Commentary and Review Series 2-93
Comparison of numerical results of repeated measurements of height based on two growth curve models with random-effects and general covariance structures
Otake M, Nakashima E, Fujikoshi Y, Carter RL, Tanaka S, Kubo YJ Jpn Stat Soc 24(1):1-14, 1994
Summary
A numerical comparison of two growth curve models, one with a random-effects covariance structure, and the other a general covariance structure, was made for a complete data set of 455 individuals with measurements of stature conducted annually from ages 10 to 18 years. The components of the variance-covariance matrix of the estimators of regression coefficients for a random-effects covariance structure were larger than those of a general variance-covariance matrix, ranging from 1.1 to 3.0 for the ratios of the elements of diagonal matrices, and 2.4 for an off-diagonal matrix. The ratios of elements of two off-diagonal matrices were about 2.7 and 4.3 if evaluated by an absolute value of these ratios for all elements with opposite signs. While the absolute difference between components in the two cases are small, the test statistics are almost the same except for the test value of the sex difference. The results obtained from the two models show that both are valid for the interpretation of the data set. For the data used here, the general model seems to fit the annually measured data better than the random-effects model for females 10-18 years old at the time of examination (ATE). The fit between observed and expected values is better in the general model for males 16-18 years old ATE, but it is better in the random-effects model for males 10-15 years of age ATE. The Akaike Information Criterion (AIC) value for a complete data set of 455 individuals as a measure of goodness of fit was 20,953.76 for the random-effects covariance structure, while for the general covariance structure it was 19,013.40. The random-effects model permits the use of an incomplete data set for 1264 individuals with four or more measurements, However, the results obtained are almost equal to those of a complete data set.
A numerical comparison of two growth curve models, one with a random-effects covariance structure, and the other a general covariance structure, was made for a complete data set of 455 individuals with measurements of stature conducted annually from ages 10 to 18 years. The components of the variance-covariance matrix of the estimators of regression coefficients for a random-effects covariance structure were larger than those of a general variance-covariance matrix, ranging from 1.1 to 3.0 for the ratios of the elements of diagonal matrices, and 2.4 for an off-diagonal matrix. The ratios of elements of two off-diagonal matrices were about 2.7 and 4.3 if evaluated by an absolute value of these ratios for all elements with opposite signs. While the absolute difference between components in the two cases are small, the test statistics are almost the same except for the test value of the sex difference. The results obtained from the two models show that both are valid for the interpretation of the data set. For the data used here, the general model seems to fit the annually measured data better than the random-effects model for females 10-18 years old at the time of examination (ATE). The fit between observed and expected values is better in the general model for males 16-18 years old ATE, but it is better in the random-effects model for males 10-15 years of age ATE. The Akaike Information Criterion (AIC) value for a complete data set of 455 individuals as a measure of goodness of fit was 20,953.76 for the random-effects covariance structure, while for the general covariance structure it was 19,013.40. The random-effects model permits the use of an incomplete data set for 1264 individuals with four or more measurements, However, the results obtained are almost equal to those of a complete data set.