Statistico-genetic considerations in longitudinal data analysis

Abstract

The methodology of longitudinal data analysis (LDA) has been discussed with particular reference to applications in studies on nutrition and animal breeding. It is based on the concept of intra-individual variation first advocated by Sukhatme in nutrition studies. First the process view of nutrition is discussed with an auto-regressive Markov process for analysing data on protein or energy intake. The general theory of linear models with correlated errors is then used, in the context of half-sib mating design used in animal breeding, to develop the structure of covariance matrix. Its elements are in terms of four components of variation and one serial correlation coefficient. The observational components of variance are related to the causal components of variation based on genetic considerations. Intra-individual heritability (h₂^w)in a narrow sense, in contrast to the usual heritability (h²) used in quantitative genetics literature, is introduced that depends on the process variance and the average serial correlation coefficient. As a consequence, a useful test for the existence or otherwise of additive × local environmental interaction effects has become available. A significant process variance with a significant autocorrelation function or its associated variogram indicates a significant h₂^w. The heritability of k repeated measurements is derived and used to develop a new formular for the heritability of the progeny test used in animal breeding. This formula indicates that the LDA leads to increased accuracy in predicting the breeding value of the male on the basis of offspring's performance. The estimation of the parameters of the linear model with correlated errors, particularly the covariances, by restricted maximum likelihood method is also described.