dev/Beers.R
In timriffe/DemoTools: Standardize, Evaluate, and Adjust Demographic Data
# TODO: make require abridged data if johnson = TRUE
###############################################################################
# Based on BeersMSplit.R, whose header was:
########################################################################
## Interpolation of of event data (five year periods)
## fifth/single years by Beers Modified six-term formula
## (Siegel and Swanson, 2004, p. 729)
## This formula applies some smoothing to the interpolant, which is
## recommended for time series of events with some dynamic
## R implementation by Thomas Buettner (21 Oct. 2015)
########################################################################
#' create the Beers ordinary or modified coefficient matrix
#'
#' @description The resulting coefficient matrix is based on the number of rows in \code{popmat}
#' which must be in 5-year age groups (not abridged). The final row may be an open
#' or closed age group, as indicated by the \code{OAG} argument.
#'
#' @param popmat numeric matrix of age-period population counts in 5-year age groups
#' @param OAG logical (default \code{TRUE}. Is the final age group open?
#' @param method character (default \code{"mod"}. Valid values are \code{"mod"} or \code{"ord"}.
#'
#' @details The \code{popmat} matrix is really just a placeholder in this case. This function is
#' a utility called by the Beers family of functions, where it is most convenient to just pass
#' in the same matrix being used in those calcs to determine the layout of the coefficient matrix.
#'
#' @references
#' \insertRef{beers1945modified}{DemoTools}
#' \insertRef{siegel2004methods}{DemoTools}
#' @export
#' @examples
#' popmat <- structure(c(54170, 44775, 42142, 38464, 34406, 30386, 26933,
#' 23481, 20602, 16489, 14248, 9928, 8490, 4801, 3599, 2048, 941,
#' 326, 80, 17, 0, 57424, 44475, 41752, 39628, 34757, 30605, 27183,
#' 23792, 20724, 17056, 14059, 10585, 8103, 5306, 3367, 2040, 963,
#' 315, 80, 16, 1, 60272, 44780, 41804, 40229, 35155, 30978, 27456,
#' 24097, 20873, 17546, 13990, 11146, 7841, 5738, 3184, 2062, 961,
#' 311, 80, 15, 1, 62727, 45681, 42101, 40474, 35599, 31439, 27758,
#' 24396, 21055, 17958, 14046, 11589, 7731, 6060, 3086, 2083, 949,
#' 312, 79, 14, 1, 64816, 47137, 42508, 40532, 36083, 31940, 28092,
#' 24693, 21274, 18299, 14223, 11906, 7785, 6255, 3090, 2084, 938,
#' 316, 80, 14, 2),
#' .Dim = c(21L, 5L),
#' .Dimnames = list(seq(0,100,by=5), 1950:1954))
#'
#' coefsOA <- beersExpand(popmat, OAG = TRUE, method = "mod")
#' coefsclosed <- beersExpand(popmat, OAG = FALSE, method = "mod")
#' dim(beersExpand(popmat, TRUE))
#' dim(beersExpand(popmat, FALSE))
#' coefso <- beersExpand(popmat, OAG = TRUE, method = "ord")
#'
#' # how to use (under the hood in beers()
#'
beersExpand <- function(popmat, OAG = FALSE, method = "Mod"){
method <- tolower(method)
stopifnot(method %in% c("mod","ord"))
popmat <- as.matrix(popmat)
# figure out ages and years
Age5 <- as.integer(rownames(popmat))
Age1 <- min(Age5):max(Age5)
yrs <- as.integer(colnames(popmat))
# nr 5-year age groups
m <- nrow(popmat)
