Parkinsonism refers to Parkinsons disease (PD) and Atyp-ical parkinsonian syndromes (APS). Speech disorder is a common and early symptom in Parkinsonism which makes speech analysis a very important research area for the purpose of early diagnosis. Most of research have however focused on discrimination between PD and healthy controls. Such research does not take into account the fact that PD and APS syndromes are very similar in early disease stages. The main problem that has to be addressed first is then differential diagnosis: discrimination between PD and APS and within APS. This paper is a continuation of an earlier pioneer work in differential diagnosis where we mostly address the machine learning problem due to the small amount of training data. We show that classical linear and generalized linear models can provide interpretable and robust classifiers in term of accuracy and generalization ability.