MESA Note 6: Iterations and Convergence of Estimation

by John M. Linacre
MESA Research Note 6, November 1998

The Rasch model is based on the non-linear logistic function. In general, estimates for measures cannot be obtained directly, but must be obtained through a process of improving estimates until they are good enough ("converged"). The process requires performing the same computations over and over again ("iteration").

The iterative process is shorter when:

1. The distribution of the person, item, judge, etc., measures is close to normal.
2. The range of measures is narrow.
3. The data are "complete".
4. The data fit the Rasch model.
5. The persons and items are on-target.
6. The items are dichotomies.

In one data set with very adverse characteristics, over 600 iterations were required before meaningful estimates were obtained.

In many cases, the estimates are good enough after only a few iterations. A large number of iterations may only be needed for the final, definitive analysis.

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