locust, dependence="MC2R"                                                   
str(locust)                                                                            
                                                                                       
Integ <- bildIntegrate(li=-2.5,ls=2.5, lig=-2.5, lsg=2.5)                              
locust2r_feed1 <- bild(move~(time+I(time^2))*sex, data=locust,              
    trace=TRUE, subSET=feed=="1", aggregate=sex, dependence="MC2R",                    
    integrate=Integ)                                                                   
                                                                                       
summary(locust2r_feed1)                                                                
getAIC(locust2r_feed1)                                                                 
getLogLik(locust2r_feed1)                                                              
plot(locust2r_feed1)                                                                   
}}

\keyword{function}