# nr rows in coef mat.
n <- m * 5 - ifelse(OAG, 4, 0)
# number of middle blocks
MP <- m - ifelse(OAG, 5, 4)
if (method == "mod"){
## Beers Modified Split
g1g2 <- matrix(c(
0.3332, -0.1938, 0.0702, -0.0118, 0.0022 ,
0.2569, -0.0753, 0.0205, -0.0027, 0.0006 ,
0.1903, 0.0216, -0.0146, 0.0032, -0.0005 ,
0.1334, 0.0969, -0.0351, 0.0059, -0.0011 ,
0.0862, 0.1506, -0.0410, 0.0054, -0.0012 ,
0.0486, 0.1831, -0.0329, 0.0021, -0.0009 ,
0.0203, 0.1955, -0.0123, -0.0031, -0.0004 ,
0.0008, 0.1893, 0.0193, -0.0097, 0.0003 ,
-0.0108, 0.1677, 0.0577, -0.0153, 0.0007 ,
-0.0159, 0.1354, 0.0972, -0.0170, 0.0003
), nrow = 10, ncol = 5, byrow = TRUE)
g3 <- matrix(c(
-0.0160, 0.0973, 0.1321, -0.0121, -0.0013 ,
-0.0129, 0.0590, 0.1564, 0.0018, -0.0043 ,
-0.0085, 0.0260, 0.1650, 0.0260, -0.0085 ,
-0.0043, 0.0018, 0.1564, 0.0590, -0.0129 ,
-0.0013, -0.0121, 0.1321, 0.0973, -0.0160
), 5, 5, byrow = TRUE)
g4g5 <- matrix(c(0.0003, -0.0170, 0.0972, 0.1354, -0.0159 ,
0.0007, -0.0153, 0.0577, 0.1677, -0.0108 ,
0.0003, -0.0097, 0.0193, 0.1893, 0.0008 ,
-0.0004, -0.0031, -0.0123, 0.1955, 0.0203 ,
-0.0009, 0.0021, -0.0329, 0.1831, 0.0486 ,
-0.0012, 0.0054, -0.0410, 0.1506, 0.0862 ,
-0.0011, 0.0059, -0.0351, 0.0969, 0.1334 ,
-0.0005, 0.0032, -0.0146, 0.0216, 0.1903 ,
0.0006, -0.0027, 0.0205, -0.0753, 0.2569 ,
0.0022, -0.0118, 0.0702, -0.1938, 0.3332
), nrow = 10, ncol = 5, byrow = TRUE)
}
if (method == "ord"){
## Beers Oscillatory (Johnson spreadsheet)
g1g2 <- matrix(c(
0.3333, -0.1636, -0.021, 0.0796, -0.0283,
0.2595, -0.078, 0.013, 0.01, -0.0045,
0.1924, 0.0064, 0.0184, -0.0256, 0.0084,
0.1329, 0.0844, 0.0054, -0.0356, 0.0129,
0.0819, 0.1508, -0.0158, -0.0284, 0.0115,
0.0404, 0.2, -0.0344, -0.0128, 0.0068,
0.0093, 0.2268, -0.0402, 0.0028, 0.0013,
-0.0108, 0.2272, -0.0248, 0.0112, -0.0028,
-0.0198, 0.1992, 0.0172, 0.0072, -0.0038,
-0.0191, 0.1468, 0.0822, -0.0084, -0.0015
), nrow = 10, ncol = 5, byrow = TRUE)
g3 <- matrix(c(
-0.0117, 0.0804, 0.157, -0.0284, 0.0027,
-0.002, 0.016, 0.22, -0.04, 0.006,
0.005, -0.028, 0.246, -0.028, 0.005,
0.006, -0.04, 0.22, 0.016, -0.002,
0.0027, -0.0284, 0.157, 0.0804, -0.0117
), 5, 5, byrow = TRUE)
g4g5 <- matrix(c(-0.0015, -0.0084, 0.0822, 0.1468, -0.0191,
-0.0038, 0.0072, 0.0172, 0.1992, -0.0198,
-0.0028, 0.0112, -0.0248, 0.2272, -0.0108,
0.0013, 0.0028, -0.0402, 0.2268, 0.0093,
0.0068, -0.0128, -0.0344, 0.2, 0.0404,
0.0115, -0.0284, -0.0158, 0.1508, 0.0819,
0.0129, -0.0356, 0.0054, 0.0844, 0.1329,
0.0084, -0.0256, 0.0184, 0.0064, 0.1924,
-0.0045, 0.01, 0.013, -0.078, 0.2595,
-0.0283, 0.0796, -0.021, -0.1636, 0.3333
), nrow = 10, ncol = 5, byrow = TRUE)
}
## create a Beers coefficient matrix for 5-year age groups
bm <- matrix(0, nrow = n, ncol = m)
## insert upper left block
bm[1:10, 1:5] <- g1g2
# determine positions of middle blocks
rowpos <- matrix(11:((MP * 5) + 10), ncol = 5, byrow = TRUE)
colpos <- row(rowpos) + col(rowpos) - 1
for (i in (1:MP)) {
# calculate the slices and add middle panels accordingly
bm[rowpos[i, ], colpos[i, ]] <- g3
}
## standard format for Beers coefficients
## insert last two panels
fr <- nrow(bm) - ifelse(OAG,10,9)
lr <- fr + 9
fc <- ncol(bm) - ifelse(OAG, 5, 4)
lc <- fc + 4
bm[fr:lr,fc:lc] <- g4g5
if (OAG){
# preserve open ended age group
bm[nrow(bm), ncol(bm)] <- 1
}
bm
}
#' the ordinary modified Beers splitting methods
#'
#' @description This method offers both ordinary and modified Beers splitting,
#' with an optional DAPPS adjustment \code{johnson} for ages under 10.
