dev/SpragueSplit.R
In timriffe/DemoTools: Standardize, Evaluate, and Adjust Demographic Data
########################################################################
## Interpolation of five year age groups into single year age groups by
## Sprague's fifth-difference osculatory formula
## (Siegel and Swanson, 2004, p. 727)
## R implementation by Thomas Buettner (21 Oct. 2015)
## expanded by Patrick Gerland (18 feb. 2016):
## - added monotonic decline for age 90+ (and to avoid negative values at upper ages)
## - added cohort interpolation between pivotal years ending in 0 and 5
## - implemented exponential growth rate cohort interpolation instead of linear growth (WPP default)
## - enforced consistency between annually interpolated total using Beers
## and interpolated pop1x1 for intermediate years between pivotal years (use only age distribution)
########################################################################
## used for pchip interpolation
if(!require(signal)){
install.packages("signal")
library(signal)
}
# save working directory
wd <- getwd()
# set working directory:
setwd("C:/Users/Patrick/Dropbox/R/interpolation/wpp/")
ifn <- "/home/tim/git/DemoTools/dev/Data/IND_Pop2015B1_1.7.csv"
# read data to be interpolated
# input data are expected to have age as rows, and countries as columns.
# The first column has the row labels (=age), the first row holds column labels (countrIDs, year...)
# it is assumed that input data have a last, open-ended age group which must not be interpolated.
#
# file name convention is shown below.
# In the example, the original inpout file is named WPP2012Pop5.csv, or *5.csv
# The script produces two outputs:
# *1.csv -> Interpolated data tabulated like to the input data (over time and by age)
# *1c.csv -> Interpolated data tabulated like to the input data (over time and by age, and then by cohort)
# input
#fn <- "IND_Pop2015B" # annually interpolated using Beers in column
#ifn <- paste(fn, "1_1.7.csv", sep = "")
#
## output
#ofn <- paste(fn, "1x1_1.7.csv", sep = "")
#ofncl <- paste(fn, "1x1-cohort-linear-interpol.csv", sep = "") ## cohort interpolated
#ofnc <- paste(fn, "1x1-cohort-exponential-interpol.csv", sep = "") ## cohort interpolated
## read annually interpolated data (transposed by age in rows and time in column)
tp <- t(read.csv(ifn, header = TRUE, row.names = 1, check.names = FALSE))
Age5 <- as.numeric(row.names(tp))
FAGE <- Age5[1]
LAGE <- Age5[length(Age5)]
Age1 <- seq(FAGE, LAGE, by = 1)
# Age1
## interpolation period
YEAR <- as.numeric(substr(colnames(tp),1,5))
FYEAR <- min(YEAR) #1950
LYEAR <- max(YEAR) #2100
LYEAR1 <- LYEAR
## dimensions
NCOL <- dim(tp)[2]
NAG5 <- dim(tp)[1]
# number of single year age groups (closed age groups only)
NAG1 <- NAG5 * 5 - 5
## Sprague's Split
bc <- c(
0.3616, -0.2768, 0.1488, -0.0336, 0.0000,
0.2640, -0.0960, 0.0400, -0.0080, 0.0000,
0.1840, 0.0400, -0.0320, 0.0080, 0.0000,
0.1200, 0.1360, -0.0720, 0.0160, 0.0000,
0.0704, 0.1968, -0.0848, 0.0176, 0.0000,
0.0336, 0.2272, -0.0752, 0.0144, 0.0000,
0.0080, 0.2320, -0.0480, 0.0080, 0.0000,
-0.0080, 0.2160, -0.0080, 0.0000, 0.0000,
-0.0160, 0.1840, 0.0400, -0.0080, 0.0000,
-0.0176, 0.1408, 0.0912, -0.0144, 0.0000,
-0.0128, 0.0848, 0.1504, -0.0240, 0.0016,
-0.0016, 0.0144, 0.2224, -0.0416, 0.0064,
0.0064, -0.0336, 0.2544, -0.0336, 0.0064,
0.0064, -0.0416, 0.2224, 0.0144, -0.0016,
0.0016, -0.0240, 0.1504, 0.0848, -0.0128,
