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Modeling Trajectories and Time Series

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Modern Psychometrics with R

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Abstract

This chapter presents various modeling options for trajectories and time series. The first part covers hidden Markov models where the aim is to find latent states between which a participant can switch back and forth during an experimental task. Extended modeling options in terms of including covariates are presented as well. The second part introduces time series analysis. The main focus is on a parametric model class called ARIMA, representing a flexible regression framework for time series able to handle autocorrelated residuals. As a special ARIMA flavor, intervention analysis is presented which allows researchers to study whether a critical event had an impact on the series or not. The third part covers functional data analysis, applicable to data settings where each individual produces its own trajectory, subject to smoothing. In addition to functional regression modeling, a functional version of principal component analysis is presented.

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Notes

  1. 1.

    We omit any positive feelings here since this is simply not realistic.

  2. 2.

    See https://implicit.harvard.edu/; data are publicly available on https://osf.io/y9hiq/.

  3. 3.

    The SMA function in TTR (Ulrich, 2017) can be used for decomposition nonseasonal data.

  4. 4.

    Instead of decompose the stl function can be used which provides additional decomposition options.

  5. 5.

    For simplicity in notation, let us ignore for the moment that we differenced the time series and write y t instead of yt′.

  6. 6.

    Note that the first value in the correlogram is the lag-0 correlation which is of course 1 and can be ignored.

  7. 7.

    Note the similarity of this equation to the classical true score model in the first chapter.

  8. 8.

    A simplified version of this plot can be produced via summary( fpca) .

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Authors and Affiliations

  1. Department of Psychology, Harvard University, Cambridge, MA, USA

    Patrick Mair

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  1. Patrick Mair
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Mair, P. (2018). Modeling Trajectories and Time Series. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_13

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