Nonparametric analysis of adolescent deviant behavior

The impact of certain personal characteristics on marijuana use while controlling for routine activities in everyday life is analyzed. The assumptions underlying several logistic regression models, as well as the parametric analysis of covariance (ANCOVA) model, are violated in this example. More critical from the practical point of view is the fact that the covariate is measured on an ordinal (noninterval) scale, implying that the results from such analyses depend on the chosen scale. The analysis of main effects and interactions while accounting for the presence of the covariate using this nonparametric model is compared with similar analyses using the parametric ANCOVA and logistic regression models. The formal analysis is supplemented by new exploratory data analysis plots. Significance tests for certain ordered and other patterned alternatives are proposed and evaluated via simulations. Results are compared with those using logistic regression models treating the levels of the factors as ordinal.