Objective function to minimize Feeney's zigzag method residual — smooth_age_5_zigzag

This function is auxiliary to smooth_age_5_zigzag_inner(), see ?smooth_age_5_zigzag_inner for a description.

smooth_age_5_zigzag_min(Value, Age, ageMin = 40, ageMax = 80, p)

Arguments

Value	numeric vector of (presumably) counts in 5-year age groups.
Age	integer vector of age group lower bounds.
ageMin	integer. Lower age bound to adjust values.
ageMax	integer. Upper age bound to adjust values.
p	numeric vector of adjustment parameters.

Value

positive residual to minimize.

Details

This function is not intended to be used at the top level, but just in case, make sure that ageMax = ageMin + 10 * length(p). Age groups >= ageMin AND <= ageMin must be in 5-year age groups. This function does no checks.

References

Feeney, G. 2013 "Removing "Zigzag" from Age Data," http://demographer.com/white-papers/2013-removing-zigzag-from-age-data/

Examples

Age <- c(0,1,seq(5,90,by=5))
smooth_age_5_zigzag_min(dth5_zigzag,Age,ageMin=40,ageMax = 80,p=rep(.05,4))
#> [1] 233.0282
# it's used like this in zigzag()
(p <- optim(
    rep(.05,4),
    smooth_age_5_zigzag_min,
    Value = dth5_zigzag,
    Age = Age,
    ageMin = 40,
    ageMax = 80)$par)
#> [1] 0.02287705 0.07425311 0.01993714 0.09800848
Smoothed <- smooth_age_5_zigzag_p(dth5_zigzag,Age,40,80,p)
# de facto unit test:
# check result using results frozen in Feeney spreadsheet
# after fixing probable cell range 'error'
p.feeney <- c(0.0235802695087692,0.0724286618207911,
          0.0242327829742267,0.0883411499065237)
ans      <- 106.1147411629
stopifnot(abs(smooth_age_5_zigzag_min(dth5_zigzag, Age, 40,80,p.feeney) - ans) < 1e-6)