#'
#' @param popmat a numeric matrix of population counts in 5-year age groups, with integer-labeled
#' margins (age in rows and year in columns).
#' @param OAG logical (default \code{TRUE}. Is the final age group open?
#' @param method character (default \code{"mod"}). Options are presently \code{"mod"} and \code{"ord"}.
#' @param johnson logical (deault \code{FALSE}). Do we want to adjust young ages according to the DAPPS method?
#' @param Age0 numeric. If doing the \code{johnson} adjustment, we need a separate estimate of age 0. Taken from \code{popmat} if missing.
#' @details Ages should refer to lower age bounds.
#' The rows of \code{popmat} must be labelled with ages unless \code{Age} is given separately.
#' There must be at least six 5-year age groups (including the open group, 5 otherwise). One year of data will
#' work as well, as long as it's given as a single-column matrix. If you want the \code{johnson} adjustment of young
#' ages, a separate estimate of \code{Age0} can either be specified directly, or else it is taken from age 0 if \code{popmat}
#' is specified in single or standard abridged ages.
#' @return an age-period matrix od split population counts with the same number of
#' columns as \code{popmat}, and single ages in rows.
#' @references
#' \insertRef{beers1945modified}{DemoTools}
#' \insertRef{shryock1973methods}{DemoTools}
#' \insertRef{siegel2004methods}{DemoTools}
#' \insertRef{stover2008spectrum}{DemoTools}
#' @export
#' @examples
#' p5 <- structure(c(54170, 44775, 42142, 38464, 34406, 30386, 26933,
#' 23481, 20602, 16489, 14248, 9928, 8490, 4801, 3599, 2048, 941,
#' 326, 80, 17, 0, 57424, 44475, 41752, 39628, 34757, 30605, 27183,
#' 23792, 20724, 17056, 14059, 10585, 8103, 5306, 3367, 2040, 963,
#' 315, 80, 16, 1, 60272, 44780, 41804, 40229, 35155, 30978, 27456,
#' 24097, 20873, 17546, 13990, 11146, 7841, 5738, 3184, 2062, 961,
#' 311, 80, 15, 1, 62727, 45681, 42101, 40474, 35599, 31439, 27758,
#' 24396, 21055, 17958, 14046, 11589, 7731, 6060, 3086, 2083, 949,
#' 312, 79, 14, 1, 64816, 47137, 42508, 40532, 36083, 31940, 28092,
#' 24693, 21274, 18299, 14223, 11906, 7785, 6255, 3090, 2084, 938,
#' 316, 80, 14, 2),
#' .Dim = c(21L, 5L),
#' .Dimnames = list(seq(0,100,by=5), 1950:1954))
#' head(p5) # this is the entire matrix
#' p1 <- beersModSimple(p5, OAG = FALSE)
#' head(p1)
#' # note some negatives in high ages
#' tail(p1)
#' colSums(p1) - colSums(p5)
#'
#' # another case, starting with single ages
#' # note beers() groups ages.
#' Value <- c(9544406,7471790,11590109,11881844,11872503,12968350,11993151,10033918,
#' 14312222,8111523,15311047,6861510,13305117,7454575,9015381,10325432,
#' 9055588,5519173,12546779,4784102,13365429,4630254,9595545,4727963,
#' 5195032,15061479,5467392,4011539,8033850,1972327,17396266,1647397,
#' 6539557,2233521,2101024,16768198,3211834,1923169,4472854,
#' 1182245,15874081,1017752,3673865,1247304,1029243,12619050,1499847,
#' 1250321,2862148,723195,12396632,733501,2186678,777379,810700,
#' 7298270,1116032,650402,1465209,411834,9478824,429296,1190060,
#' 446290,362767,4998209,388753,334629,593906,178133,
#' 4560342,179460,481230,159087,155831,1606147,166763,93569,182238,
#' 53567,1715697,127486,150782,52332,48664,456387,46978,34448,
#' 44015,19172,329149,48004,28574,9200,7003,75195,13140,5889,
#' 18915,21221,72373)
#' Age <- 0:100
#' names(Value) <- Age
#' (ord1 <- beers(Value, OAG = TRUE, method = "ord"))
#' (mod1 <- beers(Value, OAG = TRUE, method = "mod"))
#' plot(Age,Value)
#' lines(Age, ord1)
#' lines(Age, mod1)
#' # in the case
#' # this replaces ages 90+, guaranteed no negatives.
