Incoherent discourse in schizophrenia has long been recognized as a dominant symptom of the mental disorder (Bleuler, 1911/1950). Recent studies have used modern sentence and word embeddings to compute coherence metrics for spontaneous speech in schizophrenia. While clinical ratings always have a subjective element, computational linguistic methodology allows quantification of speech abnormalities. Clinical and empirical knowledge from psychiatry provide the theoretical and conceptual basis for modelling. Our study is an interdisciplinary attempt at improving coherence models in schizophrenia. Speech samples were obtained from healthy controls and patients with a diagnosis of schizophrenia or schizoaffective disorder and different severity of positive formal thought disorder. Interviews were transcribed and coherence metrics derived from different embeddings. One model found higher coherence metrics for controls than patients. All other models remained non-significant. More detailed analysis of the data motivates different approaches to improving coherence models in schizophrenia, e.g. by assessing referential abnormalities.