People are variables too: Multilevel structural equations modeling

Psychological Methods

Volumn 10, Issue 3, 2005, Pages 259-284

  Mehta, Paras D ^a   Neale, Michael C ^b  

^a UNIVERSITY OF HOUSTON   (United States)

^b VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

Author keywords

Mixed effects models; Multilevel modeling; Multilevel confirmatory factor analysis; Multilevel structural equations modeling; Structural equations modeling

Indexed keywords

ANALYSIS OF VARIANCE; ARTICLE; CLUSTER ANALYSIS; COMPUTER PROGRAM; HUMAN; INDIVIDUALITY; LITERATURE; MATHEMATICAL COMPUTING; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ANALYSIS OF VARIANCE; CLUSTER ANALYSIS; DATA INTERPRETATION, STATISTICAL; HUMANS; INDIVIDUALITY; MATHEMATICAL COMPUTING; METAPHOR; MODELS, STATISTICAL; SOFTWARE;

EID: 27344454846     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.10.3.259     Document Type: Article

References (72)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csake (Eds.), Second International Symposium on Information Theory (pp. 267-281). Budapest, Hungary: Akademiai Kiado.
2. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
3. Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155-173.
4. Arbuckle, J. A. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 243-277). Hillsdale, NJ: Erlbaum.
5. Bauer, D. J. (2003). Estimating multilevel linear models as structural models. Journal of Educational and Behavioral Statistics, 28, 135-167.
6. Bentler, P. M., & Liang, J. (2003). Two-level mean and covariance structures: Maximum likelihood via and EM algorithm. In S. P. Reise & N. Duan (Eds.), Multilevel modeling: Methodological advances, issues, and applications (pp. 53-70). Hillsdale, NJ: Erlbaum.
7. Bollen, K. A. (1986). Sample size and Bentler and Bonett's nonnormed fit index. Psychometrika, 51, 375-377.
8. Bollen, K. A. (1990). Overall fit in covariance structure models: Two types of sample size effects. Psychological Bulletin, 107, 256-259.
9. Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. Bollen & K. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
10. Bryk, A. S., & Raudenbush, S. W. (1987). Application of hierarchical linear models to assessing change. Psychological Bulletin, 101, 147-158.
11. Bryk, A. S., Raudenbush, S. W., Seltzer, M., & Congdon, R. (1988). An introduction to HLM: Computer program and user's guide (2nd ed.) Chicago, University of Chicago, Department of Education.
12. Chou, C.-P., Bentler, P. M., & Pentz, M. A. (1998). Comparisons of two statistical approaches to study growth curves: The multilevel model and the latent curve analysis. Structural Equation Modeling, 5, 247-266.
13. Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529-569.
14. Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory analysis. Psychological Methods, 1, 16-29.
15. Duncan, S. C., Duncan, T. E., & Hops, H. (1996). Analysis of longitudinal data within accelerated longitudinal design. Psychological Methods, 1, 236-248.
16. du Toit, S., & du Toit, M. (2003). Multilevel structural equation modeling. In J. De Leeuw & I. G. G. Kreft (Eds.), Handbook of quantitative multilevel analysis (pp. 273-321). Boston: Kluwer.
17. Eaves, L. J., Neale, M. C., & Maes, H. H. (1996). Multivariate multipoint linkage analysis of quantitative trait loci. Behavior Genetics, 26, 519-526.
18. Foorman, B., Chen, D., Carlson, C., Moats, L., Francis, D., & Fletcher, J. (2003). The necessity of the alphabetic principle to phonemic awareness instruction. Reading and Writing, 16, 289-324.
19. Fox, J.-P., & Glas, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 269-286.
20. Gerbing, D. W., & Anderson, J. C. (1993). Monte Carlo evaluations of goodness-of-fit indices, In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 40-65). Newbury Park, CA: Sage.
21. Goldstein, H. (2003). Multilevel statistical models (3rd ed.). London: Arnold.
