Modeling latent growth with multiple indicators: A comparison of three approaches

Psychological Methods

Volumn 20, Issue 1, 2015, Pages 43-62

  Bishop, Jacob ^a   Geiser, Christian ^a   Cole, David A ^b  

^a UTAH STATE UNIVERSITY   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Latent state trait theory; Measurement invariance; Multiple indicator latent growth curve models; Proportionality constraint; Second order growth curve models

Indexed keywords

COMPARATIVE STUDY; HUMAN; PSYCHOLOGICAL MODEL; STATISTICAL MODEL;

HUMANS; MODELS, PSYCHOLOGICAL; MODELS, STATISTICAL;

EID: 84926393458     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/met0000018     Document Type: Article

References (59)

1. Arnett, J. J. (2000). Emerging adulthood: A theory of development from the late teens through the twenties. American Psychologist, 55, 469-480. doi:10.1037/0003-066X.55.5.469
2. Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley-Interscience.
3. Byrne, B., Shavelson, R., & Muthén, B. (1989). Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin, 105, 456-466. doi:10.1037/0033-2909.105.3.456
4. Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach incorporating longitudinal mean and covariance structures analysis (LMACS) and multiple indicator latent growth modeling (MLGM). Organizational Research Methods, 1, 421-483. doi: 10.1177/109442819814004
5. Cheung, G. W., & Rensvold, R. B. (1999). Testing factorial invariance across groups: A reconceptualization and proposed new method. Journal of Management, 25, 1-27. doi:10.1177/014920639902500101
6. Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9, 233-255. doi:10.1207/S15328007SEM0902_5
7. Conway, J. M., Lievens, F., Scullen, S. E., & Lance, C. E. (2004). Bias in the correlated uniqueness model for MTMM data. Structural Equation Modeling, 11, 535-559. doi:10.1207/s15328007sem1104_3
8. Deinzer, R., Steyer, R., Eid, M., Notz, P., Schwenkmezger, P., Ostendorf, F., & Neubauer, A. (1995). Situational effects in trait assessment: The FPI, NEOFFI, and EPI questionnaires. European Journal of Personality, 9, 1-23. doi:10.1002/per.2410090102
9. Duncan, S. C., & Duncan, T. E. (1996). A multivariate latent growth curve analysis of adolescent substance use. Structural Equation Modeling, 3, 323-347. doi:10.1080/10705519609540050
10. Duncan, T. E., Duncan, S. C., & Strycker, L. A. (2006). An introduction to latent variable growth curve modeling: Concepts, issues, and applications. (2nd ed.). Mahwah, NJ: Erlbaum.
11. Eid, M. (1996). Longitudinal confirmatory factor analysis for polytomous item responses: Model definition and model selection on the basis of stochastic measurement theory. Methods of Psychological Research Online, 1, 65-85.
12. Eid, M., Courvoisier, D. S., & Lischetzke, T. (2012). Structural equation modeling of ambulatory assessment data. In M. R. Mehl & T. S. Connor (Eds.), Handbook of research methods for studying daily life (pp. 384-406). New York, NY: Guilford Press.
13. Eid, M., & Hoffmann, L. (1998). Measuring variability and change with an item response model for polytomous variables. Journal of Educational and Behavioral Statistics, 23, 193-215. doi:10.3102/10769986023003193
14. Enders, C. (2010). Applied missing data analysis. New York, NY: Guilford Press.
15. Ferrer, E., Balluerka, N., & Widaman, K. (2008). Factorial invariance and the specification of second-order latent growth models. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 4, 22-36. doi:10.1027/1614-2241.4.1.22
16. Geiser, C. (2013). Data analysis with Mplus. New York, NY: Guilford Press.
17. Geiser, C., Eid, M., & Nussbeck, F. W. (2008). On the meaning of the latent variables in the CT-C(M-1) model: A comment on Maydeu-Olivares and Coffman (2006). Psychological Methods, 13, 49-57. doi: 10.1037/1082-989X.13.1.49
