Diagnostic classification models (DCMs) are psychometric models designed to classify examinees according to their proficiency or nonproficiency of specified latent characteristics. These models are well suited for providing diagnostic and actionable feedback to support intermediate and formative assessment efforts. Several DCMs have been developed and applied in different settings. This study examines a DCM with functional form similar to the 1-parameter logistic item response theory model. Using data from a large-scale mathematics education research study, we demonstrate and prove that the proposed DCM has measurement properties akin to the Rasch and one-parameter logistic item response theory models, including sum score sufficiency, item-free and person-free measurement, and invariant item and person ordering. We introduce some potential applications for this model, and discuss the implications and limitations of these developments, as well as directions for future research.