Adams, R. J. , Wilson, M., & Wang, W. (1997). The multidimensional random coefficients multinomial logits model. Applied Psychological Measurement, 21, 1–23.
2.
Akkermans, L. M. W. (1998). Studies on statistical models for polytomously scored items. Doctoral dissertation, University of Twente, Enschede, The Netherlands.
3.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–574.
4.
Andrich, D. (1988). Rasch models for measurement. Newbury Park CA: Sage.
5.
Bartholomew, D. J. (1987). Latent variable models and factor analysis. New York: Oxford University Press.
6.
Bartolucci, F. , & Forcina, A. (2000). A likelihood ratio test for MTP2 within binary variables. Annals of Statistics, 28, 1206–1218.
7.
Béguin, A. A. , & Glas, C. A. W. (1998). MCMC estimation of multidimensional IRT models (Research Report No. 98-14). Enschede, The Netherlands: University of Twente, Department of Education and Data Analysis.
8.
Bock, R. D. , & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of an E-M algorithm. Psychometrika, 46, 443–459.
9.
Bock, R. D. , Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261–280.
10.
Bolt, D. (2001). Conditional covariance-based representation of multidimensional test structure. Applied Psychological Measurement, 25, 244–257.
11.
Bolt, D. , & Stout, W. F. (1996). Differential item functioning: Its multidimensional model and resulting SIBTEST detection procedure. Behaviormetrika, 23, 67–95.
12.
Croon, M. A. (1991). Investigating Mokken scalability of dichotomous items by means of ordinal latent class analysis. British Journal of Mathematical and Statistical Psychology, 44, 315–332.
13.
DiBello, L. V. , Stout, W. F., & Roussos, L. A. (1995). Unified cognitive/psychometric diagnostic assessment likelihood-based classification techniques. In P. D. Nichols, S. F. Chipman, & R. L. Brennan (Eds), Cognitively diagnostic assessment (pp. 361–389). Hillsdale NJ: Erlbaum.
14.
Douglas, J. (1997). Joint consistency of nonparametric item characteristic curve and ability estimation. Psychometrika, 62, 7–28.
15.
Douglas, J. , & Cohen, A. (2001). Nonparametric item response function estimation for assessing parametric model fit. Applied Psychological Measurement, 25, 234–243.
16.
Douglas, J. , Kim, H. R., Habing, B., & Gao, F. (1998). Investigating local dependence with conditional covariance functions. Journal of Educational and Behavioral Statistics, 23, 129–151.
17.
Douglas, J. A. , Stout, W. F., & DiBello, L. V. (1996). A kernel-smoothed version of SIBTEST with applications to local DIF inference and function estimation. Journal of Educational and Behavioral Statistics, 21, 333–363.
18.
Drasgow, F. , Levine, M. V., Tsien, S., Williams, B., & Mead, A. D. (1992). Fitting polytomous item response theory models to multiple-choice tests. Applied Psychological Measurement, 19, 143–165.
19.
Ellis, J. L. , & van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model. Psychometrika, 58, 417–429.
20.
Embretson, S. E. (1985). Multicomponent latent trait models for test design. In S. E. Embretson (Ed.), Test design: Developments in psychology and psychometrics (pp. 195–218). New York: Academic Press.
21.
Embretson, S. E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495–515.
22.
Embretson, S. E. (1997). Multicomponent response models. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 305–321). New York: Springer.
23.
Emons, W. H. M. , Meijer, R. R., & Sijtsma, K. (in press). Comparing the empirical and the theoretical sampling distributions of the U3 person-fit statistic. Applied Psychological Measurement.
24.
Fischer, G. H. (1974). Einführung in die Theorie psychologischer Tests (Introduction to psychological test theory). Bern, Switzerland: Huber.
25.
Fischer, G. H. (1995). The linear logistic test model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 131–156). New York: Springer Verlag.
26.
Gelman, A. , Meng, X.-L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733–760.
27.
Gessaroli, M. E. , & de Champlain, A. F. (1996). Using an approximate chi-square statistic to test the number of dimensions underlying the responses to a set of items. Journal of Educational Measurement, 33, 157–179.
28.
Glas, C. A. W. , & Verhelst, N. D. (1995). Testing the Rasch model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 69–95). New York: Springer-Verlag.
29.
Grayson, D. A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383–392.
30.
Habing, B. (2001). Nonparametric regression and the parametric bootstrap for local dependence assessment. Applied Psychological Measurement, 25, 221–233.
31.
Habing, B. , & Donoghue, J. (in press). Local dependence assessment for exams with polytomous items and incomplete item-examinee layouts. Journal of Educational and Behavioral Statistics.
32.
