Rasch Analysis is Important to Understand and Use for Measurement

• In measurement, our intent is to use numbers (which are really raw scores/ratings) to indicate "more" or "less" of the trait that is presumed to be homogeneous; actually an important part of investigation is to verify that the data reflect that homogeneity.

• Rasch Analysis (RA) is a unique approach of mathematical modeling based upon a latent trait and accomplishes stochastic (probabilistic) conjoint additivity (conjoint means measurement of persons and items on the same scale and additivity is the equal-interval property of the scale ).

• The purposes of RA are to maximize the homogeneity of the trait and to allow greater reduction of redundancy at no sacrifice of measurement information by decreasing items and/or scoring levels to yield a more valid and simple measure. At times this requires extracting from messy data measures that conform to a homogeneous latent variable and/or identifying for removal features of the data (e.g., bad items, mis-categorization) which contradict measure homogeneity.

• RA permits rating of a limited set of attributes that are representative of the underlying trait, limited means that a small set may be sufficient.

• Whether observed or self-reported, the summed rating of the attributes represents how much of the trait has been mastered, since the raw score is the "sufficient statistic" for the Rasch measure.

• The model assumes that the probability of a given person/item interaction (in terms of rating high or low) is only governed by the difficulty of the item and the ability of the person, that are determined by the item locations on the presumed latent variable along with the rating scale structure.

• Raw scores have unknown spacing between them. Rasch builds estimates of true intervals of item difficulty and person ability by creating linear measures.

• In this process, item values are calibrated and person abilities are measured on a shared continuum that accounts for the latent trait. Should an item rating be missing, the model estimates the person's probable rating without imputing the missing data.

• Concurrently, the improbability of a person's passing or failing a particular item is estimated item by item in terms of fit statistics. This is a comparison between what actually happened and what the model predicts should have happened based on the estimated measures.

• INFIT and OUTFIT statistics are the most widely used diagnostic Rasch fit statistics. Comparison is with an estimated value that is near to or far from the expected value. INFIT is more diagnostic when item measures are close to the person measures. OUTFIT is more diagnostic when item measures are far from the person measures. But, for long rating scales, like the FIMTM instrument, this difference tends to disappear.

• The fit statistics indicate where the operator should decide whether to either delete, rescore, or reword an item. Deciding to how to select the number and cut-points of the rating categories is more complex, requiring a combination of fit, reliability and substantive meaning. See www.rasch.org/rmt/rmt101k.htm.

• The Rasch linear measures are originally expressed in log-odd units but may be rescaled to suit conventional scaling, as from 0 to 100 while still retaining conjoint additivity. The model also estimates the scoring error at each level as standard errors of the measure.

• Error is always greater at the upper and lower ends of a scale because the Rasch model is not limited at the extremes, but measures from the middle of the range of values and anticipates infinity in both directions. Measurement is better when the middle values of subjects lie close to the middle values of the measure. In other words, the true score is more uncertain as the limits of the scale are approached. See www.rasch.org/rmt/rmt204f.htm.

• RA transforms ordinal scales into interval measures that may be used in parametric statistical analyses and the measures are characterized with standard errors for even more sophisticated analyses. Patient measures and calibration of individual item values are measured on the same metric and are locally independent, provided that Rasch criteria are met.

• Measures constructed using RA are unidimensional and have predictable hierarchies of item calibrations that span the range of difficulty within a domain of assessment.

• Final measures are built by the operator based upon the best judgments of:

  - spread of item values (evenness of steps)

  - reduced error of measurement (precision)

  - probability and improbability (fit) of item and person values to that expected from the model

  - overall reliability (noise)

  - simplicity, and

  - conformity to the nature of the clinical values that are being measured

• Building measures using RA requires that the data fit the model, not that the model fit the data.

• Rasch modeling facilitates analysis of responsiveness of individual items with respect to their calibrated positions within a measure.

• In summary, Rasch analysis provides an internally valid measure that, when developed from an appropriate sample, is independent of the particular sample to which it is applied, meaning that the findings for the sample extrapolate to its population.

Dr. Carl V. Granger, SUNY at Buffalo

Rasch Analysis is Important to Understand and Use for Measurement. … C. Granger, Rasch Measurement Transactions, 2008, 21:3 p. 1122-3

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