#' monoCloseout(Val5, pops = pops)
#' # Note: there are no kludges built into beersModSimple() to handle such cases.
#' # these ought to be handled by wrappers as appropriate.
#'
#' This replicates Johnson_2016_BEERSP.XLS, males
#' M <- c(752124,582662,463534,369976,286946,235867,
#' 199561,172133,151194,131502,113439,95614,
#' 78777,60157,40960,21318,25451)
#' dim(M) <- c(length(M),1)
#' rownames(M) <- seq(0,80,by=5)
#' Age0 <- 184499
#' johnson <- beers(
#' popmat = M,
#' OAG = TRUE,
#' method = "ord",
#' johnson = TRUE,
#' Age0 = Age0)
#' # copied from spreadsheet output, a de facto unit test,
#' output <- c(184499,158163,143895,135416,130151,
#' 126153,122028,117182,111566,105733,
#' 101088,96719,92551)
#' # allow for rounding differences, so maximum absolute
#' # difference of 1
#' stopifnot(max(abs(round(johnson)[1:length(output)] - output)) == 1)
beers <- function(popmat, Age, OAG = FALSE, method = "mod", johnson = FALSE, Age0){
popmat <- as.matrix(popmat)
if (missing(Age)){
Age <- as.integer(rownames(popmat))
}
# this is innocuous if ages are already grouped
pop5 <- apply(popmat, 2, groupAges, Age = Age, N = 5, shiftdown = 0)
# generate coefficient matrix
bm <- beersExpand(pop5, OAG = OAG, method = method)
# redistribute
pop1 <- bm %*% pop5
# can only do the Johnson adjust if ages are single or abridged.
# cuz we need a separate age 0
if (johnson & ((min(Age) == 0 & 1 %in% Age) | !missing(Age0))){
if (missing(Age0)){
Age0 = popmat[1, , drop = FALSE]
}
pop1 <- johnsonAdjust(Age0 = Age0, pop5 = pop5, pop1 = pop1)
}
zero <- min(as.integer(rownames(popmat)))
ages <- zero:(nrow(bm) - 1 + zero)
dimnames(pop1) <- list(ages, colnames(popmat))
pop1
}
#' adjust ages under 10 using a modification of Beers
#' @description Assuming we have an external estimate of age 0, this method
#' refits to the ordinary Beers single age results, remaining constrained to the
#' original 5-year age groups and smoothly blending into ages greater than 10.
#' @param Age0 numeric an estimate of age 0
#' @param pop5 numeric matrix population in 5-year age groups
#' @param pop1 numeric matrix population split using Beers ordinary (or some other) method
#'
#' @return numeric matrix of single age population estimates
#' @details This has not been tested using \code{pop1} as generated from other methods, such as
#' the Beers modified, Sprague, or Grabill methods. Called internally by \code{beers()}.
#' @export
#' @references
#' \insertRef{stover2008spectrum}{DemoTools}
johnsonAdjust <- function(Age0, pop5, pop1){
# coefficient matrix
DAPPSmod <- matrix(c(0.2333, 0.3445, -0.1222, 0.3778, -0.1556,
-0.0875, 0.3847, -0.0236, 0.0389, -0.0111,
-0.1458, 0.2708, 0.1458, -0.4167, 0.1667,
-0.0833, 0.1151, 0.2817, -0.6111, 0.2222,
0.0000, -0.0080, 0.3254, -0.3889, 0.1111,
0.0458, -0.0613, 0.2637, 0.1833, -0.1000,
0.0375, -0.0458, 0.1292, 0.8167, -0.2333), ncol = 5, byrow = TRUE)
# the composite pop thing
py <- rbind(pop1[2, ],
pop5[1, ] - (Age0 + pop1[2, ]),
colSums(pop1[6:9, , drop = FALSE]),
pop1[10:11, , drop = FALSE])
# gives new ages 2-8
pynew <- DAPPSmod %*% py
# recompose output (still constrained)
pop1[1, ] <- Age0 # keep Age0 est
pop1[3:9, ] <- pynew
pop1
}
timriffe/DemoTools documentation built on Jan. 28, 2024, 5:13 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
# TODO: make require abridged data if johnson = TRUE
###############################################################################
# Based on BeersMSplit.R, whose header was:
########################################################################
## Interpolation of of event data (five year periods)
## fifth/single years by Beers Modified six-term formula
## (Siegel and Swanson, 2004, p. 729)
## This formula applies some smoothing to the interpolant, which is
## recommended for time series of events with some dynamic
## R implementation by Thomas Buettner (21 Oct. 2015)
########################################################################
#' create the Beers ordinary or modified coefficient matrix
#'
#' @description The resulting coefficient matrix is based on the number of rows in \code{popmat}
#' which must be in 5-year age groups (not abridged). The final row may be an open
#' or closed age group, as indicated by the \code{OAG} argument.
