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SSI Betaware: AUXAL

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 cross-sectionally.

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 easy-to-prepare ASCII command file
    • Data may be read from fixed-column or free-column ASCII files
    • Free-column 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


    • Structural analysis with the Bock-Thissen-du Toit (BTT) model or the Jolicoeur-Pontier-Abidi (JPA2) model.
    • Nonstructural analysis by the Gasser-Müller 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.
    • Case-by-case 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.


    • Cross-sectional 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.


    • The plotting facility selects, displays and prints individual growth curves for height and velocity.
    • Velocity maxima and minima identified on the plots.


A 170-page User's Guide includes:

    • Introduction to analysis procedures.
    • Data layouts.
    • Command references.

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