0.0000, -0.0144, 0.0912, 0.1408, -0.0176,
0.0000, -0.0080, 0.0400, 0.1840, -0.0160,
0.0000, 0.0000, -0.0080, 0.2160, -0.0080,
0.0000, 0.0080, -0.0480, 0.2320, 0.0080,
0.0000, 0.0144, -0.0752, 0.2272, 0.0336,
0.0000, 0.0176, -0.0848, 0.1968, 0.0704,
0.0000, 0.0160, -0.0720, 0.1360, 0.1200,
0.0000, 0.0080, -0.0320, 0.0400, 0.1840,
0.0000, -0.0080, 0.0400, -0.0960, 0.2640,
0.0000, -0.0336, 0.1488, -0.2768, 0.3616
)
## standard format for Sprague coefficients
sm <- matrix(bc, 25, 5, byrow = TRUE)
# number of middle panels
MP <- NAG5 - 5
## creating a Spragues coefficient matrix for 5-year age groups
scm <- array(0, dim = c(NAG1 + 1, NAG5))
## insert first two panels
scm[1:10,1:5] <- sm[1:10,]
for (i in (1:MP)) {
# calculate the slices and add middle panels accordingly
scm[((i + 1)*5 + 1):((i + 2)*5), i:(i + 4)] <- sm[11:15,]
}
## insert last two panels
fr <- (NAG5 - 3) * 5 + 1
lr <- (NAG5 - 1) * 5
fc <- MP
lc <- MP + 4
#scm[((NAG5 - 3)*5 + 1):((NAG5-1)*5),MP - 1:(MP-1 + 4)] <- sm[16:25,]
scm[fr:lr,fc:lc] <- sm[16:25,]
# last open ended age group
scm[NAG1 + 1,NAG5] <- 1
options(max.print = 10000000)
pop <- scm %*% as.matrix(tp)
rownames(pop) <- Age1
## write intermediate results for checking
write.csv(pop, paste(fn, "1x1-step1-sprague.csv", sep = ""))
##############################################################################
# add check and treatment for negative values (usually at highest ages) here
# P. Gerland (18 Feb 2016) -- Note: don't know what/how WPP .VB code is doing for this step
# but conceptually this approach is robust and effective in imposing a monotonically
# declining population at upper ages and preventing negative values.
##############################################################################
y <- c(0,cumsum(tp[,1]))
x <- seq(0,105,by=5)
single <- diff(splinefun(y ~ x, method = "monoH.FC")(0:100))
Value <- tp[,1]
splitMono <- function(Value, Age5 = seq(0, length(Value)*5-5, 5), keep.OAG = FALSE){
AgePred <- min(Age5):(max(Age5) + 1)
y <- c(0, cumsum(Value))
x <- c(0, Age5 + 5)
y1 <- splinefun(y ~ x, method = "monoH.FC")(AgePred)
single.out <- diff(y1)
if (keep.OAG){
single.out[length(single.out)] <- Value[length(Value)]
}
single.out
}
colSums(apply(tp,2,splitMono, keep.OAG = TRUE)) - colSums(tp)
singlepchip <- diff(interp1(c(0, Age5+5), c(0, cumsum(tp[,1])), c(0, Age1+1), 'pchip', extrap = TRUE))
plot(single[1:101] - singlepchip)
plot(single[45:55])
lines(singlepchip[45:55])
mean(abs(diff(single[1:101])))
mean(abs(diff(singlepchip[1:101])))
pop.pchip <- NULL
for (j in 1:NCOL){
## interpolate on cumulated distribution
yinterpol <- interp1(c(0, Age5+5), c(0, cumsum(tp[,j])), c(0, Age1+1), 'pchip', extrap = TRUE)
## decumulate
yinterpol <- diff(yinterpol)
pop.pchip <- cbind(pop.pchip, yinterpol)
}
colnames(pop.pchip) <- colnames(pop)
## tail(pop, 12)
## tail(pop.pchip, 12)
## combine Sprague interpolation up to age 90 with pchip interpolation for age 90+
## 90-94
# tp[19,] # Pop 90-94
# pop[(91:95),] # Sprague
# pop.pchip[(91:95),] # pchip
## Pivotal age 90
## impute pchip interpolation as default
pop.combined <- pop.pchip[91,]
## substitute Sprague interpolation if > pchip for better belnding of the two series
pop.combined[pop[91,] > pop.pchip[91,]] <- pop[91,pop[91,] > pop.pchip[91,]]
## combine age 91-94 from pchip
pop.combined <- rbind(pop.combined, pop.pchip[(92:95),])
