Modern Test Theory Techniques for Adaptive Testing in Short Scales Comprising Polytomous Items: A Monte Carlo Simulation Study Comparing Rasch Measurement Theory to Unidimensional and Multidimensional Graded Response Models. (Preprint)

Abstract

BACKGROUND There are two philosophical approaches to contemporary psychometrics: Rasch measurement theory (RMT) and item response theory (IRT). Either measurement strategy can be applied to computerized adaptive testing (CAT). There are potential benefits of IRT over RMT with regards to measurement precision, but also potential risks to measurement generalizability. RMT CAT assessments have demonstrated good performance with the CLEFT-Q, a patient-reported outcome measure for use in orofacial clefting. OBJECTIVE To test whether the post-hoc application of IRT (graded response models, GRMs, and multidimensional GRMs) to RMT-validated CLEFT-Q appearance scales could improve CAT accuracy at given assessment lengths. METHODS Partial credit Rasch models, unidimensional GRMs and a multidimensional GRM were calibrated for each of the 7 CLEFT-Q appearance scales (which measure the appearance of the: face, jaw, teeth, nose, nostrils, cleft lip scar and lips) using data from the CLEFT-Q field test. A second, simulated dataset was generated with 1000 plausible response sets to each scale. Rasch and GRM scores were calculated for each simulated response set, scaled to 0-100 scores, and compared by Pearson’s correlation coefficient, root mean square error (RMSE), mean absolute error (MAE) and 95% limits of agreement. For the face, teeth and jaw scales, we repeated this in a an independent, real patient dataset. We then used the simulated data to compare the performance of a range of fixed-length CAT assessments that were generated with partial credit Rasch models, unidimensional GRMs and the multidimensional GRM. Median standard error of measurement (SEM) was recorded for each assessment. CAT scores were scaled to 0-100 and compared to linear assessment Rasch scores with RMSE, MAE and 95% limits of agreement. This was repeated in the independent, real patient dataset with the RMT and unidimensional GRM CAT assessments for the face, teeth and jaw scales to test the generalizability of our simulated data analysis. RESULTS Linear assessment scores generated by Rasch models and unidimensional GRMs showed close agreement, with RMSE ranging from 2.2 to 6.1, and MAE ranging from 1.5 to 4.9 in the simulated dataset. These findings were closely reproduced in the real patient dataset. Unidimensional GRM CAT algorithms achieved lower median SEM than Rasch counterparts, but reproduced linear assessment scores with very similar accuracy (RMSE, MAE and 95% limits of agreement). The multidimensional GRM had poorer accuracy than the unidimensional models at comparable assessment lengths. CONCLUSIONS Partial credit Rasch models and GRMs produce very similar CAT scores. GRM CAT assessments achieve a lower SEM, but this does not translate into better accuracy. Commonly used SEM heuristics for target measurement reliability should not be generalized across CAT assessments built with different psychometric models. In this study, a relatively parsimonious multidimensional GRM CAT algorithm performed more poorly than unidimensional GRM comparators.