Infusion (version 2.3.0)

constr_crits: Specificying arbitrary constraints on parameters

Description

constr_crits is an argument of init_reftable, add_reftable, infer_SLik_joint, and profile.SLik_j, allowing to specify constraints on parameters, beyond the ones defined by the ranges over each parameter. Depending on the function it controls, this argument will affect the generation of parameter points or the maximization of the summary-likelihood.

It is advised to use the constr_crits when calling init_reftable so that the initial reference table satisfies the constraints. But it is more important to use it when calling infer_SLik_joint, whose return value contains the constr_crits information it was given, allowing subsequent refine calls to take constraints into account.

The constraints are represented as a mathematical expression for a vector of quantities that should all be negative when the constraints are satisfied. For example, to incorporate the constraint t1 < t3 && t2 < t3 between three time parameters t1, t2 and t3 present in the reference table, one can use
constr_crits = quote({ c(t1-t3, t2-t3) }).

For computational efficiency, it may be better to avoid using this feature when the constraints can be represented as box constraints (i.e., independent ranges for each parameter) by some intuitive reparametrization.

Examples

## A toy example
if (Infusion.getOption("example_maxtime")>9) {
  myrnorm <- function(mu,s2,sample.size=40L) {
    s <- rnorm(n=sample.size,mean=mu,sd=sqrt(s2))
    return(c(mean=mean(s),var=var(s)))
  } # simulate means and variances of normal samples of size 'sample.size'
  
  # The constraint (the final plot produced by refine() explains it):
  heart <- quote({ x <- 3*(mu-4.25);  y <- 3*(s2-0.75); x^2+(y-(x^2)^(1/3))^2-1})
  
  set.seed(123)
  Sobs <- myrnorm(mu=4,s2=1) 
  parsp_h <- init_reftable(lower=c(mu=2.8,s2=0.4), upper=c(mu=5.2,s2=2.4),
                           constr_crits=heart)
  simuls_h <- add_reftable(Simulate="myrnorm", parsTable=parsp_h)
  c_densv <- infer_SLik_joint(simuls_h, stat.obs=Sobs, constr_crits = heart)
  c_slik_j <- MSL(c_densv, CIs=FALSE, eval_RMSEs=FALSE) 
  c_slik_j <- refine(c_slik_j, target_LR=10, ntot=3000, eval_RMSEs=FALSE) 
}