In this article we consider objects for which we have a matrix of dissimilarities and we are interested in their links with covariates. We focus on state sequences for which pairwise dissimilarities are given for instance by edit distances. The methods discussed apply however to any kind of objects and measures of dissimilarities. We start with a generalization of the analysis of variance (ANOVA) to assess the link of complex objects (e.g. sequences) with a given categorical variable. The trick is to show that discrepancy among objects can be derived from the sole pairwise dissimilarities, which permits then to identify factors that most reduce this discrepancy. We present a general statistical test and introduce an original way of rendering the results for state sequences. We then generalize the method to the case with more than one factor and discuss its advantages and limitations especially regarding interpretation. Finally, we introduce a new tree method for analyzing discrepancy of complex objects that exploits the former test as splitting criterion. We demonstrate the scope of the methods presented through a study of the factors that most discriminate Swiss occupational trajectories. All methods presented are freely accessible in our TraMineR package for the R statistical environment.