In the repeated measures experiment, testing procedures for ordered group effects are proposed using the likelihood ratio principle. The constrained maximum likelihood estimators of ordered group effects are approximated by the isotonic regression of the unconstrained maximum likelihood estimators. Based on these constrained maximum likelihood estimators, test statistics are constructed and are used for detecting ordered group effects. The limiting distributions of the proposed test statistics are shown to be mixtures of chi-squared distributions. A simulation study shows that the proposed tests have improved powers over the usual chi-squared statistic for testing equality of group effects. A real data set is analysed to illustrate the proposed statistics.
- Isotonic regression
- Likelihood ratio statistic
- Maximum likelihood estimation
- Ordered hypothesis
- Repeated measurements