The analysis of longitudinal agricultural experiments

(joint work with Prof. C.G.B Demétrio, Depatmento de Ciências Exatas, ESALQ, Universidade de São Paulo, Caixa Postal 9, 13418-900 Piracicaba, SP, Brasil.)

Rowell and Walters (1976) is the classic paper on the analysis of longitudinal agriculturual experiments. The technique recommended in this paper is that low order polynomials be fitted to individual profiles and that the coefficients of the same order be analyzed according to the design of the experiment. Recent work has proposed the modelling of such data using nonlinear mixed-effects models (Lindstrom & Bates, 1990, Davidian & Giltinan, 1995) and nonparametric models (Hoover et al., 1998, Verbyla, 1999). We are particularly interested in the methods of Verbyla et al. (1999) as these allow nonparamteric smoothing of time trends using a linear mixed model formulation. Their methods include the class of random coefficient models, are easily extended to multistratum designs and, for many applications, obviate the need to choose a parametric model for the covariance structure.

In two recent papers Piepho, Büchse and Emrich (2003) and Piepho, Büchse and Richter (2004) describe a method for formulating mixed models for longitudinal experiments.

We have been investigating the applicability of the methods of Verbyla et al. (1999) to the analysis of a range of longitudinal agricultural experiments and comparing the results with traditional methods. Further, we have formulated a general method of deriving mixed models for longitudinal experiments that is based on Brien and Bailey (2006, Section 7) and so is randomization based and applies to two-tiered and multitiered experiments. It is described in Brien and Bailey (2008) that includes the mixed-model analysis of a three-phase, longitudinal experiment incorporating the methoods of Verbyla et al. (1999).

References