Fitting a Mixture Rasch Model to Visual Sequential Processing Memory Sub-dimension of ASIS: The Role of Covariates
Keywords:
Mixture Rasch Method, Concomitant/Covariate, Latent Class, Visiual Processing MemoryAbstract
Advanced Item Response Theory (IRT) practices serve well in understanding the nature of latent variables which have been subject to research in various disciplines. In the current study, 7-12 aged 2536 children’s responses to 20-item Visual Sequential Processing Memory (VSPM) sub-test of Anadolu-Sak Intelligence Scale (ASIS) were analyzed with Mixture Rasch Method (MRM). In the first phase of the study, concomitant (covariate) variables were not used. In the second phase, age and gender were added to the model, and then the two models were compared in terms of fit indices, the number of latent classes and the distribution of item difficulties in the latent classes. The results of the study suggested that there were three latent classes in both models; however, the latter model had greater fit compared to the former model. In addition, the latent classes in both models had similar characteristics, and the distributions of item difficulties in latent classes were also quite similar in both models while they had some differences in some aspects. The sizes of identical latent classes in both models varied between 15% and 30%. The results of the current study are expected to provide a deeper insight to researchers studying measurement theory and/or intelligence measurement.
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References
Abad, F. J., Colom, R., Rebollo, I., & Escorial, S. (2004). Sex differential item functioning in the Raven's Advanced Progressive Matrices: Evidence for bias. Personality and Individual Differences, 36(6), 1459–1470. https://doi.org/10.1016/S0191-8869(03)00241-1
Alloway, T. P. (2009). Working memory, but not IQ, predicts subsequent learning in children with learning difficulties. European Journal of Psychological Assessment, 25(2), 92–98
Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1-29.
Beaujean, A. A., & Osterlind, S. J. (2008). Using Item Response Theory to assess the Flynn Effect in the National Longitudinal Study of Youth 79 Children and Young Adults data. Intelligence, 36(5), 455–463. https://doi.org/10.1016/j.intell.2007.10.004
Brockmole, J. R. & Logie, R. H. (2013). Age-related change in visual working memory: A study of 55,753 participants aged 8–75, Frontiers in Psychology, 4.
Colom, R., Escorial, S., & Rebollo, I. (2004). Sex differences on the Progressive Matrices are influenced by sex differences on spatial ability. Personality and Individual Differences, 37(6), 1289–1293. https://doi.org/10.1016/j.paid.2003.12.014
Cohen, A. S., & Bolt, D. M. (2005). A mixture model analysis of differential item functioning. Journal of Educational Measurement, 42, 133–148.
Cowan, N., Morey, C. C., AuBuchon, A. M., Zwilling, C.E. & Gilchrist, A. L. (2010). Seven-year-olds allocate attention like adults unless working memory is overloaded. Developmental Science, 13, 120–133.
Cowan, N., AuBuchon, A. M., Gilchrist, A. L., Ricker, T. J. & Saults, J. S. (2011). Age differences in visual working memory capacity: Not based on encoding limitations. Developmental Science, 14(5): 1066–1074. doi:10.1111/j.1467-7687.2011.01060.x.
Cubaynes, S., Lavergne, C., Marboutin, E. & Gimenez, O. (2012). Assessing individual heterogeneity using model selection criteria: How many mixture components in capture–recapture models? Methods in Ecology and Evolution, 3, 564–573.
Dai, Y. (2013). A mixture Rasch model with a covariate: A simulation study via Bayesian Markov chain Monte Carlo estimation. Applied Psychological Measurement, 37, 375- 396.
Dehn, M. J. (2014). Essentials of Processing Assessment. 2. Edition. NJ: Wiley.
Embretson, S. E., & Reise, S. P. (2000). Item Response Theory for Psychologists. Mahwah, NJ: Erlbaum.
Ferreira, A. I., Almeida, L. S. & Prieto, G. (2012). Construction of a memory battery for computerized administration, using Item-Response Theory. Psychological Reports, 111(2), 585-609.
Fischer G. H. (1995). Derivations of the Rasch Model. In Fischer & Molenaar (Ed.), Rasch Models Foundations, Recent Developments, and Applications, (pp. 15-38).
Frick, H., Strobl, C. & Zeiles, A. (2015). Rasch mixture models for DIF detection: A comparison of old and new score specifications. Educational and Psychological Measurement, 75(2), 208–234.
Geary D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
Hambleton, R. K. & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston, MA: Kluwer Academic Publishers.