## sum of rows
pop.combined.sum <- colSums(pop.combined, na.rm = TRUE)
## adjust back on initial pop 5x5 for age 90-94
## proportional distribution
pop.combined[is.na(pop.combined)] <- 0
prop <- prop.table(as.matrix(pop.combined), margin=2)
rownames(prop) <- c(91:95)
df <- as.data.frame(prop)
## vector of initial pop 5x5 for age 90-94
v <- as.vector(tp[19,])
pop.combined <- data.frame(mapply(`*`,df,v))
## append the remaining of the age groups (except last open age)
## 95-99 onward
# tp[(20:(NAG5-1)),] ## pop5
# pop[(96:NAG1),]
# pop.pchip[(96:NAG1),]
colnames(pop.combined) <- colnames(pop.pchip)
pop.combined <- rbind(pop.combined, pop.pchip[(96:NAG1),])
pop.combined <- rbind(pop.combined, pop[(NAG1+1),])
## append Sprague interpolation before age 90
pop.combined <- rbind(pop[(1:90),], pop.combined)
## deal with negative values if applicable (but in principle should not be happening)
pop.combined[pop.combined<0] <- 0
rownames(pop.combined) <- Age1
## write intermediate results for checking
write.csv(pop.combined, paste(fn, "1x1-step2-pchipGE90.csv", sep = ""))
# TR: 26-7-2017
# have not yet implemented from here down. Will take some examination of what's going on here.
## extra step: P. Gerland - cohort interpolation on WPP pivotal years ending in 0 and 5 for age 0-94 in year t to age 5-99 in year t+5
## use exponential growth rate (r=ln(pt2/pt1)/5 with ptn = pt1*(exp(r*n)) ) instead of linear interpolation (WPP default which causes convex hump by age over time at age 80+)
## keep pop1x1 interpolation for intermediate years for cohorts < age 5 in year t+5 not available in year t
## keep pop1x1 interpolation for intermediate years for cohorts age 95+ in year t not available in year t+5
## get pivotal years
index <- seq(from = 1, to = NCOL, by = 5)
n.index <- length(index)
data <- pop.combined[,index]
## get Sprague interpolated pop1x1 for intermediate years (used to impute pop for cohorts that cannot be interpolated)
sprague1 <- pop.combined[,(index+1)[1:(n.index-1)]]
sprague2 <- pop.combined[,(index+2)[1:(n.index-1)]]
sprague3 <- pop.combined[,(index+3)[1:(n.index-1)]]
sprague4 <- pop.combined[,(index+4)[1:(n.index-1)]]
## pop1 in year t
data1 <- data[1:(NAG1-5),]
## head(data1, 10)
## tail(data1, 10)
## pop2 in year t+5
data2 <- data[6:NAG1,]
## head(data2, 10)
## tail(data2, 10)
## growth rate between yeart (t, t+5)
r.linear <- (data2[,2:length(index)] / data1[,1:(length(index)-1)]) / 5
r <- log(data2[,2:length(index)] / data1[,1:(length(index)-1)]) / 5
## head(r)
## cohort interpolated pop in year t+1 to t+4
popt1.linear <- data1[,1:(n.index-1)] + 1 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt2.linear <- data1[,1:(n.index-1)] + 2 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt3.linear <- data1[,1:(n.index-1)] + 3 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt4.linear <- data1[,1:(n.index-1)] + 4 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt1 <- data1[,1:(n.index-1)] * exp(r*1)
popt2 <- data1[,1:(n.index-1)] * exp(r*2)
popt3 <- data1[,1:(n.index-1)] * exp(r*3)
popt4 <- data1[,1:(n.index-1)] * exp(r*4)
## head(popt1)
## combined dataset
## linear
pop1x1.linear <- pop.combined ## initial pop1x1 from Sprague
## t+1 substitute with popt1
pop1x1.linear[2:(NAG1-4), (index+1)[1:(n.index-1)]] <- popt1.linear
## t+2 substitute with popt2
pop1x1.linear[3:(NAG1-3), (index+2)[1:(n.index-1)]] <- popt2.linear
