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A comparison of unidimensional and multidimensional rasch models using parameter estimates and fit indices when assumption of unidimensionality is violated

Yang, Seungho
http://rave.ohiolink.edu/etdc/view?acc_num=osu1195695378

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Educational Policy and Leadership.
This study investigated the effect of the violation of the unidimensionality assumption on parameter estimation and data-model fit in the unidimensional and multidimensional Rasch models. Three factors were manipulated: degree of multidimensionality, sample size, and test length. The accuracy of parameter estimation was evaluated by RMSE, Bias, and Pearson correlation. Data-model fit was investigated in terms of Infit and Outfit mean square and its corresponding t statistic, and Type I error rate. The results indicated that test length had the largest influence on person ability parameter estimation while sample size had the largest effect on item difficulty parameter estimation. The degree of multidimensionality showed an interesting pattern of effects on parameter estimation. Specifically, when a test has a moderate or higher degree of multidimensionality, the multidimensional Rasch model yielded more accurate person ability estimates compared to the unidimensional Rasch models, while when a test has a low degree of multidimensionality, the unidimensional models showed robustness to violation of the unidimensionality assumption. However, in item difficulty parameter estimation, the degree of multidimensionality did not affect on the accuracy of the item parameter estimation. The results of data-model fit analysis indicated that sample size had a significant influence on the mean square fit of item difficulty estimates while it did not affect the t statistic fit. Also, test length affected both the mean square and its t statistic fit indices of person ability estimates. In general, Infit mean square and its t statistic indices were more stable than Outfit indices. The unidimensional and multidimensional Rasch models showed little difference in the Type I error rate as multidimensionality increased. However, the Type I error rate of the mean square fit of item parameter estimates tended to decrease with increase in sample size and that of ability parameter estimates decreased with increase in test length. The Type I error rate of the t statistic fit was not affected by sample size and test length.
Ayres D'Costa (Advisor)
Education, Tests and Measurements
Multidimensional Rasch model; unidimensional Rasch model; multidimensionality

Recommended Citations

Citations

  • Yang, S. (2007). A comparison of unidimensional and multidimensional rasch models using parameter estimates and fit indices when assumption of unidimensionality is violated [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1195695378

    APA Style (7th edition)

  • Yang, Seungho. A comparison of unidimensional and multidimensional rasch models using parameter estimates and fit indices when assumption of unidimensionality is violated. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1195695378.

    MLA Style (8th edition)

  • Yang, Seungho. "A comparison of unidimensional and multidimensional rasch models using parameter estimates and fit indices when assumption of unidimensionality is violated." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1195695378

    Chicago Manual of Style (17th edition)

osu1195695378
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© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.