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Conditions for the Equivalence of the Autoregressive Latent Trajectory Model and a Latent Growth Curve Model With Autoregressive Disturbances

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  • Ellen L. Hamaker

    (University of Amsterdam)

Abstract

Curran and Bollen combined two models for longitudinal panel data: the latent growth curve model and the autoregressive model. In their model, the autoregressive relationships are modeled between the observed variables. This is a different model than a latent growth curve model with autoregressive relationships between the disturbances. However, when the autoregressive parameter is invariant over time and lies between-1 and 1, it can be shown that these models are algebraically equivalent. This result can be shown to generalize to the multivariate case. When the autoregressive parameters in the autoregressive latent trajectory model vary over time, the equivalence between the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances no longer holds. However, a latent growth curve model with time-varying autoregressive parameters for the disturbances could be considered an interesting alternative to the autoregressive latent trajectory model with time-varying autoregressive parameters.

Suggested Citation

  • Ellen L. Hamaker, 2005. "Conditions for the Equivalence of the Autoregressive Latent Trajectory Model and a Latent Growth Curve Model With Autoregressive Disturbances," Sociological Methods & Research, , vol. 33(3), pages 404-416, February.
    • Handle: RePEc:sae:somere:v:33:y:2005:i:3:p:404-416
    DOI: 10.1177/0049124104270220
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    References listed on IDEAS

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    1. Lloyd Humphreys, 1960. "Investigations of the simplex," Psychometrika, Springer;The Psychometric Society, vol. 25(4), pages 313-323, December.
    2. William Meredith & John Tisak, 1990. "Latent curve analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 107-122, March.
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    1. Anand, Paul & Behrman, Jere R. & Dang, Hai-Anh H. & Jones, Sam, 2018. "Varied patterns of catch-up in child growth: Evidence from Young Lives," Social Science & Medicine, Elsevier, vol. 214(C), pages 206-213.
    2. Halleröd, Björn & Gustafsson, Jan-Eric, 2011. "A longitudinal analysis of the relationship between changes in socio-economic status and changes in health," Social Science & Medicine, Elsevier, vol. 72(1), pages 116-123, January.
    3. 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.
    4. 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.

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