Variety selection in Horticulture crops usually involves testing varieties in field trials at multiple locations over a number of years with repeated measurements on each tree or plant. The aim of these trials is to get accurate predictions for variety performance over times and environments and to investigate variety by environment (location and time) interaction. In the analysis of such data there are a number of issues to account for including the spatial and temporal correlation between repeated measurements on plants in the field. There is also the need to adequately model the genetic covariance structure between varieties across sites and harvest times. In this talk we will look at the linear mixed model analysis of yield data from macadamia varieties grown on two rootstocks at multiple sites, measured over multiple years. This four-way multi-harvest, multi-environment variety by rootstock data may be modelled using separable or non-separable models at both the genetic and residual levels. While separable models are desirable for their ease of interpretation and computing advantages, the structure they assume is quite restrictive and may not hold in practice. Alternatives may include the 2DIMVAR1 (De Faveri et al 2017) residual models and four-way genetic models using factor analytic models (Smith et al 2001). We investigate and compare the different approaches.

References:

J De Faveri, A.P Verbyla, B. Cullis, W.Pitchford and R.Thompson (2017) Residual variance-covariance modelling in analysis of multivariate data from variety selection trials. Journal of Agricultural, Biological & Environmental Statistics 22, 1-22

Smith A, Cullis B and Thompson R (2001) Analysing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics 57, 1138-1147