Asymptotic variances for the multiplicative interaction model

When modelling two-way analysis of variance interactions by a multiplicative term-Formula] asymptotic variances and covariances are derived for the parameters p, yi and Sj using maximum likelihood theory. The asymptotic framework is defined by a2/K where K is the number of observations per combination of the two factors and a2 the common variance of the eijk values. The results can be applied when K = 1. Two Monte Carlo studies were carried out to check the validity of the formulae for small values of 02/K and to assess their usefulness when replacing the unknown parameters by their estimations. The formulae fit well but the confidence regions produced are too narrow if the interaction term is small. The procedure is illustrated with two examples.