The diagnosis of autism spectrum disorder (ASD) is a complex, challenging task as it depends on the analysis of interactional behaviors by psychologists rather than the use of biochemical diagnostics. In this paper, we present a modeling approach to ASD diagnosis by analyzing acoustic/prosodic and linguistic features extracted from diagnostic conversations between a psychologist and children who either are typically developing (TD) or have ASD. We compare the contributions of different features across a range of conversation tasks. We focus on finding a minimal set of parameters that characterize conversational behaviors of children with ASD. Because ASD is diagnosed through conversational interaction, in addition to analyzing the behavior of the children, we also investigate whether the psychologist's conversational behaviors vary across diagnostic groups. Our results can facilitate fine-grained analysis of conversation data for children with ASD to support diagnosis and intervention.