## t+3 substitute with popt3
pop1x1.linear[4:(NAG1-2), (index+3)[1:(n.index-1)]] <- popt3.linear
## t+4 substitute with popt4
pop1x1.linear[5:(NAG1-1), (index+4)[1:(n.index-1)]] <- popt4.linear
## exponential
pop1x1 <- pop.combined ## initial pop1x1 from Sprague
## t+1 substitute with popt1
pop1x1[2:(NAG1-4), (index+1)[1:(n.index-1)]] <- popt1
## t+2 substitute with popt2
pop1x1[3:(NAG1-3), (index+2)[1:(n.index-1)]] <- popt2
## t+3 substitute with popt3
pop1x1[4:(NAG1-2), (index+3)[1:(n.index-1)]] <- popt3
## t+4 substitute with popt4
pop1x1[5:(NAG1-1), (index+4)[1:(n.index-1)]] <- popt4
## check
## round(head(pop1x1, 101)[,(NCOL-6):NCOL],3)
## insure consistency on annual total (interpolated using Beers) by sex for intermediate years
## linear cohort interpolation
## proportional distribution
prop <- prop.table(as.matrix(pop1x1.linear), margin=2)
rownames(prop) <- rownames(pop1x1.linear)
df <- as.data.frame(prop)
## vector of total pop by sex to use to enforce overall consistency by year (annually interpolated Beers total by sex)
total <- apply(tp, 2, sum, na.rm=TRUE)
pop1x1.adjusted <- data.frame(mapply(`*`,df,total))
## combine back with IDs
rownames(pop1x1.adjusted) <- rownames(pop1x1)
colnames(pop1x1.adjusted) <- colnames(pop1x1)
## Round to significant digit
output.wide <- round(pop1x1.adjusted, 3)
## write results
write.csv(pop1x1.adjusted, ofncl)
## write results (Rounded to significant digit)
write.csv(output.wide, ofncl)
## exponential cohort interpolation
## proportional distribution
prop <- prop.table(as.matrix(pop1x1), margin=2)
rownames(prop) <- rownames(pop1x1)
df <- as.data.frame(prop)
## vector of total pop by sex to use to enforce overall consistency by year (annually interpolated Beers total by sex)
total <- apply(tp, 2, sum, na.rm=TRUE)
pop1x1.adjusted <- data.frame(mapply(`*`,df,total))
## combine back with IDs
rownames(pop1x1.adjusted) <- rownames(pop1x1)
colnames(pop1x1.adjusted) <- colnames(pop1x1)
## Round to significant digit
output.wide <- round(pop1x1.adjusted, 3)
## write results
write.csv(pop1x1.adjusted, ofnc)
## write results (Rounded to significant digit)
write.csv(output.wide, ofnc)
colSums(tp) -
colSums(pop)
#head(scm,10) -
#head(scm2,10)
#scm[11, ]
#scm2[10, ]
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########################################################################
## Interpolation of five year age groups into single year age groups by
## Sprague's fifth-difference osculatory formula
## (Siegel and Swanson, 2004, p. 727)
## R implementation by Thomas Buettner (21 Oct. 2015)
## expanded by Patrick Gerland (18 feb. 2016):
## - added monotonic decline for age 90+ (and to avoid negative values at upper ages)
## - added cohort interpolation between pivotal years ending in 0 and 5
## - implemented exponential growth rate cohort interpolation instead of linear growth (WPP default)
## - enforced consistency between annually interpolated total using Beers
## and interpolated pop1x1 for intermediate years between pivotal years (use only age distribution)
########################################################################
## used for pchip interpolation
if(!require(signal)){
install.packages("signal")
library(signal)
}
# save working directory
wd <- getwd()
# set working directory:
setwd("C:/Users/Patrick/Dropbox/R/interpolation/wpp/")
ifn <- "/home/tim/git/DemoTools/dev/Data/IND_Pop2015B1_1.7.csv"
