DNAtools (version 0.1-8)

optim.relatedness: Estimate theta and the fraction of comparisons between close relatives

Description

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.

Usage

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

## 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)