Optimal Calibration of Items for Multidimensional Achievement Tests

• Multidimensional achievement tests are recently gaining more importance in educational and psychological measurements. For example, multidimensional diagnostic tests can help students to determine which particular domain of knowledge they need to improve for better performance. To estimate the characteristics of candidate items (calibration) for future multidimensional achievement tests, we use optimal design theory. We generalize a previously developed exchange algorithm for optimal design computation to the multidimensional setting. We also develop an asymptotic theorem saying which item should be calibrated by examinees with extreme abilities. For several examples, we compute the optimal design numerically with the exchange algorithm. We see clear structures in these results and explain them using the asymptotic theorem. Moreover, we investigate the performance of the optimal design in a simulation study. 

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Achievement tests

exchange algorithm

item calibration

multidimensional item response model

optimal restricted design

statistik

Statistics

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