General Linear Model for a Latin Square:
In design of experiment, a Latin square is a threefactor experiment in which for each pair of factors in any combination of factor values occurs only once.
Consider the following Latin Square,

where rows correspond to 4 values of factor I, columns  to 4 values of factor II, and letters to 4 values of factor III.
A general linear model for this experiment is

where Y_{ijk} are observed values of the dependent variable, a_{i}, i=1,4 are effects corresponding to the 4 values of factor I, b_{j}  of factor II, g_{k}  of factor III, e_{ijk} are random variations.
Note: the Latin square is appropriate only if effects of all three factors are additive  that is, all interaction effects are zero.
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