#'
#' @param popmat numeric matrix of age-period population counts in 5-year age groups
#' @param OAG logical (default \code{TRUE}. Is the final age group open?
#' @param method character (default \code{"mod"}. Valid values are \code{"mod"} or \code{"ord"}.
#'
#' @details The \code{popmat} matrix is really just a placeholder in this case. This function is
#' a utility called by the Beers family of functions, where it is most convenient to just pass
#' in the same matrix being used in those calcs to determine the layout of the coefficient matrix.
#'
#' @references
#' \insertRef{beers1945modified}{DemoTools}
#' \insertRef{siegel2004methods}{DemoTools}
#' @export
#' @examples
#' popmat <- structure(c(54170, 44775, 42142, 38464, 34406, 30386, 26933,
#' 23481, 20602, 16489, 14248, 9928, 8490, 4801, 3599, 2048, 941,
#' 326, 80, 17, 0, 57424, 44475, 41752, 39628, 34757, 30605, 27183,
#' 23792, 20724, 17056, 14059, 10585, 8103, 5306, 3367, 2040, 963,
#' 315, 80, 16, 1, 60272, 44780, 41804, 40229, 35155, 30978, 27456,
#' 24097, 20873, 17546, 13990, 11146, 7841, 5738, 3184, 2062, 961,
#' 311, 80, 15, 1, 62727, 45681, 42101, 40474, 35599, 31439, 27758,
#' 24396, 21055, 17958, 14046, 11589, 7731, 6060, 3086, 2083, 949,
#' 312, 79, 14, 1, 64816, 47137, 42508, 40532, 36083, 31940, 28092,
#' 24693, 21274, 18299, 14223, 11906, 7785, 6255, 3090, 2084, 938,
#' 316, 80, 14, 2),
#' .Dim = c(21L, 5L),
#' .Dimnames = list(seq(0,100,by=5), 1950:1954))
#'
#' coefsOA <- beersExpand(popmat, OAG = TRUE, method = "mod")
#' coefsclosed <- beersExpand(popmat, OAG = FALSE, method = "mod")
#' dim(beersExpand(popmat, TRUE))
#' dim(beersExpand(popmat, FALSE))
#' coefso <- beersExpand(popmat, OAG = TRUE, method = "ord")
#'
#' # how to use (under the hood in beers()
#'
beersExpand <- function(popmat, OAG = FALSE, method = "Mod"){
method <- tolower(method)
stopifnot(method %in% c("mod","ord"))
popmat <- as.matrix(popmat)
# figure out ages and years
Age5 <- as.integer(rownames(popmat))
Age1 <- min(Age5):max(Age5)
yrs <- as.integer(colnames(popmat))
# nr 5-year age groups
m <- nrow(popmat)
