Title: Quadratic Majorization of the Rating Scale Model

Authors: Pieter Schoonees, Patrick Groenen, Kathrin Gruber

Abstract:
We present penalised joint maximum likelihood estimation for the class of
polytomous Rasch (rating scale) models (Andrich, 1978). Thereby, we derive the
estimates of the person, item and answer category parameters jointly within an
iterative majorization procedure. We restrict infinite parameter estimates
with a quadratic penalty on the linear predictors (Hoerl & Kennard, 1970). The
simple form of the updates enables a speedy computation which is guaranteed to
converge monotonically to the global optimum of the likelihood function.
Moreover, missing values and case weights can be handled seamlessly. We
demonstrate the applicability of our method on data from the European Social
Survey.

Andrich, D. (1978). A rating formulation for ordered response categories. 
Psychometrika, 43(4):561-573.

Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation
for nonorthogonal problems. Technometrics, 12(1):55-67.