Beschreibung:
Consider the multiplicative interaction model defined by y<sub>ij</sub> = μ + τ<sub>i</sub> + β<sub>j</sub> + λα<sub>i</sub> γ<sub>j</sub> + ε<sub>ij</sub>, i = 1, 2, ..., t, j = 1, 2, ..., b, where it is assumed that ∑<sub>i</sub> τ<sub>i</sub> = ∑<sub>j</sub> β<sub>j</sub> = ∑<sub>i</sub> α<sub>i</sub> = ∑<sub>j</sub> γ<sub>j</sub> = 0 and ∑<sub>i</sub> α<sup>2</sup><sub>i</sub> = ∑<sub>j</sub> γ<sup>2</sup><sub>j</sub> = 1. It is also assumed that the ε<sub>ij</sub> are distributed NID (0, σ<sup>2</sup>). This article derives the likelihood ratio test of H<sub>0</sub>:Hα = 0 and Gγ = 0 vs. H<sub>a</sub>:Hα ≠ 0 or Gγ ≠ 0, where H is a q × t matrix of row constrasts of rank q and G is a r × b matrix of row constrasts of rank r. An approximation to the critical points of the test statistic is given and tables are given for a few selected values of b, t, q, and r. An improved estimator of σ<sup>2</sup> is derived, and all results are illustrated with an example.