Effects of Within-Group Homogeneity on Parameter Estimation of the Multilevel Rasch Model
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
If a hierarchical structure exists in educational measurement data and examinees within groups are homogeneous, a multilevel item response theory (MLIRT) model may be appropriate. Among the MLIRT models, the multilevel Rasch model is equivalent to a generalized linear mixed model (GLMM) with a logit link where person abilities are considered random effects and item difficulties fixed effects. Then the lme4 package in R can be used to fit the multilevel Rasch model. In this study, it was shown how the multilevel Rasch model can be formulated as a three-level GLMM, followed by a simulation analysis, where intraclass correlation (ICC) of latent abilities as a measure of within-group homogeneity was manipulated from low to high under the conditions of small to large numbers of examinees and items. Item parameter estimates by marginal maximum likelihood estimation (MMLE) were compared with those obtained under the GLMM framework. Biases of item parameter estimates by both methods were not evident in all conditions. However, estimation results by MMLE became proportionally less accurate as the ICC increased when the number of examinees was small. If the number of examinees was large, estimation accuracies of MMLE were acceptable even when a high level of within-group homogeneity existed. GLMM produced stable results at all levels of ICC. In all conditions, the number of examinees was more influential than the number of items.
Abstract
If a hierarchical structure exists in educational measurement data and examinees within groups are homogeneous, a multilevel item response theory (MLIRT) model may be appropriate. Among the MLIRT models, the multilevel Rasch model is equivalent to a generalized linear mixed model (GLMM) with a logit link where person abilities are considered random effects and item difficulties fixed effects. Then the lme4 package in R can be used to fit the multilevel Rasch model. In this study, it was shown how the multilevel Rasch model can be formulated as a three-level GLMM, followed by a simulation analysis, where intraclass correlation (ICC) of latent abilities as a measure of within-group homogeneity was manipulated from low to high under the conditions of small to large numbers of examinees and items. Item parameter estimates by marginal maximum likelihood estimation (MMLE) were compared with those obtained under the GLMM framework. Biases of item parameter estimates by both methods were not evident in all conditions. However, estimation results by MMLE became proportionally less accurate as the ICC increased when the number of examinees was small. If the number of examinees was large, estimation accuracies of MMLE were acceptable even when a high level of within-group homogeneity existed. GLMM produced stable results at all levels of ICC. In all conditions, the number of examinees was more influential than the number of items.
참고문헌 (32)
- Adams, R. J., "The multidimensional random coefficients multinomial logit model", Applied Psychological Measurement, 21, pp.1~23 (1997)
- Adams, R. J., "Multilevel item response models : An approach to errors in variable regression", Journal of Educational and Behavioral Statistics, 22, pp.47~76 (1997)
- Akaike, H., "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19, pp.716~723 (1974)
- Albert, J. H., "Bayesian estimation of normal ogive item response curves using Gibbs sampling", Journal of Educational Statistics, 17, pp.251~269 (1992)
- Baker, F. B., "Item response theory: Parameter estimation techniques" (2004), Dekker
- (2010)[URL]
- Bock, R. D., "Marginal maximum likelihood estimation of item parameters : Application of an EM algorithm", Psychometrika, 46, pp.443~459 (1981)
- de Ayala, R. J., "The theory and practice of item response theory" (2009), The Guilford Press
- De Boeck, P., "The estimation of item response models with the lmer function from the lme4 package in R", Journal of Statistical Software, 39, pp.1~28 (2011)
- Doran, H., "Estimating the multilevel Rasch model : With the lme4 package", Journal of Statistical Software, 20, pp.1~18 (2007)
- Fox, J. P., "Multilevel IRT using dichotomous and polytomous response data", British Journal of Mathematical and Statistical Psychology, 58, pp.145~172 (2005)
- Fox, J. P., "Multilevel IRT modeling in practice with the package mlirt", Journal of Statistical Software, 20, pp.1~16 (2007)
- Fox, J. P., "Bayesian estimation of a multilevel IRT model using Gibbs sampling", Psychometrika, 66, pp.269~286 (2001)
- Kamata, A., "Item analysis by the hierarchical generalized linear model", Journal of Educational Measurement, 38, pp.79~93 (2001)
- Kamata, A., "Procedures to perform item response data analysis by HLM", Paper presented at the annual meeting of American Educational Research Association (2002)
- Kamata, A., "Multilevel Rasch models, In Multivariate and mixture distribution Rasch models: Extensions and applications" (2007), Springer
- Linacre, J. M., "A user's guide to WINSTEPS and MINISTEP: Rasch-model computer programs", ~ (2006)
- McCulloch, C. E., "Generalized, linear, and mixed models" (2001), Wiley
- Natesan, P., "Bayesian estimation of graded response multilevel models using Gibbs sampling : Formulation and illustration", Educational and Psychological Measurement, 70, pp.420~439 (2010)
- Patz, R. J., "A straightforward approach to Markov chain Monte Carlo methods for item response models", Journal of Educational and Behavioral Statistics, 24, pp.146~178 (1999)
- Patz, R. J., "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses", Journal of Educational and Behavioral Statistics, 24, pp.342~366 (1999)
- Rasch, G., "Probabilistic models for some intelligence and attainment tests" (1960), Danish Institute for Educational Research
- Raudenbush, S. W., "Hierarchical linear models: Applications and data analysis methods" (2002), Sage
- "Scientific Software International", 2006
- R Development Core Team, "R: A language and environment for statistical computing", R Foundation for Statistical Computing, ~ (2012)
- Rijmen, F., "A nonlinear mixed model framework for item response theory", Psychological Methods, 8, pp.185~205 (2003)
- Schwarz, G., "Estimating the dimension of a model", Annals of Statistics, 6, pp.461~464 (1978)
- Snijders, T., "Multilevel analysis: An introduction to basic and advanced multilevel modeling" (1999), Sage
- "MRC Biostatistics Unit", 2003
- Wright, B. D., "Misunderstanding the Rasch model", Journal of Educational Measurement, 14, pp.219~226 (1977)
- Wu, M. L., "ConQuest: Multi-Aspect Test Software", Australian Council for Educational Research, ~ (1997)
- "Scientific Software International", 2003