Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices

• We propose a parametric bootstrap (PB) test in heteroscedastic two-way MANOVA.
• The PB test is invariant under affine- and permutation-transformations.
• The PB test is independent of the choices of weights used to identify the parameters.

In this article, we propose a parametric bootstrap (PB) test for testing main, simple and interaction effects in heteroscedastic two-way MANOVA models under multivariate normality. The PB test is shown to be invariant under permutation-transformations, and affine-transformations, respectively. Moreover, the PB test is independent of the choice of weights used to define the parameters uniquely. The proposed test is compared with existing Lawley–Hotelling trace (LHT) and approximate Hotelling T2T2 (AHT) tests by the invariance and the intensive simulations. Simulation results indicate that the PB test performs satisfactorily for various cell sizes and parameter configurations when the homogeneity assumption is seriously violated, and tends to outperform the LHT and AHT tests for moderate or larger samples in terms of power and controlling size. In addition, simulation results also indicate that the PB test does not lose too much power when the homogeneity assumption is actually valid or the model assumptions are approximately correct.