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Autoregressive Latent Trajectory (ALT) Models A Synthesis of Two Traditions

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  • Kenneth A. Bollen
  • Patrick J. Curran

Abstract

Although there are a variety of statistical methods available for the analysis of longitudinal panel data, two approaches are of particular historical importance: the autoregressive (simplex) model and the latent trajectory (curve) model. These two approaches have been portrayed as competing methodologies such that one approach is superior to the other. We argue that the autoregressive and trajectory models are special cases of a more encompassing model that we call the autoregressive latent trajectory (ALT) model. In this paper we detail the underlying statistical theory and mathematical identification of this model, and demonstrate the ALT model using two empirical data sets. The first reanalyzes a simulated repeated measures data set that was previously used to argue against the autoregressive model, and we illustrate how the ALT model can recover the true latent curve model. Second, we apply the ALT model to real family income data on N=3912 adults over a seven year period and find evidence for both autoregressive and latent trajectory processes. Extensions and limitations are discussed.

Suggested Citation

  • Kenneth A. Bollen & Patrick J. Curran, 2004. "Autoregressive Latent Trajectory (ALT) Models A Synthesis of Two Traditions," Sociological Methods & Research, , vol. 32(3), pages 336-383, February.
    • Handle: RePEc:sae:somere:v:32:y:2004:i:3:p:336-383
    DOI: 10.1177/0049124103260222
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    5. Marc J. M. H. Delsing & Johan H. L. Oud, 2008. "Analyzing reciprocal relationships by means of the continuous‐time autoregressive latent trajectory model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 58-82, February.
    6. Areti Gkypali & Kostas Kounetas & Kostas Tsekouras, 2019. "European countries’ competitiveness and productive performance evolution: unraveling the complexity in a heterogeneity context," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 665-695, April.
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    9. Santos, David Ferreira Lopes & Basso, Leonardo Fernando Cruz & Kimura, Herbert, 2018. "The trajectory of the ability to innovate and the financial performance of the Brazilian industry," Technological Forecasting and Social Change, Elsevier, vol. 127(C), pages 258-270.

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