Rasch Analysis of Repeated Measures

Repeated measures are common in rehabilitation studies where patients are scored on assessments at both admission and discharge. There are often intermediate or follow-up data collection periods in addition. The amount of change in patient functional status is an important indicator of rehabilitation quality. In order to determine that it is indeed the patients who have changed and not the item difficulty, constant "anchor" values are needed to fix item difficulties at admission and discharge (or any other time point) within a common frame of reference. Yet creating an anchor file is problematic.

One approach is to create a file of item anchor values by "stacking" the admission and discharge data so that each item corresponds to one column, and each time-point for each person is a row the combined dataset. However this approach may violate the Rasch assumption of local independence in the observations because some characteristics of the patients span time-points . Yet creating item anchor values from either the admission data only, or the discharge data only, and then applying those values to the whole data set may not be reasonable either. Generally, patients are quite disabled at admission to rehabilitation so performance on difficult items of assessment tools are rarely observed or are scored in their lower rating-scale categories. At discharge, patients have often made considerable improvement and most will be scored in the top categories of easier items. At either admission or discharge, some items will be "off-target" compared to patient ability and, for some items (the hardest ones at admission, and the easiest ones at discharge), only one or two categories of the rating scale may be observed.

This suggests a different approach:

1) Create a random sample of patients across the time-points so that each patient is only in the data set once but all time-points are equally represented.

2) Analyze this "random" data set and estimate the item difficulties and Rasch-Andrich thresholds. Save these values in anchor files. They become the definitive set of item difficulties, defining the measurement framework of the latent variable.

3) Apply the anchor files to the estimation of the person abilities at all time points. This can be done either with each time-point in a separate dataset or with all time-points stacked in one dataset. There will be no interaction between the observations of each person at the different person because they are isolated from each other by the item anchor values.

4) With all the data stacked, and a time-point code in each patient record, do an item-by-time-point DIF analysis to verify that nothing unexpected has happened to the items.

The suggested approach was applied to a dataset of 459 older adults measured on a 13-item self-report survey at 5 time points. Time 1 is before treatment; Time 2 is after treatment. Not all adults were observed at all time-points. All 13 items fit the Rasch model. In accordance with (1), a random sample was selected across all 5 time points so that each person was only in the "random" dataset once but all 5 time points were equally represented. Then (2), this random sample was used to create the anchor files. Finally (3), the anchor files were used in the estimation of 327 adults with both Time 1 and Time 2 records. For comparison, an unanchored "stacked" analysis of all 1527 available records for all adults at all time-points was performed. In this last analysis, the estimates for Time 1 and Time 2 would be influenced by local dependency across time-points, if there is any.

The Figures show the relationship between the "stacked" and "anchored" measures of the first 10 persons with both Time 1 and Time 2 records. We can see that in this dataset the influence of local dependency is small, much less than the S.E.s of the measures which are 0.3 logits or more.

In this dataset, dependencies in the data have little effect on person measures. However, using anchor values from a random sample (selected to be without intra-person dependencies) should satisfy manuscript reviewers that a possible source of time-series dependency has been eliminated.

Trudy Mallinson,

University of Southern California

Figure 1. Time 1 - stacked and anchored

Figure 2. Time 2 - stacked and anchored

    See also:
  1. Repeated Measure Designs (Time Series) and Rasch
  2. Rack and Stack: Time 1 vs. Time 2: Repeated Measures

Rasch Analysis of Repeated Measures, Trudy Mallinson ... Rasch Measurement Transactions, 2011, 251:1, 1317

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: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. 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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