# read data to be interpolated
# input data are expected to have age as rows, and countries as columns.
# The first column has the row labels (=age), the first row holds column labels (countrIDs, year...)
# it is assumed that input data have a last, open-ended age group which must not be interpolated.
#
# file name convention is shown below.
# In the example, the original inpout file is named WPP2012Pop5.csv, or *5.csv
# The script produces two outputs:
# *1.csv -> Interpolated data tabulated like to the input data (over time and by age)
# *1c.csv -> Interpolated data tabulated like to the input data (over time and by age, and then by cohort)
# input
#fn <- "IND_Pop2015B" # annually interpolated using Beers in column
#ifn <- paste(fn, "1_1.7.csv", sep = "")
#
## output
#ofn <- paste(fn, "1x1_1.7.csv", sep = "")
#ofncl <- paste(fn, "1x1-cohort-linear-interpol.csv", sep = "") ## cohort interpolated
#ofnc <- paste(fn, "1x1-cohort-exponential-interpol.csv", sep = "") ## cohort interpolated
## read annually interpolated data (transposed by age in rows and time in column)
tp <- t(read.csv(ifn, header = TRUE, row.names = 1, check.names = FALSE))
Age5 <- as.numeric(row.names(tp))
FAGE <- Age5[1]
LAGE <- Age5[length(Age5)]
Age1 <- seq(FAGE, LAGE, by = 1)
# Age1
## interpolation period
YEAR <- as.numeric(substr(colnames(tp),1,5))
FYEAR <- min(YEAR) #1950
LYEAR <- max(YEAR) #2100
LYEAR1 <- LYEAR
## dimensions
NCOL <- dim(tp)[2]
NAG5 <- dim(tp)[1]
# number of single year age groups (closed age groups only)
NAG1 <- NAG5 * 5 - 5
## Sprague's Split
bc <- c(
0.3616, -0.2768, 0.1488, -0.0336, 0.0000,
0.2640, -0.0960, 0.0400, -0.0080, 0.0000,
0.1840, 0.0400, -0.0320, 0.0080, 0.0000,
0.1200, 0.1360, -0.0720, 0.0160, 0.0000,
0.0704, 0.1968, -0.0848, 0.0176, 0.0000,
0.0336, 0.2272, -0.0752, 0.0144, 0.0000,
0.0080, 0.2320, -0.0480, 0.0080, 0.0000,
-0.0080, 0.2160, -0.0080, 0.0000, 0.0000,
-0.0160, 0.1840, 0.0400, -0.0080, 0.0000,
-0.0176, 0.1408, 0.0912, -0.0144, 0.0000,
-0.0128, 0.0848, 0.1504, -0.0240, 0.0016,
-0.0016, 0.0144, 0.2224, -0.0416, 0.0064,
0.0064, -0.0336, 0.2544, -0.0336, 0.0064,
0.0064, -0.0416, 0.2224, 0.0144, -0.0016,
0.0016, -0.0240, 0.1504, 0.0848, -0.0128,
0.0000, -0.0144, 0.0912, 0.1408, -0.0176,
0.0000, -0.0080, 0.0400, 0.1840, -0.0160,
0.0000, 0.0000, -0.0080, 0.2160, -0.0080,
0.0000, 0.0080, -0.0480, 0.2320, 0.0080,
0.0000, 0.0144, -0.0752, 0.2272, 0.0336,
0.0000, 0.0176, -0.0848, 0.1968, 0.0704,
0.0000, 0.0160, -0.0720, 0.1360, 0.1200,
0.0000, 0.0080, -0.0320, 0.0400, 0.1840,
0.0000, -0.0080, 0.0400, -0.0960, 0.2640,
0.0000, -0.0336, 0.1488, -0.2768, 0.3616
)
## standard format for Sprague coefficients
sm <- matrix(bc, 25, 5, byrow = TRUE)
# number of middle panels
MP <- NAG5 - 5
## creating a Spragues coefficient matrix for 5-year age groups
scm <- array(0, dim = c(NAG1 + 1, NAG5))
