Estimate theta and the fraction of comparisons between close relatives

Estimates the fraction of comparisons between pairs of close relatives while fitting the theta parameter minimising the object function. The function makes use of the R-package 'Rsolnp' which is an implementation of an solver for non-linear minimisation problems with parameter constraints.

optim.relatedness(
  obs,
  theta0 = 0,
  theta1 = 0.03,
  theta.tol = 10^(-7),
  theta.step = NULL,
  max.bisect = 15,
  probs,
  var.list = NULL,
  init.alpha = 10^c(-4, -6, -8, -10),
  init.keep = FALSE,
  objFunction = c("T2", "T1", "C3", "C2", "C1"),
  collapse = FALSE,
  trace = FALSE,
  solnp.ctrl = list(tol = 10^(-9), rho = 10, delta = min(init.alpha) * 0.01, trace =
    FALSE)
)

Arguments

obs	The matrix or vector of observed matches/partial-matches as returned by the dbCompare()-function
theta0	The left value of the interval in which a bisection-like search is performed for theta
theta1	Right value of interval (see theta0)
theta.tol	A stopping criterion for the search. If the search narrows within theta.tol the function terminates
theta.step	Default is NULL. If not a grid search will be performed on seq(from = theta0, to = theta1, by = theta.step)
max.bisect	The maximum number of bisectional iterations perform prior to termination
probs	List of vectors with allele probabilities for each locus
var.list	A named list of components for computing variances, see dbVariance. The names of the elements are the associated theta-values, and each component is a list of (V1,V2,V3) - see dbVariance with n=1
init.alpha	Initial values for alpha, where the order is (First-cousins, Avuncular, Parent-child, Full-siblings). The value for Unrelated is computed as 1-sum(init.alpha)
init.keep	Whether the initial values should be used in successive steps for the current optimum should be used.
objFunction	Which of the five different object functions should be used to compare observed and expected
collapse	Not yet implemented
trace	Should iteration steps and other process indicators be printed
solnp.ctrl	See solnp for details

Value

Returns a list of three components: value, solution and var.list. The first element, value, is a dataframe with the value of the objection function for each of the theta values investigated. Solution is the estimated alpha-vector where the objection function was minimised. Finally, var.list is a names list of components for computing variances. May be reused in later computations for increased speed in some iterations.

Details

Computes the proportion of comparisons between close relatives in a database matching exercise for each theta value under investigation.

References

T Tvedebrink, PS Eriksen, J Curran, HS Mogensen, N Morling. 'Analysis of matches and partial-matches in Danish DNA reference profile database'. Forensic Science International: Genetics, 2011.

Examples

  if (FALSE) {
  ## Simulate some allele frequencies:
  freqs <-  replicate(10, { g = rgamma(n=10,scale=4,shape=3); g/sum(g)},
              simplify=FALSE)
  ## Load the sample database:
  data(dbExample)
  obs <- dbCompare(dbExample,trace=FALSE)$m
  C3 <- optim.relatedness(obs,theta0=0.0,theta1=0.03,probs=freqs,
          objFunction='C3',max.bisect=30,trace=TRUE)
  }