Merge small PSUs up to a minimum size

merge_psus() recodes primary sampling unit (PSU) ids so that every PSU holds at least min_size units, merging small PSUs with their neighbours in the current row order. A PSU register for n_alloc() must not hold a PSU smaller than its stratum's take, and merging small enumeration areas before the register is built is the usual remedy.

It is a vector function. Apply it within each stratum, after sorting the frame so that neighbours in row order are neighbours on the ground, and build the register from the merged ids, so the register and the frame agree.

Usage

merge_psus(id, min_size, size = NULL)

Arguments

id

The PSU id of each row. Any atomic type.

min_size

The smallest size a PSU may have, a positive number. Usually the largest take n_per_psu.

size

The size each row contributes, for a frame with one row per PSU or with weighted rows. NULL (default) counts rows.

Value

A vector like id, each row's merged PSU id. A merged PSU takes the id of its first PSU in row order, so its type and class are those of id and every merged PSU traces to one source PSU.

Details

PSUs are taken in order of first appearance. A PSU of at least min_size stays as it is. A run of smaller PSUs between two of them is merged in order, closing a merged PSU as soon as its size reaches min_size, and a remainder below min_size at the end of the run joins the merged PSU before it. A run that is below min_size in total joins the PSU before it, or the one after it when it opens the stratum. A stratum below min_size in total becomes one PSU, which n_alloc() refuses as smaller than its take unless the register flags it as certainty.

Merging is by order only, so neighbours in row order are neighbours on the ground only as far as the sort makes them so. Valliant, Dever and Kreuter (2018, sec. 10.3) form PSUs to a minimum size from contiguous areas.

Called on a whole frame, merge_psus() sees one stratum and can merge PSUs of different strata. Apply it per stratum, with split() or a grouped dplyr::mutate(). A merge that crosses strata gives one id to PSUs of two strata, which n_alloc() refuses as a duplicated psu_id.

References

Valliant, R., Dever, J. A., & Kreuter, F. (2018). Practical Tools for Designing and Weighting Survey Samples (2nd ed.). Springer. Section 10.3.

See also

n_alloc() for the register the merged ids feed.

Examples

listing <- data.frame(
  stratum = rep(c("urban", "rural"), c(7, 6)),
  ea = c(sprintf("U%d", 1:7), sprintf("R%d", 1:6)),
  households = c(120, 6, 4, 95, 110, 3, 80, 70, 8, 60, 5, 2, 90)
)

# One row per enumeration area, already in geographic order
by_stratum <- split(listing, listing$stratum)
listing$psu_id <- unsplit(lapply(by_stratum, function(d) {
  merge_psus(d$ea, min_size = 10, size = d$households)
}), listing$stratum)
listing
#>    stratum ea households psu_id
#> 1    urban U1        120     U1
#> 2    urban U2          6     U2
#> 3    urban U3          4     U2
#> 4    urban U4         95     U4
#> 5    urban U5        110     U5
#> 6    urban U6          3     U5
#> 7    urban U7         80     U7
#> 8    rural R1         70     R1
#> 9    rural R2          8     R1
#> 10   rural R3         60     R3
#> 11   rural R4          5     R3
#> 12   rural R5          2     R3
#> 13   rural R6         90     R6

# The register n_alloc() reads
aggregate(households ~ stratum + psu_id, listing, sum)
#>   stratum psu_id households
#> 1   rural     R1         78
#> 2   rural     R3         67
#> 3   rural     R6         90
#> 4   urban     U1        120
#> 5   urban     U2         10
#> 6   urban     U4         95
#> 7   urban     U5        113
#> 8   urban     U7         80