Haertel, E. H. , & Wiley, D. E. (1993). Representations of ability structures: Implications for testing. In N. Fredriksen & R. J. Mislevy (Eds.), Test theory for a new generation of tests (pp. 359–384). Hillsdale NJ: Erlbaum.
33.
Hambleton, R. K. (1989). Principles and selected applications of item response theory. In R. L. Linn (Ed.), Educational measurement (3rd ed.) (pp. 201–220). New York: Macmillan.
34.
Hemker, B. T. , Sijtsma, K., & Molenaar, I. W. (1995). Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model. Applied Psychological Measurement, 19, 337–352.
35.
Hemker, B. T. , Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1997). Stochastic ordering using the latent trait and the sum score in polytomous IRT models. Psychometrika, 62, 331–347.
36.
Hoijtink, H. & Molenaar, I. W. (1997). A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks. Psychometrika, 62, 171–189.
37.
Holland, P. W. , & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent trait models. Annals of Statistics, 14, 1523–1543.
38.
Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77–79.
39.
Junker, B. W. (1991). Essential independence and likelihood-based ability estimation for polytomous items. Psychometrika, 56, 255–278.
40.
Junker, B. W. (1993). Conditional association, essential independence and monotone unidimensional item response models. Annals of Statistics, 21, 1359–1378.
41.
Junker, B. W. , & Ellis, J. L. (1997). A characterization of monotone unidimensional latent variable models. Annals of Statistics, 25, 1327–1343.
42.
Junker, B. W. , & Sijtsma, K. (2000). Latent and manifest monotonicity in item response models. Applied Psychological Measurement, 24, 65–81.
43.
Junker, B. W. , & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258–272.
44.
Kelderman, H. , & Rijkes, C. P. M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 149–176.
45.
Kim, H. R., Zhang, J., & Stout, W. F. (1995). Anew index of dimensionality—DETECT. Unpublished manuscript.
46.
Li, H.-H. , & Stout, W. F. (1996). A new procedure for detection of crossing DIF. Psychometrika, 61, 647–677.
47.
Lindsay, B. , Clogg, C., & Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86, 96–107.
48.
Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of “scale analysis” and factor analysis. Psychological Bulletin, 45, 507–530.
49.
Lord, F. M. (1980). Application of item response theory to practical testing problems. Hillsdale NJ: Erlbaum.
50.
McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 257–269). New York: Springer.
51.
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
52.
Meijer, R. R. (1994). Nonparametric person fit analysis. Unpublished doctoral dissertation, Vrije Universiteit, Amsterdam, The Netherlands.
53.
Meredith, W. (1965). Some results based on a general stochastic model for mental tests. Psychometrika, 30, 419–440.
54.
Miecskowski, T. A. , Sweeney, J. A., Haas, G., Junker, B. W., Brown, R. P., & Mann, J. J. (1993). Factor composition of the Suicide Intent Scale. Suicide and Life Threatening Behavior, 23, 37–45.
55.
Mislevy, R. J. (1996). Test theory reconceived. Journal of Educational Measurement, 33, 379–416.
56.
Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague: Mouton.
57.
Mokken, R. J. (1997). Nonparametric models for dichotomous responses. In W. J. van der Linden, & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 351–368). New York: Springer.
58.
Mokken, R. J. , & Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417–430.
59.
Molenaar, I. W. (1991). A weighted Loevinger H-coefficient extending Mokken scaling to multicategory items. Kwantitatieve Methoden, 37, 97–117.
60.
Molenaar, I. W. (1997). Nonparametric methods for polytomous responses. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 369–380). New York: Springer.
61.
Molenaar, I. W. (2001). Thirty years of nonparametric item response theory. Applied Psychological Measurement, 25, 295–299.
62.
Molenaar, I. W. , & Sijtsma, K. (2000). MSP5 for Windows [Computer program]. Groningen, The Netherlands: ProGAMMA.
63.
Nandakumar, R. , & Stout, W. F. (1993). Refinements of Stout’s procedure for assessing latent trait unidimensionality. Journal of Educational Statistics, 18, 41–68.
64.
Nandakumar, R. , Yu, F., Li, H.-H., & Stout, W. F. (1998). Assessing unidimensionality of polytomous data, Applied Psychological Measurement, 22, 99–115.
65.
Oshima, T. C. , & Miller, M. D. (1992). Multidimensionality and item bias in item response theory. Applied Psychological Measurement, 16, 237–248.
66.
Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611–630.
67.
Ramsay, J. O. (1997). A functional approach to modeling test data. In W. J. van der Linden & R. K. Hambleton (Eds), Handbook of modern item response theory (pp. 381–394). New York: Springer.
68.
Ramsay, J. O. (2000). TESTGRAF98: A program for the graphical analysis of multiple choice test and questionnaire data [Computer program]. Available from http://www.psych.mcgill.ca/faculty/ramsay/ramsay.html.
