A Comparison of Latent Class Analysis and the Mixture Rasch Model Using 8th Grade Mathematics Data in the Fourth International Mathematics and Science Study (TIMSS-2011)

Abstract

This study provides a comparison of the results of latent class analysis (LCA) and mixture Rasch model (MRM) analysis using data from the Trends in International Mathematics and Science Study – 2011 (TIMSS-2011) with a focus on the 8th-grade mathematics section. The research study focuses on the comparison of LCA and MRM to determine if results obtained differ when the assumed psychometric model differs. Also, a log-linear analysis was conducted to understand the interactions between latent classes identified by LCA and MRM. Response data to the three booklets were used to run latent class analysis using Mplus 7.31 (Muthén & Muthén, 2012a) for LCA and WINMIRA (von Davier, 2001a). The findings of this paper do not reveal unequivocally whether a model based on primarily qualitative differences (LCA), that is, different strategies, instructional differences, curriculum etc. or a model including additional factors of quantitative differences within strategies (MRM) should be used with this particular dataset. Both of the tests provided similar results with more or less similar interpretations. Both techniques fit the data similarly, a result found in prior research. Nonetheless, for tests similar to TIMSS exams, item difficulty parameters can be useful for educational researchers giving potential priority to use of MRM.

Keywords

• Latent class analysis
• The Mixture Rasch model
• Psychometrics
• Mathematics
• Validation.

References

1. Akaike, H. (1998). Information theory and an extension of the maximum likelihood principle. Springer Series in Statistics, 199-213. https://doi.org/10.1007/978-1-4612-1694-0_15
2. Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345 370. https://doi.org/10.1007/bf02294361
3. Büsch, D., Hagemann, N., & Bender, N. (2010). The dimensionality of the Edinburgh handedness inventory: An analysis with models of the item response theory. Laterality: Asymmetries of Body, Brain and Cognition, 15(6), 610 628. https://doi.org/10.1080/13576500903081806
4. Clark, S. L. (2010). Mixture modeling with behavioral data (3405665) [Doctoral dissertation]. ProQuest Dissertations and Theses Global.
5. Cressie, N., & Read, T. R. C. (1984a). Multinomial Goodness-Of-Fit Tests. Journal of the Royal Statistical Society: Series B (Methodological), 46(3), 440 464. https://doi.org/10.1111/j.2517-6161.1984.tb01318.x
6. Dallas, A. D., & Willse, J. T. (2013). Survey analysis with mixture Rasch models. Journal of Applied Measurement,15(4), 394 404. https://europepmc.org/article/med/25232672
7. Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.
8. Frick, H., Strobl, C., & Zeileis, A. (2015). Rasch mixture models for DIF detection: A comparison of old and new score specifications. Educational and Psychological Measurement, 75(2), 208-234. https://doi.org/10.1177/0013164414536183

9. McCutcheon, A. L. (1987). Latent class analysis. SAGE.
10. Muthén, L. K., & Muthén, B. O. (2012a). Mplus (Version 7.31) [Computer Software]. Los Angeles, Muthén&Muthén.
11. Muthén, L. K., & Muthén, B. O. (1998). 2014. Mplus User’s Guide, 7th edition. Muthén & Muthén.
12. Nagin, D. (2005). Group-based modeling of development. Harvard University Press.
13. Rasch, G. (1960). Probabilistic models for some intelligence and achievement tests. Danish Institute for Educational Research. https://doi.org/10.4135/9781412961288.n335
14. Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14(3), 271 282. https://doi.org/10.1177/014662169001400305
15. Rutkowski, L., & Rutkowski, D. (2016). A call for a more measured approach to reporting and interpreting PISA results. Educational Researcher, 45(4), 252 257. https://doi.org/10.3102/0013189X16649961
16. Sigott, G. (2004). Towards identifying the C-Test construct. Peter Lang.
17. Sternberg, R. J. (1985). Beyond IQ: A triarchic theory of human intelligence. CUP Archive.
18. Vermunt, J. K., & Magidson, J. (2004). Latent class analysis. The Sage Encyclopedia of Social Sciences Research Methods, 2, 549 553. Methods. https://doi.org/10.4135/9781412950589.n472
19. von Davier, M. (2001). WINMIRA [Computer software]. Institut für die Pädagogik der Naturwissenschaften
20. von Davier, M. (2001b). WINMIRA user manual [Computer software manual]. Institut für die Pädagogik der Naturwissenschaften
21. Wang, J., & Wang, X. (2019). Structural equation modeling: Applications using Mplus. John Wiley & Sons.