apportion {glmmrOptim}

Generate exact designs from approximate weights

Description

Given a set of optimal weights for experimental conditions generate exact designs using several rounding methods.

Usage

apportion(w, n)

Arguments

w

A vector of weights.

n

The size of the exact designs to return.

Details

Allocating 'n' items to 'k' groups proportionally to set of weights 'w' is known as the apportionment problem. The problem most famously arose when determining how many members each state should have in the U.S. House of Representatives based on their proportion of the population. The solutions are named after their proposers in the early U.S. Hamilton's method initially allocates 'floor(n*w)' observations to each experimental condition and then allocates the remaining observations based on the largest remainders 'n*w - floor(n*w)'. The other methods (Adams, Jefferson, and Webster) are divisor methods. The vector of counts is 'm', which is either all zeros for Jefferson and Webster and all ones for Adams, and we define 'pi <- n*w' and then iteratively add observations based on the largest values of 'pi/alpha' where 'alpha' is either: * m + 0.5 (Webster) * m + 1 (Jefferson) * m (Adams) Pukelsheim and Rieder, 1996 <doi:10.2307/2337232> discuss efficient rounding of experimental condition weights and determine that a variant of Adam's method is the most efficient. Results using this method are labelled "Pukelsheim" in the output; there may be multiple designs using this procedure. Pukelsheim and Rieder's method assumes there is a minimum of one experimental condition of each type, whereas the other methods do not have this restriction.

Value

A named list. The names correspond to the method of rounding (see Details), and the entries are vectors of integers indicating the count of each type of experimental condition.

Examples

w <- c(0.45,0.03,0.02,0.02,0.03,0.45)
apportion(w,10)