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

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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.