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# Growth Data Analyses
# -----------------------------------------------------------------------
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#
# Overview of the analyses
#
# These analyses are intended to illustrate the analysis of nonperiod data
# where a spline basis is the logical choice. These analyses complement
# the daily growth data in that sense.
# The growth data have the additional feature of being essentially
# monotonic or, to say the same thing in another way, have an essentially
# positive first derivative or velocity. This requires monotone smoothing.
# Moreover, most of the interpretability of the growth data comes from
# inspecting the acceleration of the height curves, so that great emphasis
# is placed here on getting a good sensible and stable acceleration
# estimate.
# Finally, a large prortion of the variation in the growth curve data is due
# to phase variation, mainly through the variation in the timing of the
# pubertal growth spurt. Registration therefore plays a major role and is
# especially illustrated here.
# Most of the analyses are carried out on the Berkeley growth data, which
# have the advantage of being freely distributable, whereas as more recent
# and larger data bases require special permission from the agencies that
# are responsible for them. Not much is lost, however, since the quality
# of the Berkeley data are quite comparable to those of other datasets.
# The primary analyses are the monotone smoothing of the data. The right
# smoothing level is taken as known, and was determined by other analyses
# in the Matlab language. The monotone smoothing function used here
# requires the use of low-level code in C and C++, but even with that help,
# computation times are substantially longer than in Matlab.
# Following monotone smoothing, the growth data are registered, an
# essential step because of the large variation in the timing of the
# pubertal growth spurt. The pubertal growth spurts are aligned using
# landmark registration, and the land-mark registered curves are then
# registered using continuous registration.
# The final analysis is of a set of data on a single boy where the
# measurements are taken every three days or so, rather than twice a year.
# These data show that growth is rather more complex than the traditional
# data could have revealed.
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# Berkeley Growth Data
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# Last modified 9 March 200
# ------------------------ input the data -----------------------
age <- c( seq(1, 2, 0.25), seq(3, 8, 1), seq(8.5, 18, 0.5))
nage <- length(age)
ncasem <- 39
ncasef <- 54
hgtm <- t(matrix(scan("../data/hgtm.txt",0),ncasem,nage,byrow=T))
hgtf <- t(matrix(scan("../data/hgtf.txt",0),ncasef,nage,byrow=T))
# Save the data
growthdata <- list(hgtm = hgtm, hgtf = hgtf, age = age)
save(growthdata, file = "growthdata")