Directional Dependence in the Analysis of Single Subjects

2016-04-21, 16:40:35   Wolfgang Wiedermann and Alexander von Eye
pages 20–33.
DOI: 10.17505/jpor.2016.04
Abstract: Many statistical methods applied in person-oriented research make use of theoretical principles originally derived in a variable-oriented context. From this perspective, it naturally follows that advances originated in variable-oriented methodology may potentially contribute to the development of methods suitable for person-oriented perspectives. Direction Dependence Analysis (DDA) constitutes one of these recent advances and provides a framework to statistically evaluate asymmetric properties of observed variable relations. These asymmetric properties enable researchers to make statements whether a model of the form x ! y or a model assuming y ! x is more likely to approximate the underlying data-generating process in non-experimental settings. The present article introduces DDA to the context of person-oriented research and extends the DDA principle to (linear) vector autoregressive models (VAR) which can be used to describe individual development. We show that DDA can be used to empirically evaluate directional theories of (potentially multivariate) intraindividual development (e.g., which of two longitudinally observed variables is more likely to be the explanatory variable and which one is more likely to reflect the outcome). An illustrative example is provided from a study on the development of experienced mood and alcohol consumption behavior. It is demonstrated that VAR-DDA resolves the issue of identifying the direction of contemporaneous effects in longitudinal data. Temporality issues of directional theories used to explain intraindividual development, guidelines to achieve acceptable power, methodological requirements, and potential further extensions of DDA for person-oriented research are discussed.
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Keywords: Direction dependence, vector autoregressive model, single-subject data, intensive longitudinal data, nonnormality
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