Abstract
Abstract. The ordinal, unidimensional monotone latent variable model assumes unidimensionality, local independence, and monotonicity, and implies the observable property of conditional association. We investigated three special cases of conditional association and implemented them in a new procedure that aims at identifying locally dependent items, removing these items from the initial item set, and producing an item subset that is locally independent. A simulation study showed that the new procedure correctly identified 89.5% of the model-consistent items and up to 90% of the model-inconsistent items. We recommend using this procedure for selecting locally independent item sets. The procedure may be used in combination with Mokken scale analysis.
References
1997). Local dependence indexes for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265–289. doi: 10.3102/10769986022003265
(1994). The influence of multidimensionality on the graded response model. Applied Psychological Measurement, 18, 155–170. doi: 10.1177/014662169401800205
(2005). DS14: standard assessment of negative affectivity, social inhibition, and Type D personality. Psychosomatic Medicine, 67, 89–97.
(1998). Investigating local dependence with conditional covariance functions. Journal of Educational and Behavioral Statistics, 23, 129–151. doi: 10.3102/10769986023002129
(1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383–392. doi: 10.1007/BF02294219
(1994). Statistics (5th ed.). Orlando, FL: Holt, Rinehart, & Winston.
(1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 14, 1523–1543. doi: 10.1214/aos/1176350174
(2008). An adjusted box plot for skewed distributions. Computational Statistics and Data Analysis, 52, 5186–5201. doi: 10.1016/j.csda.2007.11.008
(2010). Empirically indistinguishable multidimensional IRT and locally dependent unidimensional item response models. British Journal of Mathematical and Statistical Psychology, 63, 395–416. doi: 10.1348/000711009X466835
(2010). Investigating an invariant item ordering for polytomously scored items. Educational and Psychological Measurement, 70, 578–595. doi: 10.1177/0013164409355697
(1971). A theory and procedure of scale analysis. Berlin, Germany: De Gruyter.
(1984). Testing conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425–435. doi: 10.1007/BF02306030
(1988). Item bundles. Psychometrika, 53, 349–359. doi: 10.1007/BF02294217
(2003).
(Developments in practical nonparametric IRT scale analysis . In H. YanaiA. OkadaK. ShigemasuY. KanoJ. J. MeulmanEds., New developments in psychometrics (pp. 183–190). Tokyo, Japan: Springer.2002). Introduction to nonparametric item response theory. Thousand Oaks, CA: Sage.
(1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
(2007). Mokken scale analysis in R. Journal of Statistical Software, 20(11), 1–19. doi: 10.18637/jss.v020.i11
(2012). New developments in Mokken scale analysis in R. Journal of Statistical Software, 48(5), 1–27. doi: 10.18637/jss.v048.i05
(2010). A note on stochastic ordering of the latent trait using the sum of polytomous item scores. Psychometrika, 75, 272–279. doi: 10.1007/S11336-010-9147-7
(1999). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213–249. doi: 10.1007/BF02294536
(