match.bb: Branch and Bound algorithm implementation for performing...
In hamlet: Hierarchical Optimal Matching and Machine Learning Toolbox

Description Usage Arguments Details Value Note Author(s) See Also Examples

This function performs multigroup non-bipartite matching of observations based on a provided distance/dissimilarity matrix 'd'. The number of elements in each submatch is defined by the parameter 'g'.

1 2	match.bb(d, g = 2, presort = "complete", progress = 1e+05, bestknown = Inf, maxbranches = Inf, verb = 0)

`d`	A distance matrix with NxN elements
`g`	Number of elements per each submatch, i.e. how many observations are always matched together
`presort`	If hierarchical clustering should be used for an initial guess, hclust method-options are valid options ("complete", "single", "ward", "average")
`progress`	How many branching operations are done before outputting information to the user
`bestknown`	If a best known solution already exists, this can be used to bound branches of the tree before initiation. The default Inf value causes whole search tree to be potential solution space.
`maxbranches`	Maximum number of branching operations before returning current best solution, by default no cutoff is defined.
`verb`	Level of verbosity

See further details in the reference Laajala et al.

The function returns a list of objects, where elements are

`branches`	Number of branching operations during the branch and bound algorithm
`bounds`	Number of bounding operations during the branch and bound algorithm
`ends`	Number of end leaf nodes visited during the branch and bound algorithm
`matrix`	The resulting binary matching matrix where rows and columns sum to g
`solution`	The resulting matching vector where each element indicates the submatch where the observation was placed
`cost`	Final cost value of the target function in the minimization task

Notice that the solution submatch vector in $solution is not the same as the intervention group allocation. Submatches should be randomly allocated to intervention arms using the match.allocate-function.

The package 'nbpMatching' provides a FORTRAN implementation for computation of paired non-bipartite matching case (g=2).

Computation may be heavy if the number of observations is high, or the number of within-submatch pairwise distances to consider is high (increases quadratically as a function of 'g').

Teemu Daniel Laajala <teelaa@utu.fi>

match.allocate match.mat2vec match.vec2mat match.dummy

data(vcapwide)

# Construct an Euclidean distance example distance matrix using 15 observations from the VCaP study
d <- as.matrix(dist(vcapwide[1:15,c("PSAWeek10", "BWWeek10")]))

bb3 <- match.bb(d, g=3)
str(bb3)

mat <- bb3$matrix 
# binary matching matrix
solvec <- bb3$solution 
# matching vector, where each element indicates to which submatch each observation belongs to

mixplot(data.frame(vcapwide[1:15,c("PSAWeek10", "BWWeek10")], 
 submatch=as.factor(paste("Submatch_",solvec, sep=""))), pch=16, col=rainbow(5))