Testing non-additivity in statistical models

In this thesis, testing non-additivity (interaction) in two-way ANOVA tables, and contingency tables are studied. For two-way ANOVA tables, methods designed especially for testing interaction when there is only one observation (no replication) per cell are the focus, whereas log-linear models are considered for contingency tables. Cressie & Read (1984) developed the family of power-divergence measures. The family of minimum power-divergence estimators is obtained by minimizing these measures for unknown parameter. Cressie & Pardo (2000, 2002) also developed unified approach to model selection problem in nested log-linear models with test statistics based on power-divergence measures. However, the weight put on empty cells is the problem with power-divergence measures which affects the performances of minimum power-divergence estimators and power-divergence test statistics. Basu & Basu (1998) developed the family of penalized power-divergence measures as a solution for this problem. In this thesis, simulation study has been performed to compare efficiency and robustness properties of ordinary and penalized minimum power-divergence estimators for log-linear independence model in 2 x 2 contingency tables. The new families of penalized power-divergence test statistics have also been proposed to over come with the problem of weight that power-divergence test statistics put on empty cells. Ordinary power-divergence test statistics developed by Cressie & Pardo (2000, 2002) and proposed penalized power-divergence test statistics have been compared by simulation study in terms of exact size and power properties for testing nested log-linear models in 2 x 2 and 2 x 2 x 2 contingency tables.