## insert first two panels
scm[1:10,1:5] <- sm[1:10,]
for (i in (1:MP)) {
# calculate the slices and add middle panels accordingly
scm[((i + 1)*5 + 1):((i + 2)*5), i:(i + 4)] <- sm[11:15,]
}
## insert last two panels
fr <- (NAG5 - 3) * 5 + 1
lr <- (NAG5 - 1) * 5
fc <- MP
lc <- MP + 4
#scm[((NAG5 - 3)*5 + 1):((NAG5-1)*5),MP - 1:(MP-1 + 4)] <- sm[16:25,]
scm[fr:lr,fc:lc] <- sm[16:25,]
# last open ended age group
scm[NAG1 + 1,NAG5] <- 1
options(max.print = 10000000)
pop <- scm %*% as.matrix(tp)
rownames(pop) <- Age1
## write intermediate results for checking
write.csv(pop, paste(fn, "1x1-step1-sprague.csv", sep = ""))
##############################################################################
# add check and treatment for negative values (usually at highest ages) here
# P. Gerland (18 Feb 2016) -- Note: don't know what/how WPP .VB code is doing for this step
# but conceptually this approach is robust and effective in imposing a monotonically
# declining population at upper ages and preventing negative values.
##############################################################################
y <- c(0,cumsum(tp[,1]))
x <- seq(0,105,by=5)
single <- diff(splinefun(y ~ x, method = "monoH.FC")(0:100))
Value <- tp[,1]
splitMono <- function(Value, Age5 = seq(0, length(Value)*5-5, 5), keep.OAG = FALSE){
AgePred <- min(Age5):(max(Age5) + 1)
y <- c(0, cumsum(Value))
x <- c(0, Age5 + 5)
y1 <- splinefun(y ~ x, method = "monoH.FC")(AgePred)
single.out <- diff(y1)
if (keep.OAG){
single.out[length(single.out)] <- Value[length(Value)]
}
single.out
}
colSums(apply(tp,2,splitMono, keep.OAG = TRUE)) - colSums(tp)
singlepchip <- diff(interp1(c(0, Age5+5), c(0, cumsum(tp[,1])), c(0, Age1+1), 'pchip', extrap = TRUE))
plot(single[1:101] - singlepchip)
plot(single[45:55])
lines(singlepchip[45:55])
mean(abs(diff(single[1:101])))
mean(abs(diff(singlepchip[1:101])))
pop.pchip <- NULL
for (j in 1:NCOL){
## interpolate on cumulated distribution
yinterpol <- interp1(c(0, Age5+5), c(0, cumsum(tp[,j])), c(0, Age1+1), 'pchip', extrap = TRUE)
## decumulate
yinterpol <- diff(yinterpol)
pop.pchip <- cbind(pop.pchip, yinterpol)
}
colnames(pop.pchip) <- colnames(pop)
## tail(pop, 12)
## tail(pop.pchip, 12)
## combine Sprague interpolation up to age 90 with pchip interpolation for age 90+
## 90-94
# tp[19,] # Pop 90-94
# pop[(91:95),] # Sprague
# pop.pchip[(91:95),] # pchip
## Pivotal age 90
## impute pchip interpolation as default
pop.combined <- pop.pchip[91,]
## substitute Sprague interpolation if > pchip for better belnding of the two series
pop.combined[pop[91,] > pop.pchip[91,]] <- pop[91,pop[91,] > pop.pchip[91,]]
## combine age 91-94 from pchip
pop.combined <- rbind(pop.combined, pop.pchip[(92:95),])
## sum of rows
pop.combined.sum <- colSums(pop.combined, na.rm = TRUE)
