Comparing the fit of item response theory and factor analysis models

Structural Equation Modeling

Volumn 18, Issue 3, 2011, Pages 333-356

  Maydeu Olivares, Alberto ^a   Cai, Li ^b   Hernández, Adolfo ^c  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Approximate fit; Attitudes; Categorical data analysis; Goodness of fit; Ordinal factor analysis; Personality; Samejima's graded model; Structural equation modeling

Indexed keywords

EID: 79960670080     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705511.2011.581993     Document Type: Article

References (52)

1. Aptech Systems, Inc. (2003). GAUSS (version 6.0.8) [Computer program]. Maple Valley, WA: Author.
2. Bartholomew, D. J., & Knott, M. (1999). Latent variable models and factor analysis (2nd ed.). London, UK: Arnold.
3. Bartholomew, D. J., & Leung, S. O. (2002). A goodness of fit test for sparse 2p 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. Sociological Methods and Research, 27, 525-546.
5. Bentler, P. M. (2004). EQS 6 [Computer program]. Encino, CA: Multivariate Software.
6. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
7. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
8. Bolt, D. (2005). Limited vs. full information estimation in IRT modeling. In A. Maydeu-Olivares & J. McArdle (Eds.), Contemporary psychometrics: A festschirft to Roderick P. McDonald (pp. 27-72). Mahwah, NJ: Lawrence Erlbaum Associates.
9. Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72-141). Cambridge, UK: Cambridge University Press.
10. Browne, M. W. (1984). Asymptotically distribution free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
11. Browne, M. W., & Arminger, G. (1995). Specification and estimation of mean and covariance structure models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-249). New York, NY: Plenum.
12. Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
13. Cai, L., Maydeu-Olivares, A., Coffman, D. L., & Thissen, D. (2006). Limited information goodness of fit testing of item response theory models for sparse 2p tables. British Journal of Mathematical and Statistical Psychology, 59, 173-194.
14. Chernyshenko, O. S., Stark, S., Chan, K.-Y., Drasgow, F., & Williams, B. (2001). Fitting item response theory models to two personality inventories: Issues and insights. Multivariate Behavioral Research, 36, 523-562.
15. Cochran, W. G. (1952). The {pipe}2 test of goodness of fit. Annals of Mathematical Statistics, 23, 315-345.
16. Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to non-normality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.
17. Diener, E., Emmons, R. A., Larsen, R. J., & Griffin, S. (1985). The Satisfaction with Life Scale. Journal of Personality Assessment, 49, 71-75.
18. 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.
19. Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum Associates.
20. Eysenck, S. B. G., Eysenck, H. J., & Barrett, P. T. (1985). A revised version of the Psychoticism scale. Personality and Individual Differences, 6, 21-29.
21. Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston, MA: Kluwer Academic.
22. Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage.
23. Hulin, C. L., Drasgow, F., & Parsons, C. K. (1983). Item response theory. Homewood, IL: Dow Jones-Irwin.
24. Jöreskog, K. G., & Sörbom, D. (2008). LISREL 8 [Computer program]. Chicago, IL: Scientific Software.
25. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
26. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
27. Maydeu-Olivares, A. (2005a). Further empirical results on parametric vs. non-parametric IRT modeling of Likert-type personality data. Multivariate Behavioral Research, 40, 275-293.
28. Maydeu-Olivares, A. (2005b). Linear IRT, non-linear IRT, and factor analysis: A unified framework. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary psychometrics: A festschrift to Roderick P. McDonald (pp. 73-100). Mahwah, NJ: Lawrence Erlbaum Associates.
29. Maydeu-Olivares, A. (2006). Limited information estimation and testing of discretized multivariate normal structural models. Psychometrika, 71, 57-77.
30. Maydeu-Olivares, A., García-Forero, C., Gallardo-Pujol, D., & Renom, J. (2009). Testing categorized bivariate normality with two-stage polychoric correlation estimates. Methodology, 5, 131-136.
31. Maydeu-Olivares, A., & Joe, H. (2005). Limited and full information estimation and testing in 2n contingency tables: A unified framework. Journal of the American Statistical Association, 100, 1009-1020.
32. Maydeu-Olivares, A., & Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables. Psychometrika, 71, 713-732.
33. McDonald, R. P. (1999). Test theory: A unified approach. Mahwah, NJ: Lawrence Erlbaum Associates.
34. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
35. Muthén, B. O. (1993). Goodness of fit with categorical and other non normal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205-234). Newbury Park, CA: Sage.
36. Muthén, B. O., & 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.
37. Muthén, L., & Muthén, B. O. (1998-2010). Mplus 6 [Computer program]. Los Angeles, CA: Muthén & Muthén.
38. Reise, S. P., & Waller, N. G. (1990). Fitting the two-parameter model to personality data. Applied Psychological Measurement, 14, 45-58.
39. Reiser, M. (1996). Analysis of residuals for the multinomial item response model. Psychometrika, 61, 509-528.
40. Reiser, M. (2008). Goodness-of-fit testing using components based on marginal frequencies of multinomial data. British Journal of Mathematical and Statistical Psychology, 61, 331-360.
41. Rubin, D. B., & Thayer, D. T. (1982). EM algorithms for ML factor analysis. Psychometrika, 47, 69-76.
42. Samejima, F. (1969). Calibration of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, No. 17.
43. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications to developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
44. Steiger, J. H., & Lind, J. M. (1980, May). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
45. Takane, Y., & de Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
46. Thissen, D., Chen, W. H., & Bock, D. (2003). MULTILOG 7 [Computer program]. Chicago, IL: SSI International.
47. Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567-577.
48. Thissen, D., & Steinberg, L. (1997). A response model for multiple-choice items. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 51-66). New York, NY: Springer Verlag.
49. van der Linden, W. J., & Hambleton, R. K. (1997). Handbook of modern item response theory. New York, NY: Springer Verlag.
50. Waller, N. G., Tellegen, A., McDonald, R. P., & Likken, D. T. (1996). Exploring non-linear models in personality research: Development and preliminary validation of a negative emotionality scale. Journal of Personality, 64, 545-576.
51. Yuan, K.-H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92, 767-774.
52. Yuan, K.-H., & Bentler, P. M. (1999). F tests for mean and covariance structure analysis. Journal of Educational and Behavioral Statistics, 24, 225-243.