An Overview of the Autoregressive Latent Trajectory (ALT) Model
Autoregressive cross-lagged models and latent growth curve models are frequently applied to longitudinal or panel data. Though often presented as distinct and sometimes competing methods, the Autoregressive Latent Trajectory (ALT) model (Bollen and Curran, 2004) combines the primary features of each into a single model. This chapter: (1) presents the ALT model, (2) describes the situations when this model is appropriate, (3) provides an empirical example of the ALT model, and (4) gives the reader the input and output from an ALT model run on the empirical example. It concludes with a discussion of the limitations and extensions of the ALT model. Our focus is on repeated measures of continuous variables.
KeywordsGrowth Curve Model Full Information Maximum Likelihood Random Slope Random Intercept Autoregressive Parameter
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Kenneth Bollen gratefully acknowledges the support from NSF SES 0617276 from NIDA 1-RO1-DA13148-01 & DA013148-05A2. We thank the editors and reviewers for valuable comments and thank Shawn Bauldry for research assistance.
- Anderson, T. W. (1960). Some stochastic process models for intelligence test scores. In K. J. Arrow, S. Karlin, & P. Suppes (Eds.), Mathematical methods in the social sciences. Stanford, CA: Stanford University Press.Google Scholar
- Bollen, K. A. (1989a). Structural equation models with latent variables. New York: Wiley.Google Scholar
- Bollen, K. A. (2007). On the origins of latent curve models. In R. Cudeck & R. MacCallum (Eds.), Factor analysis at 100 (pp. 79-98). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Bollen, K. A., & Long, J. Scott. (1993). Testing structural equation models. Newbury Park, CA: Sage Publications.Google Scholar
- Bollen, K. A., & Stine, R. A. (1993). Bootstrapping goodness-of-fit measures in structural equation models. In K. A. Bollen & J. Scott Long (Eds.), Testing structural equation models (pp. 111-135). Newbury Park, CA: Sage Publications.Google Scholar
- Boyd, J. L. (2007). Developmental and situational factors contributing to changes in eating behavior in first-year undergraduate women. Master of Arts in Psychology. University of Waterloo, Canada.Google Scholar
- Campbell, D. T. (1963). From description to experimentation: Interpreting trends as quasiexperiments. In C. W. Harris (Ed.), Problems in measuring change (pp. 212-242). Madison, WI: University of Wisconsin Press.Google Scholar
- Curran, P. J., & Bollen, K. A. (2001). The bests of both worlds: Combining autoregressive and latent curve models. In Collins L. M. & Sayar, A.G. (Eds.), New methods for the analysis of change (pp. 105-136). Washington, D.C.: American Psychological Association.Google Scholar
- Diggle, P. J., Liang, K. Y., & Zeger, S. L. (1994). Analysis of longitudinal data. Oxford: Clarendon Press.Google Scholar
- Jöreskog, K. G. (1979). Statistical models and methods for analysis of longitudinal data. In K. G. Jöreskog & D. Sörbom (Eds.), Advances in factor analysis and structural equation models. Cambridge, Mass: Abt.Google Scholar
- Meredith, W., & Tisak, J. (1984). Tuckerizing curves. Paper presented at the annual meeting of the Psychometric Society, Santa Barbara, CA.Google Scholar
- Muthén, L. K. & Muthén, B. O. (1998-2007). Mplus User’s Guide (5th ed.). Los Angeles: Muthén & Muthén.Google Scholar
- Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrika, 51, 83-90.Google Scholar
- Satorra, A., & Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. Proceedings of the American Statistical Association, 308-313.Google Scholar
- Steiger, J. H., & Lind, J. M. (1980). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.Google Scholar