Heyes, S. B., Zokaei, N. & Husain, M. (2016). Longitudinal development of visual working memory precision in childhood and early adolescence, Cognitive Development, 39, 36-44.
Jiao, H., Lissitz, R. W., Macready, G., Wang, S. & Liang, S. Exploring levels of performance using the mixture Rasch model for standard setting. Psychological Test and Assessment Modeling, 53(4), 499-522.
Karadavut, T., Cohen, A. S., Kim, S. H. (2019). Mixture Rasch model with main and interaction effects of covariates on latent class membership. International Journal of Assessment Tools in Education, 6(3), 362–377.
Li, T., Jiao, H. & Macready, G. B. (2016). Different approaches to covariate inclusion in the mixture Rasch model. Educational and Psychological Measurement, 76(5), 848–872.
Muthén, B., & Asparouhov, T. (2006). Item response mixture modeling: Application to tobacco dependence criteria. Addictive Behaviors, 31, 1050–1066. doi:10.1016/j.addbeh.2006.03.026
R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Chicago: The University of Chicago Press.
Rost J. (1990). Rasch Models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14(3), 271-282.
Rost J., von Davier M. (1995). Mixture Distribution Rasch Models. In Fischer & Molenaar (Ed.), Rasch Models Foundations, Recent Developments, and Applications, (pp. 257-268).
Sak, U., Bal-Sezerel, B., Ayas, B., Tokmak, F., Özdemir, N.N., Demirel-Gürbüz, Ş. & Öpengin, E. (2016). Anadolu Sak Intelligence Scale: ASIS Practitioner's Book.
ASIS MAnual. (2016). Anadolu Sak Zeka Ölçeği (ASİS) Uygulayıcı Kitabı. Anadolu Üniversitesi ÜYEP Merkezi, Eskişehir.
Samuelsen, K. M. (2005). Examining Differential Item Functioning From a Latent Class Perspective. Unpublished doctoral dissertation. University of Maryland, College Park.
Schleicher-Dilks, S. (2015). Exploring the item difficulty and other psychometric properties of the core perceptual, verbal and working memory subtests of the WAIS-IV using Item Response Theory. Unpublished Doctoral Dissertation. Florida: NSU.
Şen, S. & Cohen, A. S. (2019) Applications of mixture IRT models: A literature review. Measurement: Interdisciplinary Research and Perspectives. 17(4), 177-191, doi: 10.1080/15366367.2019.1583506
van der Sluis, S., Posthuma, D., Dolan, C. V., de Geus, E. J. C., Colom, R., & Boomsma, D. I. (2006). Sex differences on the Dutch WAIS-III. Intelligence, 34, 273–289.
von Davier M. & Rost, J. (2017). Logistic mixture-distribution response models. In W. J. van der Linden (Ed.), Handbook of item response theory, volume one: Models (p. 393-406). Chapman and Hall.
Alloway, T. P. (2009). Working memory, but not IQ, predicts subsequent learning in children with learning difficulties. European Journal of Psychological Assessment, 25(2), 92–98
Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1-29.
Beaujean, A. A., & Osterlind, S. J. (2008). Using Item Response Theory to assess the Flynn Effect in the National Longitudinal Study of Youth 79 Children and Young Adults data. Intelligence, 36(5), 455–463. https://doi.org/10.1016/j.intell.2007.10.004
Brockmole, J. R. & Logie, R. H. (2013). Age-related change in visual working memory: A study of 55,753 participants aged 8–75, Frontiers in Psychology, 4.
Colom, R., Escorial, S., & Rebollo, I. (2004). Sex differences on the Progressive Matrices are influenced by sex differences on spatial ability. Personality and Individual Differences, 37(6), 1289–1293. https://doi.org/10.1016/j.paid.2003.12.014
Cohen, A. S., & Bolt, D. M. (2005). A mixture model analysis of differential item functioning. Journal of Educational Measurement, 42, 133–148.
Cowan, N., Morey, C. C., AuBuchon, A. M., Zwilling, C.E. & Gilchrist, A. L. (2010). Seven-year-olds allocate attention like adults unless working memory is overloaded. Developmental Science, 13, 120–133.
Cowan, N., AuBuchon, A. M., Gilchrist, A. L., Ricker, T. J. & Saults, J. S. (2011). Age differences in visual working memory capacity: Not based on encoding limitations. Developmental Science, 14(5): 1066–1074. doi:10.1111/j.1467-7687.2011.01060.x.
