Ordinal Scaling for Clinical Scores with Inconsistent Intervals (900 Patients)
Clinical studies often have categories as outcome, like various levels of health or disease. Multinomial regression is suitable for analysis (see Chap. 28). However, if one or two outcome categories in a study are severely underpresented, multinomial regression is flawed, and ordinal regression including specific link functions may provide a better fit for the data.
This paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions.The main result is an exact combinatorial characterization of the nilpotency index of the $\bmod 2$ cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with m-inputs, p-outputs, and McMillan degree n are given. Among other results it is shown that \[2.25 \cdot \max (m,p) + \min (m,p) - 3 \geq n\] is a sufficient condition for generic real pole placement, provided $\min (m,p) \geq 4$.