Newton-Raphson step size = 0

Facets uses Joint Maximum Likelihood Estimation (JMLE) to estimate the Rasch measures from ordinal data. This requires an iterative process. Initial estimates are imputed for all the element measures. The expected observations are computed based on these estimates and totalled for each element. Then for each element, the observed and expected total scores are compared, and the element measure re-estimated to a value intended to make the expected total score the same as the observed total score. This process is repeated until the differences between the observed and the expected total scores are too small to matter. This is called convergence.

Initial estimates are obtained using the PROX (normal approximation) algorithm.

More exact estimates are obtained using iterative curve fitting (when Newton=0) or the Newton-Raphson method. Newton= can be set using the Estimation menu.

Newton=0

specifies iterative curve fitting. The expected scores follow logistic ogives. The improved measure estimates are the locations on the logistic ogives predicted to produce the observed total scores.

Newton=0.1

Newton=0.5

Newton=1

Newton= ...

specifices Newton-Raphson method. The expected scores follow local curves defined by their first and second derivatives. When Newton=1, the improved measure estimates are the locations predicted to produce the observed scores. When Newton=0.5, the improved estimates are halfway between the current estimates at the Newton=1 estimates, and similarly for other values of Newton=.