Limited information goodness-of-fit testing in multidimensional contingency tables

Psychometrika

Volumn 71, Issue 4, 2006, Pages 713-732

  Maydeu Olivares, Albert ^a   Joe, Harry ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Categorical data analysis; Composite likelihood; Item response theory; Lisrel; Multivariate discrete data; Multivariate multinomial distribution

Indexed keywords

EID: 33751502346     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-005-1295-9     Document Type: Article

References (49)

1. Agresti, A. (2002). Categorical data analysis (2nd edn.). New York: Wiley.
2. Bartholomew, D.J., & Knott, M. (1999). Latent variable models and factor analysis (2nd edn.). London: Arnold.
3. P contingency tables. British Journal of Mathematical and Statistical Psychology, 55, 1-15.
4. Bartholomew, D.J., & Tzamourani, P. (1999). The goodness of fit of latent trait models in attitude measurement. Sociolological Methods and Research, 27, 525-546.
5. Bentler, P.M. (1995). EQS. Encino, CA: Multivariate Software.
6. Bishop, Y.M.M., Fienberg, S.E., & Holland, P.W. (1975). Discrete multivariate analysis. Cambridge, MA: MIT Press.
7. Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
8. Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
9. P tables. British Journal of Mathematical and Statistical Psychology, 59, 173-194.
10. Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5-32.
11. 2 test of goodness of fit. Annals of Mathematical Statistics, 23, 315-345.
12. Collins, L.M., Fidler, P.L., Wugalter, S.E., & Long, J. (1993). Goodness-of-fit testing for latent class models. Multivariate Behavioral Research, 28, 375-389.
13. Diener, E., Emmons, R.A., Larsen, R.J., & Griffin, S. (1985). The Satisfaction with Life Scale. Journal of Personality Assessment, 49, 71-75.
14. Drasgow, F., Levine, M.V., Tsien, S., Williams, B., & Mead, A. (1995). Fitting polytomous item response theory models to multiple-choice tests. Applied Psychological Measurement, 19, 143-165.
15. D'Zurilla, T.J., Nezu, A.M., & Maydeu-Olivares, A. (2002). Manual of the social problem-solving inventory-Revised. North Tonawanda, NY: Multi-Health Systems.
16. Fraser, C., & McDonald, R.P. (1988). NOHARM: Least squares item factor analysis. Multivariate Behavioral Research, 23, 267-269.
17. Glas, C.A.W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525-546.
18. Glas, C.A.W. (1999). Modification indices for the 2-PL and the nominal response model. Psychometrika, 64, 273-294.
19. Glas, C.A.W., & Verhelst, N.D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635-659.
20. Godambe, V.P. (Ed.) (1991). Estimating functions. Oxford: Oxford University Press.
21. Joe, H. (1997). Multivariate models and dependence concepts. London: Chapman & Hall.
22. Jöreskog, K.G. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika, 59, 381-389.
23. Jöreskog, K.G., & Moustaki, I. (2001). Factor analysis of ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
24. Jöreskog, K.G., & Sörbom, D. (2001). LISREL 8. Chicago: Scientific Software.
25. Koehler, K., & Larntz, K. (1980). An empirical investigation of goodness-of-fit statistics for sparse multinomials. Journal of the American Statistical Association, 75, 336-344.
26. Kramp, U. (2006). Effects of the number of response options on personality rating scales. Unpublished doctoral dissertation. University of Barcelona.
27. Lee, S.Y., Poon, W.Y., & Bentler, P.M. (1995). A two-stage estimation of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 48, 339-358.
28. Lord, P.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
29. Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
30. Maydeu-Olivares, A. (2001 a). Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66, 209-228.
31. Maydeu-Olivares, A. (2001b). Multidimensional item response theory modeling of binary data: Large sample properties of NOHARM estimates. Journal of Educational and Behavioral Statistics, 26, 49-69.
32. Maydeu-Olivares, A. (2005). Further empirical results on parametric vs. non-parametric IRT modeling of Likert-type personality data. Multivariate Behavioral Research, 40, 275-293.
33. Maydeu-Olivares, A. (2006). Limited information estimation and testing of discretized multivariate normal structural models. Psychometrika, 71, 57-77.
34. n contingency tables: A unified framework. Journal of the American Statistical Association, 100, 1009-1020.
35. Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560.
36. Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115-132.
37. Muthén, B. ( 1993). Goodness of fit with categorical and other nonnormal variables. In K.A. Bollen, & J.S. Long (Eds.). Testing structural equation models (pp. 205-234). Newbury Park, CA: Sage.
38. Muthén, L., & Muthén, B. (2001). MPLUS. Los Angeles: Muthén & Muthén.
39. Rao, C.R. (1973). Linear statistical inference and its applications. New York: Wiley.
40. Reiser, M. (1996). Analysis of residuals for the multinomial item response model. Psychometrika, 61, 509-528.
41. Reiser, M., & Lin, Y. (1999). A goodness-of-fit test for the latent class model when expected frequencies are small. In M. Sobel, & M. Becker (Eds.), Sociological methodology 1999 (pp. 81-111). Boston: Blackwell.
42. 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.
43. Samejima, F. (1969). Calibration of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, No. 17.
44. Schott, J.R. (1997). Matrix analysis for statistics. New York: Wiley.
45. Teugels, J.L. ( 1990). Some representations of the multivariate Bernoulli and binomial distributions. Journal of Multivariate Analysis, 32, 256-268.
46. Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567-577.
47. Tollenaar, N., & Mooijaart, A. (2003). Type I errors and power of the parametric bootstrap goodness-of-fit test: Full and limited information. British Journal of Mathematical and Statistical Psychology, 56, 271 -288.
48. van der Linden, W.J., & Hambleton, R.K. (Eds.) (1997). Handbook of modern item response theory. New York: Springer-Verlag.
49. Zhao, Y., & Joe, H. (2005). Composite likelihood estimation in multivariate data analysis. Canadian Journal of Statistics, 33, 335-356.