Longitudinal studies on growth of school children. (Application of principal components analysis)

Abstract

A multivariate statistical method called “principal components analysis” can allow us to combine serveral variables into a small number of other variables which can provide almost all the information of the original variables. Since the process of growth, for example increasing height of a person from childhood to adulthood is practically expressed as a record of heights of the person measured at different times, it is expected that the principal components analysis can be a useful method to grasp the characteristics of the process of growth.Using records of heights of 731 boys and 811 girls from 6 to 17 years of age who were in the third year of senior high school in 1971, correlation coefficients among heights at each age were calculated and the correlation matrix was submitted to a principal components analysis. It was found in both boys and girls that about 95% of the total variance of the twelve variables (heights at each age) was accounted for by three components. Furthermore, from the inspection of eigenvectors corresponding to these three principal components, it was supposed that the first principal component represents the average height from 6 to 17 years old, the second principal component represents a slope of a straight line fitted to a process of growth, and the third principal component represents the curvature of the growth curve or indicates the time of the growth spurt.Because the principal component analysis was found to be useful in delineating the characteristics of the process of growth, this method was used to compare characteristics of growth of heights of children among several prefectures in Japan and between urban and rural districts. The data used were records of growth of height of 3, 018 boys and 3, 016 girls from 6 to 14 years of age who were in the third year of junior high school in 1971. The records of boys were gathered from 21 prefectures and those of girls from 22 prefectures.About 95% of the total variance of the 9 variables (heights at each age) was accounted for by two principal components in boys and by three principal components in girls. It was also recognized that each of the three principal components represents the same aspect of process of growth as in the case of senior high school students. The lack of the meaningful third principal component in boys is probably due to the fact that their growth spurt during puberty is not yet complete at 14 years of age.Mean heights at every age were significantly different among prefectures and between urban and rural districts, and means of scores of the first principal component were also significantly different among prefectures and between urban and rural districts in both boys and girls. The means of scores of the third principal components in girls were also significantly different among prefectures, and between urban and rural districts, indicating that the time of the growth spurt is not necessarily the same in every prefecture and differs between urban and rural districts.In both boys and girls, the means of scores of the second principal component were significantly different among prefectures, but a difference between urban and rural districts was not noticeable.The above findings seem to suggest that factors which affect the average height and time of growth spurt during the growth period are different from factors which affect the slope of a straight line fitted to a process of growth. At least, it must be kept in mind that the so-called causeeffect relation between environmental factors and process of growth of children is by no means simple.