Semi-Parametric Item Response Functions in the Context of Guessing. CRESST Report 844

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally efficient strategy for choosing the order of the polynomial is demonstrated and tested.