A survey that must estimate more than one total has no single "size": a unit may be large for one variable and negligible for another. The maximal measure takes, for each unit, the largest of its shares across the auxiliary variables, each share first scaled by how much sample that variable is to command (Folsom, Potter and Williams, 1987). Selecting proportional to the maximum guarantees every variable at least its intended coverage.
Arguments
- frame
Data frame with one row per unit.
- variables
Names of the auxiliary columns, non-negative numeric. Columns that sum to zero carry no information and are ignored.
- n_j
Relative sample size each variable is to command: a positive vector with one entry per variable, or
NULLfor equal shares.eqcv_allocation()searches for the factors that equalise the anticipated coefficients of variation.
Value
A numeric vector of sizes, one per row of frame. Units whose
every share is zero receive the smallest positive measure, so the
frame keeps full coverage.
References
Folsom, R. E., Potter, F. J. and Williams, S. R. (1987). Notes on a composite size measure for self-weighting samples in multiple domains. Proceedings of the American Statistical Association, Section on Survey Research Methods, 792–796.
Examples
frame <- data.frame(pupils = c(120, 45, 300, 80), staff = c(10, 20, 12, 8))
mpps_size(frame, c("pupils", "staff"))
#> [1] 0.2201835 0.4000000 0.5504587 0.1600000