69.
Rasch, G. (1960/80). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research). Expanded edition (1980), with foreword and afterword by B. D. Wright. Chicago: University of Chicago Press.
70.
Reckase, M. D. (1997). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden & R. K. Hambleton (Eds), Handbook of modern item response theory (pp. 271–286). New York: Springer.
71.
Samejima, F. (1998). Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses. Psychometrika, 63, 111–130.
72.
Santor, D. A. , Zuroff, D. C., Ramsay, J. O., Cervantes, P., & Palacios, J.(1995). Examining scale discriminability in the BDI and CES-D as a function of depressive severity. Psychological Assessment, 7, 131–139.
73.
Scheiblechner, H. (1972). Das Lernen und Lösen komplexer Denkaufgaben [The learning and solving of complex reasoning items]. Zeitschrift für experimentelle und angewandte Psychologie, 3, 476–506.
74.
Shealy, R. , & Stout, W. F. (1993). A modelbased standardization approach that separates true bias/DIF from group ability differences and detects test bias/DIF as well as item bias/DIF. Psychometrika, 58, 159–194.
75.
Sijtsma, K. (1998) Methodology review: Nonparametric IRT approaches to the analysis of dichotomous item scores. Applied Psychological Measurement, 22, 3–31.
76.
Sijtsma, K. , & Hemker, B. T. (1998). Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models. Psychometrika, 63, 183–200.
77.
Sijtsma, K. , & Junker, B. W. (1996). A survey of theory and methods of invariant item ordering. British Journal of Mathematical and Statistical Psychology, 49, 79–105.
78.
Sijtsma, K. , & Junker, B. W. (1997). Invariant item ordering of transitive reasoning tasks. In J. Rost & R. Langeheine (Eds.), Applications of latent trait and latent class models in the social sciences (pp. 100–110). Münster, Germany: Waxmann Verlag.
79.
Sijtsma, K. , & Meijer, R. R. (2001). The person response function as a tool in person-fit research. Psychometrika, 66, 191–207.
80.
Sijtsma, K. , & Van der Ark, L. A. (2001). Progress in NIRT analysis of polytomous item scores: Dilemmas and practical solutions. In A. Boomsma, M. A. J. Van Duijn, & T. A. B. Snijders (Eds.), Essays on item response theory (pp. 297–318). New York: Springer-Verlag.
81.
Sijtsma, K. , & Verweij, A. (1999). Knowledge of solution strategies and IRT modeling of items for transitive reasoning. Applied Psychological Measurement, 23, 55–68.
82.
Stone, C. A. (2000). Monte Carlo based null distribution for an alternative goodness-of-fit test statistic for IRT models. Journal of Educational Measurement, 37, 58–75.
83.
Stout, W. F. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589–617.
84.
Stout, W. F. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293–325.
85.
Stout, W. F. (2001). Nonparametric item response theory: A maturing and applicable measurement modeling approach. Applied Psychological Measurement, 25, 300–306.
86.
Stout, W. F. , Habing, B., Douglas, J., Kim, H. R., Roussos, L., & Zhang, J. (1996). Conditional covariance-based nonparametric multi dimensionality assessment. Applied Psychological Measurement, 20, 331–354.
87.
Stout, W. F. , Nandakumar, R., & Habing, B. (1996). Analysis of latent dimensionality of dichotomously and polytomously scored test data. Behaviormetrika, 23, 37–65.
88.
Suppes, P. , & Zanotti, M. (1981). When are probabilistic explanations possible?Synthese, 48, 191–199.
89.
Tatsuoka, K. K. (1995). Architecture of knowledge structures and cognitive diagnosis: A statistical pattern recognition and classification approach. In P. D. Nichols, S. F. Chipman, & R. L. Brennan (Eds.), Cognitively diagnostic assessment (pp. 327–359). Hillsdale NJ: Erlbaum.
90.
Van der Ark, L. A. (2001). Relationships and properties of polytomous item response theory models. Applied Psychological Measurement, 25, 273–282.
91.
Van Engelenburg, G. (1997). On psychometric models for polytomous items with ordered categories within the framework of item response theory. Unpublished doctoral dissertation, University of Amsterdam, The Netherlands.
92.
Vermunt, J. (2001). The use of restricted latent class models for defining and testing nonparametric and parametric item response theory models. Applied Psychological Measurement, 25, 283–294.
93.
Wright, B. D. , & Stone, M. H. (1979). Best test design. Chicago: Mesa Press.
94.
Yuan, A. , & Clarke, B. (2001). Manifest characterization and testing of certain latent traits. Annals of Statistics, 29(3).
95.
Zhang, J. , & Stout, W. F. (1999). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64, 129–152.