# nr rows in coef mat.
n <- m * 5 - ifelse(OAG, 4, 0)
# number of middle blocks
MP <- m - ifelse(OAG, 5, 4)
if (method == "mod"){
## Beers Modified Split
g1g2 <- matrix(c(
0.3332, -0.1938, 0.0702, -0.0118, 0.0022 ,
0.2569, -0.0753, 0.0205, -0.0027, 0.0006 ,
0.1903, 0.0216, -0.0146, 0.0032, -0.0005 ,
0.1334, 0.0969, -0.0351, 0.0059, -0.0011 ,
0.0862, 0.1506, -0.0410, 0.0054, -0.0012 ,
0.0486, 0.1831, -0.0329, 0.0021, -0.0009 ,
0.0203, 0.1955, -0.0123, -0.0031, -0.0004 ,
0.0008, 0.1893, 0.0193, -0.0097, 0.0003 ,
-0.0108, 0.1677, 0.0577, -0.0153, 0.0007 ,
-0.0159, 0.1354, 0.0972, -0.0170, 0.0003
), nrow = 10, ncol = 5, byrow = TRUE)
g3 <- matrix(c(
-0.0160, 0.0973, 0.1321, -0.0121, -0.0013 ,
-0.0129, 0.0590, 0.1564, 0.0018, -0.0043 ,
-0.0085, 0.0260, 0.1650, 0.0260, -0.0085 ,
-0.0043, 0.0018, 0.1564, 0.0590, -0.0129 ,
-0.0013, -0.0121, 0.1321, 0.0973, -0.0160
), 5, 5, byrow = TRUE)
g4g5 <- matrix(c(0.0003, -0.0170, 0.0972, 0.1354, -0.0159 ,
0.0007, -0.0153, 0.0577, 0.1677, -0.0108 ,
0.0003, -0.0097, 0.0193, 0.1893, 0.0008 ,
-0.0004, -0.0031, -0.0123, 0.1955, 0.0203 ,
-0.0009, 0.0021, -0.0329, 0.1831, 0.0486 ,
-0.0012, 0.0054, -0.0410, 0.1506, 0.0862 ,
-0.0011, 0.0059, -0.0351, 0.0969, 0.1334 ,
-0.0005, 0.0032, -0.0146, 0.0216, 0.1903 ,
0.0006, -0.0027, 0.0205, -0.0753, 0.2569 ,
0.0022, -0.0118, 0.0702, -0.1938, 0.3332
), nrow = 10, ncol = 5, byrow = TRUE)
}
if (method == "ord"){
## Beers Oscillatory (Johnson spreadsheet)
g1g2 <- matrix(c(
0.3333, -0.1636, -0.021, 0.0796, -0.0283,
0.2595, -0.078, 0.013, 0.01, -0.0045,
0.1924, 0.0064, 0.0184, -0.0256, 0.0084,
0.1329, 0.0844, 0.0054, -0.0356, 0.0129,
0.0819, 0.1508, -0.0158, -0.0284, 0.0115,
0.0404, 0.2, -0.0344, -0.0128, 0.0068,
0.0093, 0.2268, -0.0402, 0.0028, 0.0013,
-0.0108, 0.2272, -0.0248, 0.0112, -0.0028,
-0.0198, 0.1992, 0.0172, 0.0072, -0.0038,
-0.0191, 0.1468, 0.0822, -0.0084, -0.0015
), nrow = 10, ncol = 5, byrow = TRUE)
g3 <- matrix(c(
-0.0117, 0.0804, 0.157, -0.0284, 0.0027,
-0.002, 0.016, 0.22, -0.04, 0.006,
0.005, -0.028, 0.246, -0.028, 0.005,
0.006, -0.04, 0.22, 0.016, -0.002,
0.0027, -0.0284, 0.157, 0.0804, -0.0117
), 5, 5, byrow = TRUE)
g4g5 <- matrix(c(-0.0015, -0.0084, 0.0822, 0.1468, -0.0191,
-0.0038, 0.0072, 0.0172, 0.1992, -0.0198,
-0.0028, 0.0112, -0.0248, 0.2272, -0.0108,
0.0013, 0.0028, -0.0402, 0.2268, 0.0093,
0.0068, -0.0128, -0.0344, 0.2, 0.0404,
0.0115, -0.0284, -0.0158, 0.1508, 0.0819,
0.0129, -0.0356, 0.0054, 0.0844, 0.1329,
0.0084, -0.0256, 0.0184, 0.0064, 0.1924,
-0.0045, 0.01, 0.013, -0.078, 0.2595,
-0.0283, 0.0796, -0.021, -0.1636, 0.3333
), nrow = 10, ncol = 5, byrow = TRUE)
}
## create a Beers coefficient matrix for 5-year age groups
bm <- matrix(0, nrow = n, ncol = m)
## insert upper left block
bm[1:10, 1:5] <- g1g2
# determine positions of middle blocks
rowpos <- matrix(11:((MP * 5) + 10), ncol = 5, byrow = TRUE)
colpos <- row(rowpos) + col(rowpos) - 1
for (i in (1:MP)) {
# calculate the slices and add middle panels accordingly
bm[rowpos[i, ], colpos[i, ]] <- g3
}
## standard format for Beers coefficients
## insert last two panels
fr <- nrow(bm) - ifelse(OAG,10,9)
lr <- fr + 9
fc <- ncol(bm) - ifelse(OAG, 5, 4)
lc <- fc + 4
bm[fr:lr,fc:lc] <- g4g5
if (OAG){
# preserve open ended age group
bm[nrow(bm), ncol(bm)] <- 1
}
bm
}
#' the ordinary modified Beers splitting methods
#'
#' @description This method offers both ordinary and modified Beers splitting,
#' with an optional DAPPS adjustment \code{johnson} for ages under 10.
