Analysis of residuals for the multinomial item response model

Psychometrika

Volumn 61, Issue 3, 1996, Pages 509-528

  Reiser, Mark ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Asymptotic standard error; Factor analysis; Latent trait; Limited information

Indexed keywords

EID: 0030510836     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294552     Document Type: Article

References (38)

1. Agresti, A. (1990). Categorical data analysis. New York: John Wiley & Sons.
2. Agresti, A., Lipsitz, S., & Lang, J. B. (1992). Comparing marginal distributions of large sparse contingency tables. Computational Statistics & Data Analysis, 14, 55-73.
3. Agresti, A., & Yang, M. C. (1987). An empirical investigation of some effects of sparseness in contingency tables. Computational Statistics & Data Analysis, 5, 9-21.
4. Anderson, T. W. (1984). An introduction to multivatiate statistical analysis. (2nd ed.). New York: Wiley.
5. Andersen, E. B. (1990). The statistical analysis of categorical data. New York: Springer-Verlag.
6. Andersson, C. G., Christoffersson, A., & Muthén , B. (1974). FADIV: A computer program for factor analysis of dichotomized variables. Sweden: University of Uppsala, Department of Statistics.
7. Bartholomew, D. J. (1987). Latent variable models and factor analysis. New York: Oxford University Press.
8. Birch, M. W. (1964a). The detection of partial association, I: the 2 × 2 case. Journal of the Royal Statistical Society, Series B, 26, 313-324.
9. Birch, M. W. (1964b). A new proof of the Pearson-Fisher Theorem. Annals of Mathematical Statistics, 35, 818-824.
10. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivatiate analysis: Theory and practice. Cambridge, MA.: MIT Press.
11. Bock, R. D., & Aitken, M. (1981). Marginal Maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometnka, 46, 443-459.
12. Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197.
13. Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5-32.
14. Cochran, W. G. (1954). Some methods for strengthening the common chi-square tests. Biometircal Journal, 10, 417-451.
15. Cochran, W. G. (1955). A test of a linear function of the deviations between observed and expected numbers. Journal of the American Statistical Association, 50, 377-397.
16. Cressie, N., & Holland, P. W. (1983). Characterizing the manifest probabilities of latent trait models. Psychometrika, 48, 129-141.
17. Duncan, O. D. (1979). Indicators of sex typing: Traditional and egalitarian, situational and ideological responses. American Journal of Sociology, 85, 251-260.
18. Haberman, S. J. (1973). The analysis of residuals in cross-classified tables. Biometrics, 29, 205-220.
19. Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park: Sage Publications.
20. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
21. Koehler, K. J. (1986 ). Goodness-of-fit tests for log-linear models in sparse contingency tables. Journal of the American Statistical Association, 81, 336-344.
22. Krebs, D., & Schuessler, K. (1987). Soziole Empfindungen [Social life feelings]. New York: Campus Verlag.
23. Kreiner, S. (1987). Collapsibility of multidimensional contingency tables: Theorems, algorithms and programs. Copenhagen, Denmark: The Danish Institute for Educational Research.
24. Küsters, U. (1990). A note on sequential ML estimates and their asymptotic covariances. Statistical Papers, 31, 131-145.
25. Lehman, E. L. (1959). Testing statistical hypotheses. New York: Wiley.
26. Ludlow, L. H. (1986). Graphical analysis of item response theory residuals. Applied Psychological Measurement, 10, 217-229.
27. Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560.
28. Muthén, B. (1988). LISCOMP. Mooresville, IN.: Scientific Software.
29. Muthén, B., & Kaplan, D. (1992). A comparison of some methodologies for the factor analysis of non-normal Likert variables: a note on the size of the model. British Journal of Mathematical and Statistical Psychology, 45, 19-30.
30. Rao, C. R. (1973). Linear statistical inference and its applications (2nd ed.). New York: John Wiley.
31. Reiser, M., & Schuessler, K. (1990). A hierarchy for some latent structure models. Sociological Methods & Research, 19, 419-465.
32. Reiser, M., & VandenBerg, M. (1994). Validity of the chi-square test in dichotomous variable factor analysis when expected frequencies are small. British Journal of Mathematical and Statistical Psychology, 47, 85-107.
33. Salomaa, H. (1990). Factor analysis of dichotomous data. Helsinki, Finland: Statistical Society.
34. Stout, W. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589-617.
35. Takane, Y., & de Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
36. Tate, M. W., & Hyer, L. A. (1973). Inaccuracy of the chi-squared test of goodness of fit when expected frequencies are small. Journal of the American Statistical Association, 68, 836-841.
37. Tuch, S. A. (1981). Analyzing recent trends in prejudice toward blacks: insights from latent class models. American Journal of Sociology, 87, 130-141.
38. von Eye, A. (1990). Configural frequency analysis. London: Cambridge University Press.