We extend the sparse, spatially piecewise-contiguous linear classification framework for mesh-based data to ordinal logistic regression. The algorithm is intended for use with subcortical shape and cortical thickness data where progressive clinical staging is available, as is generally the case in neurodegenerative diseases. We apply the tool to Parkinson’s and Alzheimer’s disease staging. The resulting biomarkers predict Hoehn-Yahr and cognitive impairment stages at competitive accuracy; the models remain parsimonious and outperform one-against-all models in terms of the Akaike and Bayesian information criteria.