Linear Mixed Model


The linear mixed model is specified in ASReml as a series of model terms and qualifiers. Model terms include factor and variate labels, functions of labels, special terms and interactions of these. The model is specified immediately after the datafile and any job control qualifier and/or tabulate lines.

The syntax for specifying the model is
     response [ !wt weight ] ~ fixed [ !r random ] [ !f sparsefxed ]
  • response is the label for the response variable(s) to be analysed; a list for multivariate analysis.
  • weight is a label of a variable containing weights;
  • ~ separates response from the list of fixed and random terms,
  • fixed represents the list of fixed explanatory terms, is, variates, factors, interactions and special terms for which of variance (ANOVA) type are required.
  • random represents the list of explanatory terms to be fitted as random effects,
  • sparsefxed are additional fixed terms not included in the ANOVA table.
  • GLM qualifiers are also listed after the response

    General rules

    following general rules apply in specifying the linear mixed model
  • all elements in the model must be space separated,
  • the character ~ separates the response variables(s) from the explanatory variables in the model,
  • data fields are identified in the model by their labels
         labels are case sensitive,
         labels may be abbreviated (truncated) when used in the model line but care must be taken that the truncated form is not ambiguous. If the truncated form matches more than one label, the term associated with the first match is assumed,
        model terms may only appear once in the model line; repeated occurrences are ignored,
        model terms other than the original data fields are defined the first time they appear on the model line. They may be abbreviated (truncated) if they are referred to again provided no ambiguity is introduced.
  • if the model is written over several lines, all but the final line must end with a comma to indicate that the list is continued,
  • it is often clearer if labels are not abbreviated. If abbreviations are used then they need to be chosen to avoid confusion.

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