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A new sample-size planning approach for person-specific VAR(1) studies: Predictive accuracy analysis

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Researchers increasingly study short-term dynamic processes that evolve within single individuals using N = 1 studies. The processes of interest are typically captured by fitting a VAR(1) model to the resulting data. A crucial question is how to perform sample-size planning and thus decide on the number of measurement occasions that are needed. The most popular approach is to perform a power analysis, which focuses on detecting the effects of interest. We argue that performing sample-size planning based on out-of-sample predictive accuracy yields additional important information regarding potential overfitting of the model. Predictive accuracy quantifies how well the estimated VAR(1) model will allow predicting unseen data from the same individual. We propose a new simulation-based sample-size planning method called predictive accuracy analysis (PAA), and an associated Shiny app. This approach makes use of a novel predictive accuracy metric that accounts for the multivariate nature of the prediction problem. We showcase how the values of the different VAR(1) model parameters impact power and predictive accuracy-based sample-size recommendations using simulated data sets and real data applications. The range of recommended sample sizes is smaller for predictive accuracy analysis than for power analysis.

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  1. We used the following packages: DataFrames (version 1.6.1), DataTables (version 0.1.0), DataAPI (version 1.1.0), CSV (version 0.10.12) to handle the data; LinearAlgebra (version 0.5.1), GLM (version 1.9.0), HypothesisTests (version 0.11.0), StatsBase (version 0.34.2) to estimate the model and extract the estimated parameters; Distributions (version 0.25.107) and Distances (version 0.10.11) to handle statistical distributions.

  2. When generating (V)AR(1) time series, we have to use starting values, that is, the variable scores at the first time point. To remove the influence of these starting values, we removed the first 1000 time points (known as the burn-in phase).


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The research presented in this article was supported by research grants from the Fund for Scientific Research-Flanders (FWO; Project No. G0C9821N) and from the Research Council of KU Leuven (C14/23/062; iBOF/21/090) awarded to E. Ceulemans.

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The authors made the following contributions. Jordan Revol: Conceptualization, Formal Analysis, Methodology, Visualization, Software, Writing - Original Draft Preparation, Review & Editing; Ginette Lafit: Conceptualization, Methodology, Supervision, Writing - Original Draft Preparation, Review & Editing. Eva Ceulemans: Conceptualization, Methodology, Funding acquisition, Supervision, Writing - Original Draft Preparation, Review & Editing.

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Correspondence to Jordan Revol.

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Revol, J., Lafit, G. & Ceulemans, E. A new sample-size planning approach for person-specific VAR(1) studies: Predictive accuracy analysis. Behav Res (2024).

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