![[PDF]](/pb-assets/Icons/adobe-pdf-icon-1498649896243.png){kind=icon}
Abstract
Local independence is a central assumption of commonly used item response theory models. Violations of this assumption are usually tested using test statistics based on item pairs. This study presents two quasi-exact tests based on the statistic for testing the hypothesis of local independence in the Rasch model. The proposed tests do not require the estimation of item parameters and can also be applied to small data sets. The authors evaluate the tests with three simulation studies. Their results indicate that the quasi-exact tests hold their alpha level under the Rasch model and have higher power against different forms of local dependence than several alternative parametric and nonparametric model tests for local independence.
References
|
Andrich, D., Kreiner, S. (2010). Quantifying response dependence between two dichotomous items using the Rasch model. Applied Psychological Measurement, 34, 181-192. doi:10.1177/0146621609360202 Google Scholar | SAGE Journals | ISI | |
|
Bechger, T. M., Maris, G. (2015). A statistical test for differential item pair functioning. Psychometrika, 80, 317-340. doi:10.1007/s11336-014-9408-y Google Scholar | Crossref | Medline | |
|
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores (pp. 392-479). Reading, MA: Addison-Wesley. Google Scholar | |
|
Chen, W.-H., Thissen, D. (1997). Local dependence indexes for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265-289. doi:10.2307/1165285 Google Scholar | SAGE Journals | ISI | |
|
Christensen, K. B., Makransky, G., Horton, M. (2017). Critical values for Yen’s Q3: Identification of local dependence in the Rasch model using residual correlations. Applied Psychological Measurement, 41, 178-194. doi:10.1177/0146621616677520 Google Scholar | SAGE Journals | ISI | |
|
Cressie, N., Read, T. R. (1984). Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society: Series B (Methodological), 46, 440-464. Google Scholar | Crossref | |
|
De Ayala, R . (2009). The theory and practice of item response theory. New York, NY: Guilford Press. Google Scholar | |
|
Edwards, M. C., Houts, C. R., Cai, L. (2018). A diagnostic procedure to detect departures from local independence in item response theory models. Psychological Methods, 23, 138-149. doi:10.1037/met0000121 Google Scholar | Crossref | Medline | |
|
Fox, J., Weisberg, S. (2011). An R companion to applied regression (2nd ed.). Thousand Oaks CA: SAGE. Retrieved from http://socserv.socsci.mcmaster.ca/jfox/Books/Companion Google Scholar | |
|
Glas, C. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525-546. Google Scholar | Crossref | ISI | |
|
Glas, C. A. W., Suárez-Falcón, J. C. (2003). A comparison of item-fit statistics for the three-parameter logistic model. Applied Psychological Measurement, 27, 87-106. doi:10.1177/0146621602250530 Google Scholar | SAGE Journals | ISI | |
|
Habing, B., Roussos, L. A. (2003). On the need for negative local item dependence. Psychometrika, 68, 435-451. doi:10.1007/BF02294736 Google Scholar | Crossref | ISI | |
|
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6, 65-70. Google Scholar | ISI | |
|
Ip, H.-S. (2001). Testing for local dependency in dichotomous and polytomous item response models. Psychometrika, 66, 109-132. doi:10.1007/BF02295736 Google Scholar | Crossref | ISI | |
|
Kelderman, H. (2007). Loglinear multivariate and mixture Rasch models. In von Davier, M., Carstensen, C. H. (Eds.), Multivariate and mixture distribution Rasch models (pp. 77-97). New York, NY: Springer. Google Scholar | Crossref | |
|
Kim, D., De Ayala, R., Ferdous, A. A., Nering, M. L. (2011). The comparative performance of conditional independence indices. Applied Psychological Measurement, 35, 447-471. doi:10.1177/0146621611407909 Google Scholar | SAGE Journals | ISI | |
|
Koller, I., Alexandrowicz, R. W. (2010). Eine psychometrische Analyse der ZAREKI-R mittels Rasch-Modellen [A psychometric analysis of the ZAREKI-R by the means of Rasch models]. Diagnostica, 56, 57-67. doi:10.1026/0012-1924/a000003 Google Scholar | Crossref | |
|
Koller, I., Alexandrowicz, R. W., Hatzinger, R. (2012). Das Rasch Modell in der Praxis: Eine Einführung mit eRm [The Rasch model in practical applications: An introduction with eRm]. Vienna, Austria: facultas.wuv, UTB. Google Scholar | |
|
Koller, I., Hatzinger, R. (2013). Nonparametric tests for the Rasch model: Explanation, development, and application of quasi-exact tests for small samples. InterStat. Retrieved from http://interstat.statjournals.net/YEAR/2013/abstracts/1311002.php Google Scholar | |
