Linear mixed models with two longitudinal factors in the study of sugarcane dry root mass

There are agronomic experiments where measurements of a response variable are carried out over more than one longitudinal factor, for example, at different depths over time. These observations, made systematically in each experimental unit, can be correlated and might have heterogeneous variances at the different levels of the longitudinal factor. It was possible to model this correlation between repeated measures and the heterogeneity of variances by using mixed models. Thus, it was necessary to adapt some covariance structures that are common in experiments with only one longitudinal factor. The objective of this study was to use the class of linear mixed models to study sugarcane root dry mass. The experiment was the randomized complete blocks design and the parcels received four nitrogen doses. Repeated measurements were made over two longitudinal factors, one being qualitative ordinal (depths) and one being quantitative (distances from the planting line). It was possible to select a parsimonious covariancestructure and another one to explain the average behavior of the responses through likelihood ratio tests, Wald tests, and using the AIC and BIC information criteria. The adjustment of the selected model was verified by using residual diagnostics graphs.