Test for a general trilinear hypothesis in the generalized growth curve model

In this paper, we consider the problem of testing a general trilinear hypothesis in the generalized growth curve model. The general trilinear hypothesis was formulated to test for example the significance of the generalized growth curves or the equality of the trilinear mean between groups in the two dimensions. The null hypothesis considered is of the form $ℬ\times \{L,M,N\}=O$, where $L,M$ and $N$ are known matrices, $ℬ$ is unknown parameter tensor and $O$ is a tensor of zeros. The estimators of the parameters were obtained using a flip-flop algorithm under the null and alternative hypotheses. The likelihood ratio test for testing the general trilinear hypothesis was discussed. The proposed test is an extension of the likelihood ratio test for the general linear hypothesis under the growth curve model. A simulation study was performed to evaluate the performance of the proposed test and a real dataset was used for an illustrative example.