Bartholomew, D. J. (1980). Factor analysis for categorical data.*Journal of the Royal Statistical Society, Series B, 42*, 293–321.

Bejar, I. I. (1980). A procedure of investigating the unidimensionality of achievement tests based on item parameter estimates.*Journal of Educational Measurement, 17*, 283–296.

Bock, R. D. (1984, September). Contributions of empirical Bayes and marginal maximum likelihood methods to the measurement of individual differences. Proceedings of the 23rd International Conference of Psychology, Acapulco, Mexico.

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm.*Psychometrika, 46*, 443–459.

Bock, R. D., Gibbons, R., & Murake, E. (1985).*Full information factor analysis* (MRC Report No. 85-1). Washington, DC: Office of Naval Research.

Christoffersson, A. (1975). Factor analysis of dichotomous variables.*Psychometrika, 40*, 5–32.

Chung, K. L. (1974).*A course in probability theory*, (2nd ed.). New York: Academic Press.

Divgi, D. R. (1981, April). Potential pitfalls of item response theory. Paper presented at annual meeting of National Council of Measurement in Education, Los Angeles.

Drasgow, F. (1987). A study of the measurement bias of two standardized psychological tests.*Journal of Applied Psychology, 72*, 19–30.

Drasgow, F., & Lissak, R. (1983). Modified parallel analysis: A procedure for examining the latent dimensionality of dichotomously scored item responses.*Journal of Applied Psychology, 68*, 363–373.

Goldstein, H. (1980). Dimensionality, bias, independence, and measurement scale problems in latent trait score models.*British Journal of Mathematical and Statistical Psychology, 33*, 234–246.

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

Hambleton, R. K., & Traub, R. E. (1973). Analysis of empirical data using two logistic latent trait models.*British Journal of Mathematical and Statistical Psychology, 26*, 195–211.

Hattie, J. (1985). Methodology Review: Assessing unidimensionality of tests and items.*Applied Psychology Measurement, 9*, 139–164.

Holland, P. W. (1981). When are item response models consistent with observed data?*Psychometrika, 46*, 79–92.

Holland, P. W., & Rosenbaum, P. R. (1986).*Conditional association and unidimensionality in monotone latent variable models*.*Annals of Statistics, 14*, 1523–1543.

Hulin, C. L., Drasgow, F., & Parsons, L. K. (1983).*Item Response Theory*. Homewood, IL: Dow Jones-Irwin.

Humphreys, L. C. (1985). General intelligence: An integration of factor, test, and simplex theory. In B. J. Wolman (Ed.),*Handbook of intelligence: Theories, measurements, and applications* (pp. 201–224). New York: John Wiley and Sons.

Lord, F. M. (1957). A significance test for the hypothesis that two variables measure the same trait except for errors of measurement.*Psychometrika, 22*, 207–220.

Lord, F. M. (1968). An analysis of the verbal scholastic aptitude test using Birnbaum's three-parameter logistic model.*Educational and Psychological Measurement, 28*, 989–1020.

Lord, F. M. (1980).*Applications of item response theory to practical testing problems*. Hillsdale, NJ: Lawrence Erlbaum.

Lord, F. M., & Novick, M. R. (1968).*Statistical theories of mental test scores*. Reading, MA: Addison-Wesley.

Lumsden, J. (1976). Test theory. In Rosenzwieg, M. R. and Porter, L. W. (Eds.)*Annual Review of Psychology*. Palo Alto, CA: Annual Reviews.

McDonald, R. P. (1967a). Nonlinear factor analysis.*Psychometrika Monograph No. 15, 32*(4, Pt. 2).

McDonald, R. P. (1967b). Numerical methods for polynomial models in nonlinear factor analysis.*Psychometrika, 32*, 77–112.

McDonald, R. P. (1981). The dimensionality of test and items.*British Journal of Mathematical and Statistical Psychology, 34*, 100–117.

McDonald, R. P. (1983). Exploratory and confirmatory factor analysis. In H. Warner & S. Messick (Eds.),*Principles of modern psychological measurement*, Hillsdale, NJ: Lawrence Erlbaum.

McDonald, R. P., & Ahlawat, K. S. (1974). Difficulty factors in binary data.*British Journal of Mathematical and Statistical Psychology, 27*, 82–99.

McNemar, Q. (1946). Opinion-attitude methodology.*Psychological Bulletin, 43*, 289–374.

Meredith, W. (1965). Some results on a general stochastic model for mental tests.*Psychometrika*, 30, 419–440.

Mislevy, R. J., & Bock, R. D. (1984). Item operating characteristics of the Armed Services Aptitute Battery (ASVAB), Form 8A, (Tech. Rep. N00014-83-C-0283). Washington, DC: Office of Naval Research.

Molenaar, I. W. (1983). Some improved diagnostics for failure of the Rasch model.*Psychometrika, 48*, 49–72.

Muthén, B. (1978). Contributions to factor analysis of dichotomous variables.*Psychometrika, 43*, 551–560.

Nandakumar, R. (1987).*Refinement of Stout's procedure for assessing latent trait unidimensionality*. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.

Reckase, M. D. (1979). Unifactor latent trait models applied to multifactor tests: Results and implications.*Journal of Educational Statistics, 4*, 207–230.

Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory.*Psychometrika, 49*, 425–436.

Sarrazin, G. (1983, July).*The detection of item bias for different cultural groups using latent trait and chi-square methods*. Paper presented at the Joint Meeting of the Psychometric Society and the Classification Society, Jouy-en-Joses, France.

Serfling, R. J. (1980).*Approximation theories of mathematical statistics*. New York: John Wiley.

Stout, W. F. (1974).*Almost sure convergence*, New York: Academic Press.

Stout, W. F. (1984).*A statistical test of unidimensionality for binary data with applications* (Tech. Rep. N00014-82-K-0486). Washington, DC: Office of Naval Research.

Stout, W. F. (in press). A nonparametric multidimensional IRT approach with applications to ability estimation and test bias.*Psychometrika*.

van den Wollenberg, A. L. (1982). Two new test statistics for the Rasch model.*Psychometrika, 47*, 123–140.