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I want to fit mixed model using lme4, nlme, baysian regression package or any available. Mixed model in Asreml- R coding conventions before going into specifics, we might want to have details on asreml-R conventions, for those who are unfamiliar with ASREML codes. Y = Xτ + Zu + e..(1); the usual mixed model with, y denotes the n × 1 vector of observations,where τ is the p×1 vector of ﬁxed eﬀects, X is an n×p design matrix of full column rank which associates observations with the appropriate combination of ﬁxed eﬀects, u is the q × 1 vector of random eﬀects, Z is the n × q design matrix which associates observations with the appropriate combination of random eﬀects, and e is the n × 1 vector of residual errors.The model (1) is called a linear mixed model or linear mixed eﬀects model. It is assumed where the matrices G and R are functions of parameters γ and φ, respectively. The parameter θ is a variance parameter which we will refer to as the scale parameter. In mixed eﬀects models with more than one residual variance, arising for example in the analysis of data with more than one section or variate, the parameter θ is ﬁxed to one. In mixed eﬀects models with a single residual variance then θ is equal to the residual variance (σ2).

In this case R must be correlation matrix. Further details on the models are provided in the.

Variance structures for the errors: R structure and Variance structures for the random eﬀects: G structures can be specified. Variance modelling in asreml() it is important to understand the formation of variance structures via direct products.

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The usual least squares assumption (and the default in asreml()) is that these are independently and identically distributed (IID). However, if the data was from a field experiment laid out in a rectangular array of r rows by c columns, say, we could arrange the residuals e as a matrix and potentially consider that they were autocorrelated within rows and columns.Writing the residuals as a vector in field order, that is, by sorting the residuals rows within columns (plots within blocks) the variance of the residuals might then be are correlation matrices for the row model (order r, autocorrelation parameter ½r) and column model (order c, autocorrelation parameter ½c) respectively. More specifically, a two-dimensional separable autoregressive spatial structure (AR1 x AR1) is sometimes assumed for the common errors in a field trial analysis. The example data: nin89 is from asreml-R library, where different varities were grown in replications / blocks in rectangular field. To control additional variability in row or column direction each plot is referenced as Row and Column variables (row column design). Thus this row column design with blocking.