
Auxological
Analysis of Longitudinal Measurements of Human Stature
R. Darrell
Bock, University of Chicago, Stephen H. C. du Toit, University of Pretoria,
& David Thissen, University of North Carolina.
Fast,
comprehensive analysis of data from longitudinal growth studies is now
available on your desktop with the AUXAL program from SSI.
Structural Analysis with the BTT Model or the JPA2 Model
Nonstructural Analysis by Fourier Transform of Residuals
or Kernel Smoothing
The program
performs both structural and nonstructural auxological analysis of human
growth in standing height or recumbent length. It provides accurate fitting or
smoothing of growth curves for height, velocity, and acceleration and displays
the height and velocity curves in publication quality graphic
output.
Maxima and minima
of velocity are located and described. Data from multiple cases can be
analyzed in one pass through the program and the results summarized both
longitudinally and crosssectionally.
Employing Bayesian
methods of estimation, the program is able to fit the structural models to
incomplete longitudinal data. This facility makes it possible to estimate a
structural average curve for the full growth cycle from mixed longitudinal
data consisting of a sample of short studies beginning at random ages. It also
makes possible the prediction of height at maturity, or any other age, from
one or more measures of height prior to maturity.
Special Features
of the AUXAL program
Data
input
 Program
controlled by an easytoprepare ASCII command file
 Data may be
read from fixedcolumn or freecolumn ASCII files
 Freecolumn
fields may be selected from among other fields anywhere in the data
record
 Data for
successive time points can be on separate records or on one long
record
 Observations
may be selected by age or height ranges in each case
 Cases from a
large study may be selected or omitted as specified on a supplied list
Analysis
 Structural
analysis with the BockThissendu Toit (BTT) model or the
JolicoeurPontierAbidi (JPA2) model.
 Nonstructural
analysis by the GasserMüller optimal kernel for smoothing of distance,
velocity, and acceleration, or by Fourier analysis of residuals from either
of the structural models.
 Analytical
description of maxima and minima of the growth velocity curve of each case
and of the structural average curve.
 Maximum a
posteriori (MAP) fitting of the structural models assuming autocorrelated or
uncorrelated residuals. Estimation of the root mean square error after
fitting or smoothing individual case data.
 Estimation of
the generalized distance of each case from the population centroid of the
structural model parameters.
 Casebycase
detail listings including observed heights, empirical velocities, fitted or
smoothed
 Sample problem
input and output.
 Sample
plots.
 Technical
appendix on structural and nonstructural analysis of multiphasic
growth.
Results
 Crosssectional
means, standard deviations, standard errors, skewness and kurtosis for
height and velocity and height and velocity residuals.
 Sample means,
covariances and correlations of the estimated parameters of the structural
models.
 Sample means of
the Fourier coefficients.
 Smoothed
percentiles of the sample distributions of height and velocity.
 Summary of age,
height, and velocity at the velocity maxima and minima of all cases in the
sample.
 Analysis of the
sample structural average curve.
Plots
 The plotting
facility selects, displays and prints individual growth curves for height
and velocity.
 Velocity maxima
and minima identified on the plots.
Documentation
A 170page User's
Guide includes:
 Introduction to
analysis procedures.
 Data
layouts.
 Command
references.




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