| This thesis is concerned with ANOVA-like tests in the context of mixed discrete and continuous data. The proposed likelihood ratio approach is used to obtain so-called multi-sample location hypothesis tests in the mixed-data setting after specifying a general location model for the joint distribution of the mixed discrete and continuous variables. The approach allows the problem to be treated from a multivariate perspective to simultaneously test both the discrete and continuous parameters of the model, thus avoiding the problem of multiple significance testing. Moreover, associations among variables are accounted for, resulting in improved power performance of the test. Unlike existing distance-based alternatives which rely on asymptotic theory, the likelihood ratio test is exact and can be viewed as an extension of the classical multivariate ANOVA to the general mixed-data setting.;The size and power of the exact likelihood ratio tests are studied and compared, through Monte Carlo simulations, against Bonferroni-corrected multiple tests and existing asymptotic tests proposed earlier by Nakanishi (2003, 1996), Morales et al. (1998), and Bar-Hen and Daudin (1998, 1995). Krzanowski's (1980, 1975) advanced breast cancer data and Mardia et al.'s (1979) academic achievement data are presented to illustrate the application of the methodology. |