Cubaynes, S., Lavergne, C., Marboutin, E. & Gimenez, O. (2012). Assessing individual heterogeneity using model selection criteria: How many mixture components in capture–recapture models? Methods in Ecology and Evolution, 3, 564–573.
Dai, Y. (2013). A mixture Rasch model with a covariate: A simulation study via Bayesian Markov chain Monte Carlo estimation. Applied Psychological Measurement, 37, 375- 396.
Dehn, M. J. (2014). Essentials of Processing Assessment. 2. Edition. NJ: Wiley.
Embretson, S. E., & Reise, S. P. (2000). Item Response Theory for Psychologists. Mahwah, NJ: Erlbaum.
Ferreira, A. I., Almeida, L. S. & Prieto, G. (2012). Construction of a memory battery for computerized administration, using Item-Response Theory. Psychological Reports, 111(2), 585-609.
Fischer G. H. (1995). Derivations of the Rasch Model. In Fischer & Molenaar (Ed.), Rasch Models Foundations, Recent Developments, and Applications, (pp. 15-38).
Frick, H., Strobl, C. & Zeiles, A. (2015). Rasch mixture models for DIF detection: A comparison of old and new score specifications. Educational and Psychological Measurement, 75(2), 208–234.
Geary D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
Hambleton, R. K. & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston, MA: Kluwer Academic Publishers.
Heyes, S. B., Zokaei, N. & Husain, M. (2016). Longitudinal development of visual working memory precision in childhood and early adolescence, Cognitive Development, 39, 36-44.
Jiao, H., Lissitz, R. W., Macready, G., Wang, S. & Liang, S. Exploring levels of performance using the mixture Rasch model for standard setting. Psychological Test and Assessment Modeling, 53(4), 499-522.
Karadavut, T., Cohen, A. S., Kim, S. H. (2019). Mixture Rasch model with main and interaction effects of covariates on latent class membership. International Journal of Assessment Tools in Education, 6(3), 362–377.
Li, T., Jiao, H. & Macready, G. B. (2016). Different approaches to covariate inclusion in the mixture Rasch model. Educational and Psychological Measurement, 76(5), 848–872.
Muthén, B., & Asparouhov, T. (2006). Item response mixture modeling: Application to tobacco dependence criteria. Addictive Behaviors, 31, 1050–1066. doi:10.1016/j.addbeh.2006.03.026
R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Chicago: The University of Chicago Press.
Rost J. (1990). Rasch Models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14(3), 271-282.
Rost J., von Davier M. (1995). Mixture Distribution Rasch Models. In Fischer & Molenaar (Ed.), Rasch Models Foundations, Recent Developments, and Applications, (pp. 257-268).
Sak, U., Bal-Sezerel, B., Ayas, B., Tokmak, F., Özdemir, N.N., Demirel-Gürbüz, Ş. & Öpengin, E. (2016). Anadolu Sak Intelligence Scale: ASIS Practitioner's Book.
ASIS MAnual. (2016). Anadolu Sak Zeka Ölçeği (ASİS) Uygulayıcı Kitabı. Anadolu Üniversitesi ÜYEP Merkezi, Eskişehir.
Samuelsen, K. M. (2005). Examining Differential Item Functioning From a Latent Class Perspective. Unpublished doctoral dissertation. University of Maryland, College Park.
Schleicher-Dilks, S. (2015). Exploring the item difficulty and other psychometric properties of the core perceptual, verbal and working memory subtests of the WAIS-IV using Item Response Theory. Unpublished Doctoral Dissertation. Florida: NSU.
Şen, S. & Cohen, A. S. (2019) Applications of mixture IRT models: A literature review. Measurement: Interdisciplinary Research and Perspectives. 17(4), 177-191, doi: 10.1080/15366367.2019.1583506
van der Sluis, S., Posthuma, D., Dolan, C. V., de Geus, E. J. C., Colom, R., & Boomsma, D. I. (2006). Sex differences on the Dutch WAIS-III. Intelligence, 34, 273–289.
von Davier M. & Rost, J. (2017). Logistic mixture-distribution response models. In W. J. van der Linden (Ed.), Handbook of item response theory, volume one: Models (p. 393-406). Chapman and Hall.
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Published
2021-01-14
How to Cite
Şahin, M. D. (2021). Fitting a Mixture Rasch Model to Visual Sequential Processing Memory Sub-dimension of ASIS: The Role of Covariates. International Electronic Journal of Elementary Education, 13(2), 277–285. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/1370
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