Expertise:
Beginner
Introduction
The careful documentation of human growth is essential in order to define
what we call normal growth, so that we can detect as early as possible
when something is going wrong with the growth process. Auxologists,
the scientists that specialize in the study of growth, also need
high quality data to advance our understanding of how the body regulates
its own growth. It may come as a surprise to learn that human growth
at the macro level that we see in our children is not that well
understood.
Growth data over the entire growing period are exceedingly expensive
to collect since children must be brought into the laboratory at
preassigned ages over about a 20-year span. Meeting this observational
regime requires great dedication and persistence by the parents,
and the dropout rate is understandably high, even taking for granted
the long-term commitment of maintaining a growth laboratory. The
Fels Institute in Ohio,
for example, has been collecting growth data since 1929, and is
now measuring the third generation for some of its original cases.
The accurate measurement of height is also difficult, and requires
considerable training. Height diminishes throughout the day as the
spine compresses, but it also depends on other factors. Infants
must be measured lying down, and when the transition is made to
measuring their standing height, measurements shrink by around one
centimeter. The most careful procedures still exhibit standard deviations
over repeated measurements of about three millimeters.
Records of a child's height over 20 years display features, described
below, that are difficult for a data analyst to model. The classic
approach has been to use mathematical functions depending on a limited
number of unknown constants, and auxologists have shown much ingenuity
in developing these parametric models to capture these features.
The best models have eight or more parameters, and are still viewed
as possibly missing some aspects of actual growth.
Nonparametric modeling techniques developed over the last three decades,
such as kernel and spline smoothing methods, have been applied to growth
data. These methods have been successful at detecting new features missed by
parametric models, but they are not guaranteed to produce smoothing curves
that are monotonic, or strictly increasing. Even a small failure of monotonicity
in a height curve can have serious consequences for the corresponding growth
velocity, and even more so for acceleration curves, which are especially important
in identifying processes regulating growth.
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