22. Goldstein, H., & Browne, W. J. (2002). Multilevel factor analysis modelling using Markov Chain Monte Carlo (MCMC) estimation. In G. Marcoulides & I. Moustaki (Eds.), Latent variable and latent structure models (pp. 225-243). Hillsdale, NJ: Erlbaum.
23. Goldstein, H., & McDonald, R. P. (1987). A general model for the analysis of multilevel data. Psychometrika, 53, 455-467.
24. Gustafsson, J., & Balke, G. (1993). General and specific abilities as predictors of school achievement. Multivariate Behavioral Research, 28, 407-434.
25. Gustafsson, J.-E. (2002). Measurement from a hierarchical point of view. In H. I. Braun, D. N. Jackson, & D. E. Wiley (Eds.), The role of constructs in psychological and educational measurement (pp. 73-95). Hillsdale, NJ: Erlbaum.
26. Harnqvist, K., Gustafsson, J. E., Muthén, B., & Nelson, G. (1994). Hierarchical models of ability at class and individual levels. Intelligence, 18, 165-187.
27. Heck, R. (2001). Multilevel modeling with SEM. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 89-127). Hillsdale, NJ: Erlbaum.
28. Hox, J. (2002). Multilevel analysis: Techniques and applications. Hillsdale, NJ: Erlbaum.
29. Kaplan, D., & Elliot, P. R. (1997). A didactic example of multilevel structural equation modeling applicable to the study of organizations. Structural Equation Modeling, 4, 1-24.
30. Krull, J. L., & MacKinnon, D. P. (2001). Multilevel modeling of individual and group level mediated effects. Multivariate Behavioral Research, 36, 249-277.
31. Longford, N. T., & Muthén, B. (1992). Factor analysis for clustered observations. Psychometrika, 57, 581-597.
32. MacCallum, R. C., Kim, C., Malarkey, W. B., & Keicolt-Glaser, J. K. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215-253.
33. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391-410.
34. McArdle, J. J., & Anderson, E. T. (1990). Latent growth models for research on aging. In L. E. Birren & K. W. Schaie (Eds.), Handbook of the psychology of aging (3rd ed., pp. 21-44). San Diego, CA: Academic Press.
35. McArdle, J. J., & Boker, S. M. (1990). RAMpath: Path diagram software. Denver, CO: Data Transforms.
36. McDonald, R. P. (1993). A general model for two level data with responses missing at random. Psychometrika, 58, 575-585.
37. Mehta, P. D., Foorman, B. R., Branum-Martin, L., & Taylor, P. W. (2005). Literacy as a unidimensional multilevel construct: Validation, sources of influence, and implications in a longitudinal study in grades 1-4. Scientific Studies in Reading, 9, 85-116.
38. Mehta, P. D., & West, S. G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5, 23-43.
39. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
40. Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.
41. Muthén, B. (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28, 338-354.
42. Muthén, B. (1994). Multilevel covariance structure analysis [Special issue] Sociological Methods & Research, 22, 376-398.
43. Muthén, B. (1997). Latent variable modeling with longitudinal and multilevel data. In A. Raftery (Ed.), Sociological methodology (pp. 453-480). Boston: Blackwell Publishers.
44. Muthén, B., & Asparouhov, T. (2002). Modeling of heteroscedastic measurement errors (Version 1). Retrieved November 2003 from http://www.statmodel.com/mplus/examples/webnote.html
45. Muthén, B., & Asparouhov, T. (2003). Modeling interactions between latent and observed continuous variables using maximum-likelihood estimation in Mplus (Version 1). Retrieved November 2003 from http://www.statmodel.com/mplus/examples/webnote.html
46. Muthén, B., & Satorra, A. (1995). Complex sample data in structural equation modeling. In P. Marsden (Ed.), Sociological methodology (pp. 216-316). Boston: Blackwell Publishers.
47. Muthén, L. K., & Muthén, B. (2004). Mplus user's guide (3rd ed.). Los Angeles: Muthén & Muthén.
