﻿ Convergence (criteria to end iteration) = .5, .01

# Convergence (criteria to end iteration) = .5, .01, 0, 0

This sets the convergence criteria for the iterative joint JMLE (unconditional UCON) maximum likelihood estimation procedure (also the Facets implementation of PMLE). Both criteria (of size and change) must be satisfied for iteration to cease automatically. Select "Finish Iterating" from Files pull-down menu to override automatic operation. You may be able to speed up convergence by using the "Estimation" pull-down menu, and requesting Bigger changes.

The four criteria are:

i) the maximum size of the marginal score-point residual (i.e., difference between observed and expected "total" raw score after omission of extreme scores) for any element. The standard convergence value is 0.5 score points, half the smallest observable difference between raw scores. A value of 0 means this criterion is ignored.

ii) the maximum size of the largest logit change in any estimated measure for an element during the previous iteration (regardless of Umean=) . The standard convergence value is .01 logits, the smallest useful or printable difference. A value of 0 means this criterion is ignored.

iii) the maximum size of the largest marginal score point residual (i.e., difference between observed and expected "total" raw score) for any category. The standard convergence value is 0. A value of 0 means this criterion is ignored.

iv) the maximum size of the largest logit change in any estimated measure for a Rasch-Andrich threshold (step calibration) during the previous. The standard convergence values is 0. A value of 0 means this criterion is ignored.

If a criterion value is not specified, then its value is not changed.

If a criterion value is set to 0, then that criterion is ignored.

Example 1: In some situations, a pass-fail or other "high stakes" decision may hinge upon a difference of hundredths of a logit between a person measure and a criterion measure. For the final, decisive analysis, set the convergence criteria very tightly, e.g.,

Iterations=0 ; unlimited number of iterations

Convergence=.01, .0001 ; exaggerated accuracy: .01 score points and .0001 logits

Be prepared to let your computer run a long time!

Example 2: You want convergence to occur when no marginal score point residual (e.g., difference between any element's observed and expected raw score) is greater than 1.0 score points, and the default logit change is left at its default value:

Convergence = 1.0 ; 1.0 score points and .01 logits (the default). Category defaults are unchanged at 0 and so are ignored.

Example 3: You want to apply the convergence criterion applied in Facets 3.38.

Convergence = 0.5, .01, 0.5, 0 ; category and item residuals apply

Example 4: You want to match the convergence criterion applied in Facets 3.22, the last DOS version.

Convergence = .01, .001 ; run apparently tighter convergence criteria

Example 5: Convergence = 0.1, 0.001, 0.5, 0.01

Element measure: we want John's (and all elements) expected score to be within 0.1 of his observed score, and his measure not to change by more than 0.001 logits each iteration.

Category: we want category 1 (and 2, 3, 4) to have an expected frequency count within 0.5 of its observed frequency count, and the Rasch-Andrich threshold between categories 1 and 2 (also 2 and 3, 3 and 4) not to change by more than 0.01 logits each iteration.

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Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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