Joint assessment of the latent trait dimensionality and observed differential item functioning of students’ national tests

Bartolucci, F.: A class of multidimensional IRT models for testing unidimensionality and clustering items. Psychometrika 72, 141–157 (2007)

Bartolucci, F., Bacci, S., Gnaldi, M.: MultiLCIRT: An R package for multidimensional latent class item response models. Comput. Statistics Data Anal. 71, 971–985 (2014)

Birnbaum, A.: 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. 395–479. Addison-Wesley, Reading (1968)

Camilli, P., Shephard, L.A.: Methods for Identifying Biased Test Items. Sage, Thousand Oaks (1994)

Christensen, K., Bjorner, J., Kreiner, S., Petersen, J.: Testing unidimensionality in polytomous Rasch models. Psychometrika 67, 563–574 (2002)

Clauser, B., Mazor, K.M.: Using statistical procedures to identify differentially functioning test items. Educ. Meas. Issues Pract. 2, 31–44 (1998)

Cohen, A.S., Bolt, D.M.: A mixture model analysis of differential item functioning. J. Educ. Meas. 42, 133–148 (2005)

De Mars, C., Lau, A.: Differential item functioning detection with latent classes: how accurately can we detect who is responding differentially? Educ. Psychol. Meas. 71(4), 597–616 (2011)

Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39, 1–38 (1977)

Formann, A.K.: Linear logistic latent class analysis and the Rasch model. In: Fischer, G., Molenaar, I. (eds.) Rasch Models: Foundations, Recent Developments, and Applications, pp. 239–255. Springer, New York (1995)

Glas, C.A.W., Verhelst, N.D.: Testing the rasch model. In: Fischer, G.H., Molenaar, I. (eds.) Rasch Models. Their foundations, Recent Developments and Applications, pp. 69–95. Springer, New York (1995)

Goodman, L.A.: Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61, 215–231 (1974)

Hambleton, R.K., Swaminathan, H.: Item Response Theory: Principles and Applications. Kluwer Nijhoff, Boston (1985)

Holland, P.W., Thayer, D.T.: Differential item functioning and the Mantel-Haenszel procedure. In: Wainer, H., Braun, H.I. (eds.) Test Validity, pp. 129–145. Erlbaum, Hillsdale (1988)

INVALSI.: Prove invalsi 2009. In: Report, I. T. (ed.) Quadro di riferimento di Italiano. (2009a)

INVALSI.: Prove invalsi 2009. In: Report, I. T. (ed.) Quadro di riferimento di Matematica. (2009b)

Lazarsfeld, P.F., Henry, N.W.: Latent Structure Analysis. Houghton Mifflin, Boston (1968)

Lindsay, B., Clogg, C., Greco, J.: Semiparametric estimation in the rasch model and related exponential response models, including a simple latent class model for item analysis. J. Am. Stat. Assoc. 86, 96–107 (1991)

Lord, F.: Applications of Item Response Theory to Practical Testing Problems. Erlbaum, Hillsdale (1980)

Martin-Löf, P.: Statistiska Modeller. Institütet för Försäkringsmatemetik och Matematisk Statistisk vid Stockholms Universitet, Stockholm (1973)

Mazza, A., Punzo, A., McGuire, B.: Kernsmoothirt: an r package for kernel smoothing in item response theory. J. Stat. Softw. 58(6), 1–34 (2014)

Mokken, R.: A Theory and Procedure of Scale Analysis. De Gruyter, Berlin (1971)

Penfield, R. D., Camilli, G.: Differential item functioning and item bias. In: Handbook of Statistics, pp. 125–167. Elsevier, New York (2007)

Perkins, A.J., Stump, T.E., Monahan, P., McHorney, C.: Assessment of differential item functioning for demographic comparisons in the mos sf-36 health survey. Qual. Life Res. 15, 331–348 (2006)

Raju, N.: The area beetwen two item characteristic curves. Psychometrika 53, 495–502 (1988)

Rasch, G.: On general laws and the meaning of measurement in psychology. In: Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability, pp. 321–333. University of California Press, California (1961)

Sani, C., Grilli, L.: Differential variability of test scores among schools: a multilevel analysis of the fifth grade invalsi test using heteroscedastic random effects. J. Appl. Quant. Methods 6(4), 88–99 (2011)

Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978)

Sijtsma, K., Molenaar, I.: Introduction to Nonparametric Item Response Theory. Sage, Thousand Oaks (2002)

Stout, W.: A non parametric approach for assessing latent trait unidimensionality. Psychometrika 52(4), 589–617 (1987)

Swaminathan, H., Rogers, H.: Detecting differential item functioning using logistic regression procedures. J. Educ. Meas. 27, 361–370 (1990)

Thissen, D., Steinberg, L., Wainer, H.: Use of item response theory in the study of group differences in trace lines. In: Wainer, H., Braun, H.I. (eds.) Test Validity, pp. 147–169. Erlbaum, Hillsdale (1988)

Thissen, D., Steinberg, L., Wainer, H.: Detection of differential item functioning using the parameters of item response models. In: Holland, P., Wainer, H. (eds.) Differential Item Functioning, pp. 67–113. Lawrence Erlbaum Associates, Hillsdale (1993)

Vermunt, J.: The use of restricted latent class models for defining and testing nonparametric and parametric item response theory models. Appl. Psychol. Meas. 25, 283–294 (2001)

Wirth, R., Edwards, M.: Item factor analysis: current approaches and future directions. Psychol. Methods 12(1), 58–79 (2007)

Zhang, J., Stout, W.: Conditional covariance structure of generalized compensatory multidimensional item. Psychometrika 64(2), 129–152 (1999a)

Zhang, J., Stout, W.: The theoretical detect index of dimensionality and its application to approximate simple structure. Psychometrika 64(2), 213–249 (1999b)