48. Neale, M. C. (1998). Modeling interaction and nonlinear effects with Mx: A general approach. In G. Marcoulides & R. Schumacker (Eds.), Interaction and non-linear effects in structural equation modeling (pp. 43-61). Hillsdale, NJ: Erlbaum.
49. Neale, M. C. (2000a). Flexible QTL mapping with Mx. In T. Spector, H. Snieder, & A. MacGregor (Eds.), Advances in twin and sib pair analysis (pp. 219-243). London: Greenwich Medical Media.
50. Neale, M. C. (2000b). Individual fit, heterogeneity, and missing data in multigroup structural equation modeling. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data: Practical issues, applied approaches and specific examples (pp. 249-267). Hillsdale, NJ: Erlbaum.
51. Neale, M. C. (2003). Quantitative genetics. In D. N. Cooper (Ed.), Encyclopedia of the human genome (pp. 679-683). London: Macmillan Publishers Ltd, Nature Publishing Group.
52. Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2004). Mx: Statistical modeling (5th ed.). Richmond: Virginia Commonwealth University, Department of Psychiatry.
53. Paxton, P., Curran, P. J., & Bollen, K. A. (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8, 287-312.
54. Rabe-Hesketh, A., Pickles, A., & Skrondal, S. (2004). GLLAMM: A general class of multilevel models and a Stata program. Multilevel Modeling Newsletter, 13, 17-23.
55. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevel structural equation modelling. Psychometrika, 69, 167-190.
56. Rasbash, J., Browne, W. J., Goldstein, H., Yang, M., Plewis, I., Healy, M., et al. (2000). A user's guide to MLwiN (Version 2.1). London: University of London, Institute of Education.
57. Raudenbush, S. W. (1995). Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm. British Journal of Mathematical and Statistical Psychology, 48, 359-370.
58. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models (2nd ed.). Newbury Park, CA: Sage.
59. Raudenbush, S. W., Rowan, B., & Kang, S. J. (1991). A multilevel, multivariate model of studying school climate with estimation via the EM algorithm and application to U. S. high school data. Journal of Educational Statistics, 16, 296-330.
60. Raudenbush, S. W., & Sampson, R. (1999). Assessing direct and indirect effects in multilevel designs with latent variables. Sociological Methods & Research, 28, 123-153.
61. Rijmen, F., Tuerlinckx, F., De Boeck, P., & Kuppens, P. (2003). A nonlinear mixed model framework for item response theory. Psychological Methods, 8, 185-205.
62. Rovine, M. J., & Molenaar, P. C. (2000). A structural modeling approach to a multilevel random coefficients model. Multivariate Behavioral Research, 35, 51-88.
63. SAS Institute. (1996). SAS/STAT software: Changes and enhancements through Release 6.11. Cary, NC: Author.
64. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461-464.
65. Silberg, J. L., Rutter, M. L., Neale, M. C., & Eaves, L. J. (2001). Genetic moderation of environmental risk for depression and anxiety in adolescent girls. British Journal of Psychiatry, 179, 116-121.
66. Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent vanable modeling: Multilevel, longitudinal and structural equation models. Boca Raton, FL: Chapman & Hill.
67. Snijders, T., & Bosker, R. (1999). Multilevel analysis: An introduction to basic and advanced multilevel modeling. Thousand Oakes, CA: Sage.
68. Spiegelhalter, D., Thomas, A., & Best, N. G. (2000). WinBugs Version 1.3 user manual. Cambridge, England: MRC Biostatistics Unit.
69. Thum, Y. M. (1997). Hierarchical linear models for multivariate outcomes. Journal of Educational and Behavioral Statistics, 22, 77-108.
70. Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer.
71. Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363-381.
72. Yang, M., Goldstein, H., Browne, W., & Woodehouse, G. (2001). Multivariate multilevel analyses of examination results. Journal of the Royal Statistical society, 163, 49-62.