#'
#' @param popmat a numeric matrix of population counts in 5-year age groups, with integer-labeled
#' margins (age in rows and year in columns).
#' @param OAG logical (default \code{TRUE}. Is the final age group open?
#' @param method character (default \code{"mod"}). Options are presently \code{"mod"} and \code{"ord"}.
#' @param johnson logical (deault \code{FALSE}). Do we want to adjust young ages according to the DAPPS method?
#' @param Age0 numeric. If doing the \code{johnson} adjustment, we need a separate estimate of age 0. Taken from \code{popmat} if missing.
#' @details Ages should refer to lower age bounds.
#' The rows of \code{popmat} must be labelled with ages unless \code{Age} is given separately.
#' There must be at least six 5-year age groups (including the open group, 5 otherwise). One year of data will
#' work as well, as long as it's given as a single-column matrix. If you want the \code{johnson} adjustment of young
#' ages, a separate estimate of \code{Age0} can either be specified directly, or else it is taken from age 0 if \code{popmat}
#' is specified in single or standard abridged ages.
#' @return an age-period matrix od split population counts with the same number of
#' columns as \code{popmat}, and single ages in rows.
#' @references
#' \insertRef{beers1945modified}{DemoTools}
#' \insertRef{shryock1973methods}{DemoTools}
#' \insertRef{siegel2004methods}{DemoTools}
#' \insertRef{stover2008spectrum}{DemoTools}
#' @export
#' @examples
#' p5 <- structure(c(54170, 44775, 42142, 38464, 34406, 30386, 26933,
#' 23481, 20602, 16489, 14248, 9928, 8490, 4801, 3599, 2048, 941,
#' 326, 80, 17, 0, 57424, 44475, 41752, 39628, 34757, 30605, 27183,
#' 23792, 20724, 17056, 14059, 10585, 8103, 5306, 3367, 2040, 963,
#' 315, 80, 16, 1, 60272, 44780, 41804, 40229, 35155, 30978, 27456,
#' 24097, 20873, 17546, 13990, 11146, 7841, 5738, 3184, 2062, 961,
#' 311, 80, 15, 1, 62727, 45681, 42101, 40474, 35599, 31439, 27758,
#' 24396, 21055, 17958, 14046, 11589, 7731, 6060, 3086, 2083, 949,
#' 312, 79, 14, 1, 64816, 47137, 42508, 40532, 36083, 31940, 28092,
#' 24693, 21274, 18299, 14223, 11906, 7785, 6255, 3090, 2084, 938,
#' 316, 80, 14, 2),
#' .Dim = c(21L, 5L),
#' .Dimnames = list(seq(0,100,by=5), 1950:1954))
#' head(p5) # this is the entire matrix
#' p1 <- beersModSimple(p5, OAG = FALSE)
#' head(p1)
#' # note some negatives in high ages
#' tail(p1)
#' colSums(p1) - colSums(p5)
#'
#' # another case, starting with single ages
#' # note beers() groups ages.
#' Value <- c(9544406,7471790,11590109,11881844,11872503,12968350,11993151,10033918,
#' 14312222,8111523,15311047,6861510,13305117,7454575,9015381,10325432,
#' 9055588,5519173,12546779,4784102,13365429,4630254,9595545,4727963,
#' 5195032,15061479,5467392,4011539,8033850,1972327,17396266,1647397,
#' 6539557,2233521,2101024,16768198,3211834,1923169,4472854,
#' 1182245,15874081,1017752,3673865,1247304,1029243,12619050,1499847,
#' 1250321,2862148,723195,12396632,733501,2186678,777379,810700,
#' 7298270,1116032,650402,1465209,411834,9478824,429296,1190060,
#' 446290,362767,4998209,388753,334629,593906,178133,
#' 4560342,179460,481230,159087,155831,1606147,166763,93569,182238,
#' 53567,1715697,127486,150782,52332,48664,456387,46978,34448,
#' 44015,19172,329149,48004,28574,9200,7003,75195,13140,5889,
#' 18915,21221,72373)
#' Age <- 0:100
#' names(Value) <- Age
#' (ord1 <- beers(Value, OAG = TRUE, method = "ord"))
#' (mod1 <- beers(Value, OAG = TRUE, method = "mod"))
#' plot(Age,Value)
#' lines(Age, ord1)
#' lines(Age, mod1)
#' # in the case
#' # this replaces ages 90+, guaranteed no negatives.