## adjust back on initial pop 5x5 for age 90-94
## proportional distribution
pop.combined[is.na(pop.combined)] <- 0
prop <- prop.table(as.matrix(pop.combined), margin=2)
rownames(prop) <- c(91:95)
df <- as.data.frame(prop)
## vector of initial pop 5x5 for age 90-94
v <- as.vector(tp[19,])
pop.combined <- data.frame(mapply(`*`,df,v))
## append the remaining of the age groups (except last open age)
## 95-99 onward
# tp[(20:(NAG5-1)),] ## pop5
# pop[(96:NAG1),]
# pop.pchip[(96:NAG1),]
colnames(pop.combined) <- colnames(pop.pchip)
pop.combined <- rbind(pop.combined, pop.pchip[(96:NAG1),])
pop.combined <- rbind(pop.combined, pop[(NAG1+1),])
## append Sprague interpolation before age 90
pop.combined <- rbind(pop[(1:90),], pop.combined)
## deal with negative values if applicable (but in principle should not be happening)
pop.combined[pop.combined<0] <- 0
rownames(pop.combined) <- Age1
## write intermediate results for checking
write.csv(pop.combined, paste(fn, "1x1-step2-pchipGE90.csv", sep = ""))
# TR: 26-7-2017
# have not yet implemented from here down. Will take some examination of what's going on here.
## extra step: P. Gerland - cohort interpolation on WPP pivotal years ending in 0 and 5 for age 0-94 in year t to age 5-99 in year t+5
## use exponential growth rate (r=ln(pt2/pt1)/5 with ptn = pt1*(exp(r*n)) ) instead of linear interpolation (WPP default which causes convex hump by age over time at age 80+)
## keep pop1x1 interpolation for intermediate years for cohorts < age 5 in year t+5 not available in year t
## keep pop1x1 interpolation for intermediate years for cohorts age 95+ in year t not available in year t+5
## get pivotal years
index <- seq(from = 1, to = NCOL, by = 5)
n.index <- length(index)
data <- pop.combined[,index]
## get Sprague interpolated pop1x1 for intermediate years (used to impute pop for cohorts that cannot be interpolated)
sprague1 <- pop.combined[,(index+1)[1:(n.index-1)]]
sprague2 <- pop.combined[,(index+2)[1:(n.index-1)]]
sprague3 <- pop.combined[,(index+3)[1:(n.index-1)]]
sprague4 <- pop.combined[,(index+4)[1:(n.index-1)]]
## pop1 in year t
data1 <- data[1:(NAG1-5),]
## head(data1, 10)
## tail(data1, 10)
## pop2 in year t+5
data2 <- data[6:NAG1,]
## head(data2, 10)
## tail(data2, 10)
## growth rate between yeart (t, t+5)
r.linear <- (data2[,2:length(index)] / data1[,1:(length(index)-1)]) / 5
r <- log(data2[,2:length(index)] / data1[,1:(length(index)-1)]) / 5
## head(r)
## cohort interpolated pop in year t+1 to t+4
popt1.linear <- data1[,1:(n.index-1)] + 1 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt2.linear <- data1[,1:(n.index-1)] + 2 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt3.linear <- data1[,1:(n.index-1)] + 3 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt4.linear <- data1[,1:(n.index-1)] + 4 * (data2[,2:length(index)] - data1[,1:(length(index)-1)]) / 5
