Why model growth data?

Growth can be considered as the process that makes children change in size and shape over time. The dynamics of growth is best understood from the analysis of longitudinal data, i.e. from serial measurements taken at regular intervals on the same subject. Table 8.1 gives an example of longitudinal growth data for height of a boy measured at birth and at each birthday thereafter up to the age of 18 years. Such data usually form the basis to estimate the underlying process of growth, which is supposed to be continuous. Recent analysis of frequent measurements of size (at daily or weekly intervals) with high-precision techniques (such as knemometry where measurement error is about 0.1 mm) has shown that the growth process is, at microlevel, not as smooth as we usually assume (Hermanussen, 1998; Lampl, 1999). However, we may readily assume that the growth process is continuous when we are dealing with measurements taken at yearly intervals, or even 3- to 6-monthly intervals, using classical anthropometric techniques. Various mathematical models have been proposed to estimate such a smooth growth curve on the basis of a set of discrete measurements of growth of the same subject over time (Marubini and Milani, 1986; Hauspie, 1989, 1998; Simondon et al., 1992; Bogin, 1999).

Introduction

A common problem in the analysis of human growth data is to relate biometric variables to genetic and/or environmental or demographic factors. Quite often we refer to techniques such as multiple regression or principal components analysis. Structural equation modelling is a technique that combines the benefits of both approaches. While in principal components analysis all variables score on each factor (component or latent variable), in structural equation modelling, the investigator can decide about the set of variables that will explain a specific latent variable. The investigator also decides on which paths of relationship between observed and latent variables should be investigated by the model and which ones should not. The procedure consists of an explorative phase, essentially based on principal components analysis of the data, allowing identification of the structure of the latent variables or constructs that, at biological level, are best able to explain the various interrelationships. The second phase consists of testing several possible models and gradually coming to an optimal solution that can explain the interrelationships between the explanatory variables and the dependent variables.

From the late 1980s on, structural equations with latent variables, or so-called LISREL models, became very popular in social sciences. There are two reasons for this increased attention. The capability to include latent variables (or concepts) in the models is a major step forward compared to models where only manifest variables (observed measures or items) can be used.

INTRODUCTION

The first longitudinal growth study dates back to 1759 when Count de Montbeillard measured the body length of his son from birth to 18 years (Scammon, 1927; Tanner, 1962). Actually, when studying growth, there are two basically different approaches: longitudinal and crosssectional studies. In longitudinal growth studies, we measure the same children over several years at regular intervals (as was done by de Montbeillard) in order to be able to establish individual growth patterns. In cross-sectional growth studies, we measure children of different ages only once. A plot of the average height obtained at each age (or age group) depicts the average growth pattern in the sample. One should realize that the shape of the curve seen in an average growth pattern is different from the shape of individual growth curves (Hauspie, 1989). The information provided by the longitudinal and cross-sectional approaches is quite different. Both methods have their advantages and limitations. Whether the data concerns individual or average growth patterns, we are dealing with a series of measures of size (height or average height, for example) at particular ages, either precise chronological ages (in case of longitudinal studies) or mid-points of age classes (in case of cross-sectional studies). However, the researcher is quite often interested in determining the underlying continuous process of growth, from which he wants to derive certain characteristics, such as the age at maximum velocity at adolescence, for example.