A Diagnostic Procedure for Detecting Outliers in Linear State–Space Models

Abstract

Outliers can be more problematic in longitudinal data than in independent observations due to the correlated nature of such data. It is common practice to discard outliers as they are typically regarded as a nuisance or an aberration in the data. However, outliers can also convey meaningful information concerning potential model misspecification, and ways to modify and improve the model. Moreover, outliers that occur among the latent variables (innovative outliers) have distinct characteristics compared to those impacting the observed variables (additive outliers), and are best evaluated with different test statistics and detection procedures. We demonstrate and evaluate the performance of an outlier detection approach for multi-subject state-space models in a Monte Carlo simulation study, with corresponding adaptations to improve power and reduce false detection rates. Furthermore, we demonstrate the empirical utility of the proposed approach using data from an ecological momentary assessment study of emotion regulation together with an open-source software implementation of the procedures.

Keywords:

• outlier detection
• state space model
• innovative outlier
• additive outlier

Acknowledgments

The authors would like to thank various colleagues and students in the QuantDev group of Penn State for valuable comments on earlier drafts of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions or the funding agencies is not intended and should not be inferred. Correspondence concerning this article can be addressed to Sy-Miin Chow, the Pennsylvania State University, 409 Biobehavioral Health Building, University Park, PA 16802 or by email to [email protected].

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 Conceptually, the chi-square test statistics may be viewed as a way to perform likelihood ratio comparisons between the null model in Equations (1)–(3) and the alternative shock model in Equations (9)–(10) that includes the estimated innovative and additive outliers. Thus each ${\rho }_{\mathit{it}}^{*2}$ is akin to a likelihood ratio test. Assuming independence of each ${\rho }_{\mathit{it}}^{*2},$ the sum of them is then a joint likelihood ratio test.