#' monoCloseout(Val5, pops = pops)
#' # Note: there are no kludges built into beersModSimple() to handle such cases.
#' # these ought to be handled by wrappers as appropriate.
#'
#' This replicates Johnson_2016_BEERSP.XLS, males
#' M <- c(752124,582662,463534,369976,286946,235867,
#' 199561,172133,151194,131502,113439,95614,
#' 78777,60157,40960,21318,25451)
#' dim(M) <- c(length(M),1)
#' rownames(M) <- seq(0,80,by=5)
#' Age0 <- 184499
#' johnson <- beers(
#' popmat = M,
#' OAG = TRUE,
#' method = "ord",
#' johnson = TRUE,
#' Age0 = Age0)
#' # copied from spreadsheet output, a de facto unit test,
#' output <- c(184499,158163,143895,135416,130151,
#' 126153,122028,117182,111566,105733,
#' 101088,96719,92551)
#' # allow for rounding differences, so maximum absolute
#' # difference of 1
#' stopifnot(max(abs(round(johnson)[1:length(output)] - output)) == 1)
beers <- function(popmat, Age, OAG = FALSE, method = "mod", johnson = FALSE, Age0){
popmat <- as.matrix(popmat)
if (missing(Age)){
Age <- as.integer(rownames(popmat))
}
# this is innocuous if ages are already grouped
pop5 <- apply(popmat, 2, groupAges, Age = Age, N = 5, shiftdown = 0)
# generate coefficient matrix
bm <- beersExpand(pop5, OAG = OAG, method = method)
# redistribute
pop1 <- bm %*% pop5
# can only do the Johnson adjust if ages are single or abridged.
# cuz we need a separate age 0
if (johnson & ((min(Age) == 0 & 1 %in% Age) | !missing(Age0))){
if (missing(Age0)){
Age0 = popmat[1, , drop = FALSE]
}
pop1 <- johnsonAdjust(Age0 = Age0, pop5 = pop5, pop1 = pop1)
}
zero <- min(as.integer(rownames(popmat)))
ages <- zero:(nrow(bm) - 1 + zero)
dimnames(pop1) <- list(ages, colnames(popmat))
pop1
}
#' adjust ages under 10 using a modification of Beers
#' @description Assuming we have an external estimate of age 0, this method
#' refits to the ordinary Beers single age results, remaining constrained to the
#' original 5-year age groups and smoothly blending into ages greater than 10.
#' @param Age0 numeric an estimate of age 0
#' @param pop5 numeric matrix population in 5-year age groups
#' @param pop1 numeric matrix population split using Beers ordinary (or some other) method
#'
#' @return numeric matrix of single age population estimates
#' @details This has not been tested using \code{pop1} as generated from other methods, such as
#' the Beers modified, Sprague, or Grabill methods. Called internally by \code{beers()}.
#' @export
#' @references
#' \insertRef{stover2008spectrum}{DemoTools}
johnsonAdjust <- function(Age0, pop5, pop1){
# coefficient matrix
DAPPSmod <- matrix(c(0.2333, 0.3445, -0.1222, 0.3778, -0.1556,
-0.0875, 0.3847, -0.0236, 0.0389, -0.0111,
-0.1458, 0.2708, 0.1458, -0.4167, 0.1667,
-0.0833, 0.1151, 0.2817, -0.6111, 0.2222,
0.0000, -0.0080, 0.3254, -0.3889, 0.1111,
0.0458, -0.0613, 0.2637, 0.1833, -0.1000,
0.0375, -0.0458, 0.1292, 0.8167, -0.2333), ncol = 5, byrow = TRUE)
# the composite pop thing
py <- rbind(pop1[2, ],
pop5[1, ] - (Age0 + pop1[2, ]),
colSums(pop1[6:9, , drop = FALSE]),
pop1[10:11, , drop = FALSE])
# gives new ages 2-8
pynew <- DAPPSmod %*% py
# recompose output (still constrained)
pop1[1, ] <- Age0 # keep Age0 est
pop1[3:9, ] <- pynew
pop1
}
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.