Modeling ability differentiation in the second-order factor model

Structural Equation Modeling

Volumn 18, Issue 4, 2011, Pages 578-594

  Molenaar, Dylan ^a   Dolan, Conor V ^a   van der Maas, Han L J ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Ability differentiation; Bi factor model; Heteroscedasticity; Intelligence; Marginal maximum likelihood; Nonlinear factor analysis; Nonnormality; Schmid Leiman factor analysis

Indexed keywords

EID: 84855761968     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705511.2011.607095     Document Type: Article

References (39)

1. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171-178.
2. Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica, 46, 199-208.
3. Azzalini, A., & Capatanio, A. (1999). Statistical applications of the multivariate skew normal distribution. Journal of the Royal Statistical Society Series B, 61, 579-602.
4. Azzelini, A. (1996). Statistical inference based on the likelihood. London, England: Chapman & Hall.
5. Bauer, D. J. (2005). A semiparametric approach to modeling nonlinear relations among latent variables. Structural Equation Modeling, 12, 513-535.
6. Bauer, D. J., & Hussong, A. M. (2009). Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models. Psychological Methods, 14, 101-125.
7. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
8. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
9. Buse, A. (1982). The likelihood ratio, Wald, and Lagrange multiplier tests: An expository note. American Statistician, 36, 153-157.
10. Carlstedt, B. (2001). Differentiation of cognitive abilities as a function of level of general intelligence: A latent variable approach. Multivariate Behavioral Research, 36, 589-609.
11. Deary, I. J., Egan, V., Gibson, G. J., Austin, E., Brand, C. R., & Kellaghan, T. (1996). Intelligence and the differentiation hypothesis. Intelligence, 23, 105-132.
12. Detterman, D. K., & Daniels, D. (1989). Correlations of mental tests with each other and with cognitive variables are highest for low IQ groups. Intelligence, 13, 349-359.
13. Facon, B. (2004). Are correlations between cognitive abilities highest in low-IQ groups during childhood? Intelligence, 32, 391-401.
14. García, L. F., Ruiz, M. Á., & Abad, F. J. (2003). Factor structure of the Spanish WAIS III. Psicothema, 15, 155-160.
15. Gignac, G. E. (2008). Higher-order models versus direct hierarchical models: g as superordinate or breadth factor? Psychology Science, 50, 21-43.
16. Hartmann, P., & Teasdale, T. W. (2004). A test of Spearman's "law of diminishing returns" in two large samples of Danish military draftees. Intelligence, 32, 499-508.
17. Hessen, D. J., & Dolan, C. V. (2009). Heteroscedastic one-factor models and marginal maximum likelihood estimation. British Journal of Mathematical and Statistical Psychology, 62, 57-77.
18. Holzinger, K. J., & Swineford, E (1937). The bi-factor method. Psychometrika, 2, 41-54.
19. Jensen, A. R. (1998). The g factor: The science of mental ability. Westport, CT: Praeger.
20. Jensen, A. R. (2003). Regularities in Spearman's law of diminishing returns. Intelligence, 31, 95-105.
21. Johnson, W., & Bouchard, T. J. (2004). The structure of human intelligence: It is verbal, perceptual, and image rotation (VPR), not fluid and crystallized. Intelligence, 33, 393-416.
22. Lawley, D. N. (1943). The application of the maximum likelihood method to factor analysis. British Journal of Psychology, 33, 172-175.
23. McDonald, R. P. (1967). Nonlinear factor analysis (Psychometric Monograph No. 15). Richmond, VA: William Byrd Press.
24. Mellenbergh, G. J. (1994). A unidimensional latent trait model for continuous item responses. Multivariate Behavioral Research, 29, 223-236.
25. Molenaar, D., Dolan, C. V., & Verhelst, N. D. (2010). Testing and modeling non-normality within the one factor model. British Journal of Mathematical and Statistical Psychology, 63, 293-317.
26. Muthén, B. O. (1989). Factor structure in groups selected on observed scores. British Journal of Mathematical and Statistical Psychology, 42, 81-90.
27. Muthén, L. K., & Muthén, B. O. (2007). Mplus user's guide (5th ed.). Los Angeles, CA: Muthén & Muthén.
28. Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2002). Mx: Statistical modeling (6th ed.). Richmond, VA: Author.
29. Neale, M. C., & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113-120.
30. Nesselroade, J. R., & Thompson, W. W. (1995). Selection and related threats to group comparison: An example comparing factorial structures of higher and lower ability groups of adult twins. Psychological Bulletin, 117, 271-284.
31. Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5, 554-571.
32. Reynolds, M. R., Keith, T. Z., & Beretvas, N. (2010). Use of factor mixture modeling to capture Spearman's law of diminishing returns. Intelligence, 38, 231-241.
33. Schmid, J., & Leiman, J. M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53-61.
34. Spearman, C. E. (1927). The abilities of man: Their nature and measurement. New York, NY: Macmillan.
35. Stroud, A. H., & Secrest, D. (1966). Gaussion quadrature formulas. Englewood Cliffs, NJ: Prentice-Hall.
36. Tucker-Drob, E. M. (2009). Differentiation of cognitive abilities across the life span. Developmental Psychology, 45, 1097-1118.
37. Vermunt, J. K., & Magidson, J. (2005). Technical guide for Latent GOLD 4.0: Basic and advanced. Belmont, MA: Statistical Innovations.
38. Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12, 58-79.
39. Yung, Y. F., Thissen, D., & McLeod, L. D. (1999). On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64, 113-128.