popt1 <- data1[,1:(n.index-1)] * exp(r*1)
popt2 <- data1[,1:(n.index-1)] * exp(r*2)
popt3 <- data1[,1:(n.index-1)] * exp(r*3)
popt4 <- data1[,1:(n.index-1)] * exp(r*4)
## head(popt1)
## combined dataset
## linear
pop1x1.linear <- pop.combined ## initial pop1x1 from Sprague
## t+1 substitute with popt1
pop1x1.linear[2:(NAG1-4), (index+1)[1:(n.index-1)]] <- popt1.linear
## t+2 substitute with popt2
pop1x1.linear[3:(NAG1-3), (index+2)[1:(n.index-1)]] <- popt2.linear
## t+3 substitute with popt3
pop1x1.linear[4:(NAG1-2), (index+3)[1:(n.index-1)]] <- popt3.linear
## t+4 substitute with popt4
pop1x1.linear[5:(NAG1-1), (index+4)[1:(n.index-1)]] <- popt4.linear
## exponential
pop1x1 <- pop.combined ## initial pop1x1 from Sprague
## t+1 substitute with popt1
pop1x1[2:(NAG1-4), (index+1)[1:(n.index-1)]] <- popt1
## t+2 substitute with popt2
pop1x1[3:(NAG1-3), (index+2)[1:(n.index-1)]] <- popt2
## t+3 substitute with popt3
pop1x1[4:(NAG1-2), (index+3)[1:(n.index-1)]] <- popt3
## t+4 substitute with popt4
pop1x1[5:(NAG1-1), (index+4)[1:(n.index-1)]] <- popt4
## check
## round(head(pop1x1, 101)[,(NCOL-6):NCOL],3)
## insure consistency on annual total (interpolated using Beers) by sex for intermediate years
## linear cohort interpolation
## proportional distribution
prop <- prop.table(as.matrix(pop1x1.linear), margin=2)
rownames(prop) <- rownames(pop1x1.linear)
df <- as.data.frame(prop)
## vector of total pop by sex to use to enforce overall consistency by year (annually interpolated Beers total by sex)
total <- apply(tp, 2, sum, na.rm=TRUE)
pop1x1.adjusted <- data.frame(mapply(`*`,df,total))
## combine back with IDs
rownames(pop1x1.adjusted) <- rownames(pop1x1)
colnames(pop1x1.adjusted) <- colnames(pop1x1)
## Round to significant digit
output.wide <- round(pop1x1.adjusted, 3)
## write results
write.csv(pop1x1.adjusted, ofncl)
## write results (Rounded to significant digit)
write.csv(output.wide, ofncl)
## exponential cohort interpolation
## proportional distribution
prop <- prop.table(as.matrix(pop1x1), margin=2)
rownames(prop) <- rownames(pop1x1)
df <- as.data.frame(prop)
## vector of total pop by sex to use to enforce overall consistency by year (annually interpolated Beers total by sex)
total <- apply(tp, 2, sum, na.rm=TRUE)
pop1x1.adjusted <- data.frame(mapply(`*`,df,total))
## combine back with IDs
rownames(pop1x1.adjusted) <- rownames(pop1x1)
colnames(pop1x1.adjusted) <- colnames(pop1x1)
## Round to significant digit
output.wide <- round(pop1x1.adjusted, 3)
## write results
write.csv(pop1x1.adjusted, ofnc)
## write results (Rounded to significant digit)
write.csv(output.wide, ofnc)
colSums(tp) -
colSums(pop)
#head(scm,10) -
#head(scm2,10)
#scm[11, ]
#scm2[10, ]
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