Convergence problems

"Facets runs and runs, but does not converge! What has gone wrong?"

 

Are the current set of estimates good enough for your purposes? Estimates with extremely high precision are rarely needed, and seldom improve overall fit of the data to a Rasch model. Set Convergence= and Iterations= to reasonable values.

 

If the changes per iteration are very small or are oscillating up and down about equally, then the estimates are as good as they can be. Press Ctrl+F to stop iteration and move on to fit computation. You can also use the Estimation menu to make the changes per iteration smaller, or to change the estimation method.

 

If Facets runs for more than 100 iterations, and the residuals are not converging (approaching zero), then please force Facets to stop iterating by Ctrl+F (or use the Estimation pull-down menu) - then look at the screen and the output file. Investigate elements with large displacements and rating-scale categories with large "Observed - Expected Diagnostic Residuals".

 

There are numerous possibilities. Here are some to check.

 

1)Noncenter=
The analysis may be
i) over-constrained because all facets are centered, anchored or group-anchored,
ii) under-constrained because more than one facet is non-centered.
For most analyses, noncenter= must specify one active facet.
Make sure that facet is specified is not marked X or omitted from the model statement.
Makes sure that the non-centered facet does not include anchor or group-anchor values.
 

2)Null element= (Keepasnull=)
Element 0 in the data is usually a dummy element that means "this facet does not apply to this observation". If element 0 is an active element in your analysis, then please assign a different unused element number as the dummy element number, e.g., Null element = 999

 

3)Your facets are nested.
When one facet is nested within another facet (without anchoring or group-anchoring), Facets makes an arbitrary allocation of statistical information between the facets, this can lead to unstable estimation. For instance, if there is a "student" facet and also a "student gender" (sex) facet, then nesting needs to be resolved by anchoring or group-anchoring either the "student" facet or the "student gender" facet.
 

4)Low category frequencies
Rating (or partial credit) scale categories with very low frequencies (less than 10 observations) are difficult to use as the basis of estimation. Convergence may take a long time.
 

5)Rating (or partial credit) scales with many categories.
Estimating the parameters of long rating (or partial credit) scales (more than 10 categories) is difficult. Adjustments tend to ripple up and down the scale, like a caterpillar moving. Convergence may take a long time.

 

6)Category frequencies are lumpy.
When some categories of a rating scale have high frequencies and other categories have low frequencies, convergence may take a long time.

 

7)Clumps of data or stringy data due to missing data. Disconnected or weakly connected subsets.
Data with disjoint subsets of data, or with only thin connections between the subsets, may not converge, or may converge to non-repeatable values. For instance, your judging design may be very sparse.

 

8)The Maximum Likelihood curve is almost flat.
The data are such that there are a range of estimated measures that match the data equally well. All are equally valid.

 

9)The Maximum Likelihood curve has two peaks very close together.
The data are such that there are two almost equally good sets of estimates that match the data. Facets cannot choose between them.


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Rasch Publications
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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
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