﻿ Inestimable elements or excessive logit ranges

# Inestimable elements or excessive logit ranges

Facets reports elements are inestimable when the data cannot produce an estimate.

1. Inestimable due to all observations being in the same category of a partial-credit item.

Solution: Use Rating Scale=  to anchor the thresholds of the item at reasonable values.

2. A frequently-encountered problem in the analysis of paired-comparison data is an almost Guttman ordering of the pairings. This can lead to unrealistically huge logit ranges for the estimates of the elements or inestimable elements.

To solve this problem, we apply a little Bayesian logic. We know that the range of paired performances is not exceedingly wide, and we can also easily imagine a performance better than any of those being paired, and also a performance worse than any of the those being paired. Let's hypothesize that a reasonable logit distance between those two hypothetical performances is, say, 20 logits.

http://www.rasch.org/rmt/rmt151w.htm is a parallel situation for sports teams.

a.Hypothesize a "best"performance against which every other  performance is worse. Anchor it at 10 logits.

b.Hypothesize a "worst" performance against which every other performance is better. Anchor it at -10 logits

c.Hypothesize a dummy judge who compares the best and worst performances against all the other performances.

d.Include these dummy observations in the analysis.

e.Analyze the actual observations + the dummy observations. The analysis should make sense, and the logit range of the performances will be about 20 logits. For reporting, we don't want the dummy material, so we write an Anchorfile= from this analysis.

f.We then use the Anchorfile as the Facets specification file, commenting out the "best" and "worst" performance elements and the dummy judge. We analyze only the actual observations. All the elements are anchored at their estimates from the actual+dummy analysis. In this anchored analysis, the "displacements" indicate the impact of the dummy data on the estimates.

g.If you perceive that the logit range of 20 logits is too big or too small, please adjust the "best" and "worst" anchored values.

3. Inestimable because elements only have one observation.

Solution: add a dummy person who interacts with the other elements in a central category. Give the data for this person a very small weight. Example:

R0.01, 101, 1-9, 2,2,2,2,2,2,2,2,2 ; dummy observations weighted low to make the data estimable

Those ratings are arbitrary additions to your data to make your data estimable. Your data are too thin for an ordinary analysis. We need at least two observations of each element. Accordingly I added an extra person, 101, who interacted with every item 1-9 in the same category 2 on the 1-5 rating scale. I gave this person a very small weight R0.01 in the analysis. Person 101 ties all the items together, which makes all the items, and so all the persons, estimable. However this additional person is arbitrary. Facets produces estimates, but different arbitrary data would produce different estimates.

If you are sharing your results with a non-technical audience, remove person 101 from the output reports.

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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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