18. Geiser, C., Eid, M., Nussbeck, F. W., Courvoisier, D. S., & Cole, D. A. (2010). Multitrait-multimethod change modelling. AStA-Advances in Statistical Analysis, 94, 185-201.
19. Geiser, C., Keller, B., & Lockhart, G. (2013). First versus second order latent growth curve models: Some insights from latent state-trait theory. Structural Equation Modeling, 20, 479-503. doi:10.1080/10705511.2013.797832
20. Geiser, C., & Lockhart, G. (2012). A comparison of four approaches to account for method effects in latent state-trait analyses. Psychological Methods, 17, 255-283. doi:10.1037/a0026977
21. Grimm, K. J., Pianta, R. C., & Konold, T. (2009). Longitudinal multitrait-multimethod models for developmental research. Multivariate Behavioral Research, 44, 233-258. doi:10.1080/00273170902794230
22. Hale, W. W., III, Raaijmakers, Q., Muris, P., van Hoof, A., & Meeus, W. (2008). Developmental trajectories of adolescent anxiety disorder symptoms: A 5-year prospective community study. Journal of the American Academy of Child & Adolescent Psychiatry, 47, 556-564. doi:10.1097/CHI.0b013e3181676583
23. Hall, R., Snell, A., & Foust, M. (1999). Item parceling strategies in SEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods, 2, 233-256. doi:10.1177/109442819923002
24. Hancock, G., Kuo, W., & Lawrence, F. (2001). An illustration of secondorder latent growth models. Structural Equation Modeling, 8, 470-489. doi:10.1207/S15328007SEM0803_7
25. Hertzog, C., & Nesselroade, J. R. (1987). Beyond autoregressive models: Some implications of the trait-state distinction for the structural modeling of developmental change. Child Development, 58, 93-109. doi: 10.2307/1130294
26. Kelley, A. E., Schochet, T., & Landry, C. F. (2004). Risk taking and novelty seeking in adolescence: Introduction to Part I. Annals of the New York Academy of Sciences, 1021, 27-32. doi:10.1196/annals.1308.003
27. Kenny, D. A. (1976). An empirical application of confirmatory factor analysis to the multitrait-multimethod matrix. Journal of Experimental Social Psychology, 12, 247-252. doi:10.1016/0022-1031(76)90055-X
28. Lance, C. E., Noble, C. L., & Scullen, S. E. (2002). A critique of the correlated trait-correlated method and correlated uniqueness models for multitrait-multimethod data. Psychological Methods, 7, 228-244. doi: 10.1037/1082-989X.7.2.228
29. Leite, W. L. (2007). A comparison of latent growth models for constructs measured by multiple items. Structural Equation Modeling, 14, 581-610. doi:10.1080/10705510701575438
30. Little, T. D. (2013). Longitudinal structural equation modeling. New York, NY: Guilford Press.
31. Marsh, H. W. (1989). Confirmatory factor analyses of multitrait-multimethod data: Many problems and a few solutions. Applied Psychological Measurement, 13, 335-361. doi:10.1177/014662168901300402
32. Mayer, A., Geiser, C., Infurna, F. J., & Fiege, C. (2013). Modelling and predicting complex patterns of change using growth component models: An application to depression trajectories in cancer patients. European Journal of Developmental Psychology, 10, 40-59. doi:10.1080/17405629.2012.732721
33. Mayer, A., Steyer, R., & Mueller, H. (2012). A general approach to defining latent growth components. Structural Equation Modeling, 19, 513-533. doi:10.1080/10705511.2012.713242
34. McArdle, J. J. (1980). Causal modeling applied to psychonomic systems simulation. Behavior Research Methods & Instrumentation, 12, 193-209. doi:10.3758/BF03201598
35. McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In J. Nesselroade & R. Cattell (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 561-614). doi: 10.1007/978-1-4613-0893-5_17
36. McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110-133. doi:10.2307/1130295
37. Mehta, P. D., & West, S. G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5, 23-43. doi: 10.1037/1082-989X.5.1.23
38. Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58, 525-543. doi:10.1007/BF02294825
39. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122. doi:10.1007/BF02294746
40. Millsap, R. (2011). Statistical approaches to measurement invariance. New York, NY: Routledge.
41. Millsap, R. E., & Kwok, O.-M. (2004). Evaluating the impact of partial factorial invariance on selection in two populations. Psychological Methods, 9, 93-115. doi:10.1037/1082-989X.9.1.93
42. Muthén, L., & Muthén, B. (1998-2012). Mplus user's guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
43. Novick, M. R. (1966). The axioms and principal results of classical test theory. Journal of Mathematical Psychology, 3, 1-18. doi:10.1016/0022-2496(66)90002-2
44. Raykov, T. (1993). A structural equation model for measuring residualized change and discerning patterns of growth or decline. Applied Psychological Measurement, 17, 53-71. doi:10.1177/014662169301700110
45. Reynolds, C. R., & Richmond, B. O. (1978). What I think and feel: A revised measure of children's manifest anxiety. Journal of Abnormal Child Psychology, 6, 271-280. doi:10.1007/BF00919131
46. Sayer, A. G., & Cumsille, P. E. (2001). Second-order latent growth curve models. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 179-200). doi:10.1037/10409-006
47. Schmid, J., & Leiman, J. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53-61. doi:10.1007/BF02289209
48. Schmiedek, F., & Li, S. (2004). Toward an alternative representation for disentangling age-associated differences in general and specific cognitive abilities. Psychology and Aging, 19, 40-56. doi:10.1037/0882-7974.19.1.40
49. Steyer, R., Eid, M., & Schwenkmezger, P. (1997). Modeling true intraindividual change: True change as a latent variable. Methods of Psychological Research Online, 2, 21-33.
50. Steyer, R., Ferring, D., & Schmitt, M. (1992). States and traits in psychological assessment. European Journal of Psychological Assessment, 8, 79-98.
51. Steyer, R., Geiser, C., Cole, D. A., & Mayer, A. (in press). A theory of states and traits: Revised. Annual Review of Clinical Psychology.
52. Steyer, R., Krambeer, S., & Hannöver, W. (2004). Modeling latent traitchange. In K. V. Montfort, H. Oud, & A. Satorra (Eds.), Recent developments on structural equation modeling: Theory and applications (pp. 337-357). doi:10.1007/978-1-4020-1958-6_16
53. Steyer, R., Partchev, I., & Shanahan, M. J. (2000). Modeling true intraindividual change in structural equation models: The case of poverty and children's psychosocial adjustment. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples (pp. 109-126). Mahwah, NJ: Erlbaum.
54. Stoel, R. D., Garre, F. G., Dolan, C., & van den Wittenboer, G. (2006). On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods, 11, 439-455. doi:10.1037/1082-989X.11.4.439
55. Tisak, J., & Tisak, M. S. (2000). Permanency and ephemerality of psychological measures with application to organizational commitment. Psychological Methods, 5, 175-198. doi:10.1037/1082-989X.5.2.175
56. Van Oort, F. V. A., Greaves-Lord, K., Verhulst, F. C., Ormel, J., & Huizink, A. C. (2009). The developmental course of anxiety symptoms during adolescence: The TRAILS study. Journal of Child Psychology and Psychiatry, 50, 1209-1217. doi:10.1111/j.1469-7610.2009.02092.x
57. von Oertzen, T., Hertzog, C., Lindenberger, U., & Ghisletta, P. (2010). The effect of multiple indicators on the power to detect inter-individual differences in change. British Journal of Mathematical and Statistical Psychology, 63, 627-646. doi:10.1348/000711010X486633
58. Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance of psychological instruments: Applications in the substance use domain. In K. Bryant, M. Windle, & S. West (Eds.), The science of prevention: Methodological advances from alcohol and substance abuse research (pp. 281-324). doi:10.1037/10222-009
59. Yung, Y., Thissen, D., & McLeod, L. (1999). On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64, 113-128. doi:10.1007/BF02294531