Abstract
Items hypothesized to be dependent can be combined into higher orderpolytomous items and the data reanalysed using the PRM. If the reliability estimate from an analysis where items hypothesized to be dependent are combined into higher orderpolytomous items is lower than the reliability estimate from the original analysis, dependence is present. The spread or dispersion parameter provides another way of detecting dependence in a data set. There are ways of estimating the magnitude of response dependence or multidimensionality. One method of testing for multidimensionality is to take two subsets of items, estimate the person parameters based on each of these subsets, and then testing if the estimate for each person from the two subtests is statistically equivalent using a t-test.
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References
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Further Reading
Andrich, D., Sheridan, B. E., & Luo, G. (2018). RUMM2030: Rasch unidimensional models for measurement. Interpreting RUMM2030 Part IV multidimensionality and subtests in RUMM. RUMM Laboratory: Perth, Western Australia.
Smith, E. (2002). Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. Journal of Applied Measurement,3, 205–231.
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Exercises
Exercises
Exercise 2: Basic analysis of dichotomous andpolytomousresponses in Appendix C.
Exercise 6: Analysis of data with dependence in Appendix C.
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Andrich, D., Marais, I. (2019). Violations of the Assumption of Independence II—The Polytomous Rasch Model. In: A Course in Rasch Measurement Theory. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-7496-8_24
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DOI: https://doi.org/10.1007/978-981-13-7496-8_24
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