Explicit factor constraints

con() function

con(f) and c(f)
apply sum to zero constraints to factor f. It is not appropriate for random factors and fixed factors with missing cells. ASReml assumes you specify the correct number of levels for each factor. The formal effect of the con() function is to form a model term with the highest level formally equal to minus the sum of the preceding terms.

With sum to zero constraints, a missing treatment level will generate a singularity but in the first coefficient rather than in the coefficient corresponding to the missing treatment. In this case, the coefficients will not be readily interpretable. When interacting constrained factors, all cells in the cross-tabulation should have data.

h() function

h(f) requests ASReml to fit the model term for factor f using Helmert constraints.

Neither Sum-to-zero nor Helmert constraints generate interpretable effects if singularities occur. ASReml runs more efficiently if no constraints are applied. Following is an example of helmert and sum-to-zero covariables a factor with 5 levels.

         H1   H2   H3   H4             C1   C2   C3   C4
    F1   -1   -1   -1   -1              1    0    0    0
    F2    1   -1   -1   -1              0    1    0    0
    F3    0    2   -1   -1              0    0    1    0
    F4    0    0    3   -1              0    0    0    1
    F5    0    0    0    4             -1   -1   -1   -1

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