|
Koller, I., Maier, M. J., Hatzinger, R. (2015). An empirical power analysis of quasi-exact tests for the Rasch model: Measurement invariance in small samples. Methodology, 11, 45-54. doi:10.1027/1614-2241/a000090 Google Scholar | Crossref | |
|
Koller, I., Wiedermann, W., Glück, J. (2015). Item response models for dependent data: Quasi-exact tests for the investigation of some preconditions for measuring change. In Stemmler, M., von Eye, A., Wiedermann, W. (Eds.), Dependent data in social sciences research (pp. 263-279). Cham, Switzerland: Springer. Google Scholar | Crossref | |
|
Levy, R., Mislevy, R. J., Sinharay, S. (2009). Posterior predictive model checking for multidimensionality in item response theory. Applied Psychological Measurement, 33, 519-537. doi:10.1177/0146621608329504 Google Scholar | SAGE Journals | ISI | |
|
Liu, Y., Maydeu-Olivares, A. (2013). Local dependence diagnostics in irt modeling of binary data. Educational and Psychological Measurement, 73, 254-274. doi:10.1177/0013164412453841 Google Scholar | SAGE Journals | ISI | |
|
Mair, P., Hatzinger, R., Maier, M. J. (2018). eRm: Extended Rasch Modeling (0.16-1) [Computer software manual]. Available from https://cran.r-project.org/web/packages/eRm/index.html Google Scholar | |
|
Marais, I., Andrich, D. (2008). Formalizing dimension and response violations of local independence in the unidimensional Rasch model. Journal of Applied Measurement, 9, 200-215. Google Scholar | Medline | |
|
Maydeu-Olivares, A., Liu, Y. (2015). Item diagnostics in multivariate discrete data. Psychological Methods, 20, 276-292. doi:10.1037/a0039015 Google Scholar | Crossref | Medline | ISI | |
|
Maydeu-Olivares, A., Montaño, R. (2013). How should we assess the fit of Rasch-type models? Approximating the power of goodness-of-fit statistics in categorical data analysis. Psychometrika, 78, 116-133. doi:10.1007/s11336-012-9293-1 Google Scholar | Crossref | Medline | |
|
Ponocny, I. (2001). Nonparametric goodness-of-fit tests for the Rasch model. Psychometrika, 66, 437-459. doi:10.1007/BF02294444 Google Scholar | Crossref | ISI | |
|
Rasch, G. (1960). Probabilistic models for some intelligence and achievement tests. Copenhagen, Denmark: Danish Institute for Educational Research. Google Scholar | |
|
R Core Team . (2017). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Available from https://www.R-project.org/ Google Scholar | |
|
Robitzsch, A., Kiefer, T., Wu, M. (2018). TAM: Test analysis modules (R package version 2.12-18) [Computer software manual]. Available from https://CRAN.R-project.org/package=TAM Google Scholar | |
|
Sinharay, S. (2005). Assessing fit of unidimensional item response theory models using a Bayesian approach. Journal of Educational Measurement, 42, 375-394. doi:10.1111/j.1745-3984.2005.00021.x Google Scholar | Crossref | ISI | |
|
Suárez-Falcón, J. C., Glas, C. A. (2003). Evaluation of global testing procedures for item fit to the Rasch model. British Journal of Mathematical and Statistical Psychology, 56, 127-143. doi:10.1348/000711003321645395 Google Scholar | Crossref | Medline | ISI | |
|
van den Wollenberg, A. L . (1982). Two new test statistics for the Rasch model. Psychometrika, 47, 123-140. doi:10.1007/BF02296270 Google Scholar | Crossref | ISI | |
|
Verhelst, N. D. (2008). An efficient MCMC algorithm to sample binary matrices with fixed marginals. Psychometrika, 73, 705-728. doi:10.1007/s11336-008-9062-3 Google Scholar | Crossref | |
|
von Aster, M., Zulauf, M. W., Horn, R. (2006). Neuropsychologische Testbatterie für Zahlenverarbeitung und Rechnen bei Kindern (ZAREKI-R) [Neuropsychological Test Battery for Number Processing and Calculation in Children]. Frankfurt, Germany: Harcourt Test Services. Google Scholar | |
|
Wainer, H., Bradlow, E. T., Wang, X. (2007). Testlet response theory and its applications. Cambridge, UK: Cambridge University Press. Google Scholar | Crossref | |
|
Wang, W.-C., Wilson, M. (2005). The Rasch testlet model. Applied Psychological Measurement, 29, 126-149. doi:10.1177/0146621604271053 Google Scholar | SAGE Journals | ISI | |
|
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450. doi:10.1007/BF02294627 Google Scholar | Crossref | ISI | |
|
Wei, T., Simko, V. (2017). R package “corrplot”: Visualization of a correlation matrix (Version 0.84) [Computer software manual]. Retrieved from https://github.com/taiyun/corrplot Google Scholar | |
|
Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145. doi:10.1177/014662168400800201 Google Scholar | SAGE Journals | ISI |
