Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time

Kim De Roover*, Marieke E. Timmerman, Ilse Van Diest, Patrick Onghena, Eva Ceulemans

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Downloads (Pure)

Abstract

Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.

Original languageEnglish
Pages (from-to)113-132
Number of pages20
JournalPsychological Methods
Volume19
Issue number1
DOIs
Publication statusPublished - Mar 2014
Externally publishedYes

Keywords

  • principal component analysis
  • multivariate time series data
  • time contiguity
  • segmentation
  • dimensionality
  • HIDDEN MARKOV-MODELS
  • DYNAMIC FACTOR MODEL
  • LONGITUDINAL DATA
  • STATISTICAL-METHODS
  • GROWTH-CURVES
  • MULTIVARIATE
  • EMOTION
  • SERIES
  • SYSTEMS
  • SUBJECT

Cite this

De Roover, Kim ; Timmerman, Marieke E. ; Van Diest, Ilse ; Onghena, Patrick ; Ceulemans, Eva. / Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time. In: Psychological Methods. 2014 ; Vol. 19, No. 1. pp. 113-132.
@article{f46fd9f8107649c49fa4ffce18c9ca46,
title = "Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time",
abstract = "Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.",
keywords = "principal component analysis, multivariate time series data, time contiguity, segmentation, dimensionality, HIDDEN MARKOV-MODELS, DYNAMIC FACTOR MODEL, LONGITUDINAL DATA, STATISTICAL-METHODS, GROWTH-CURVES, MULTIVARIATE, EMOTION, SERIES, SYSTEMS, SUBJECT",
author = "{De Roover}, Kim and Timmerman, {Marieke E.} and {Van Diest}, Ilse and Patrick Onghena and Eva Ceulemans",
year = "2014",
month = "3",
doi = "10.1037/a0034525",
language = "English",
volume = "19",
pages = "113--132",
journal = "Psychological Methods",
issn = "1082-989X",
publisher = "AMER PSYCHOLOGICAL ASSOC",
number = "1",

}

Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time. / De Roover, Kim; Timmerman, Marieke E.; Van Diest, Ilse; Onghena, Patrick; Ceulemans, Eva.

In: Psychological Methods, Vol. 19, No. 1, 03.2014, p. 113-132.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time

AU - De Roover, Kim

AU - Timmerman, Marieke E.

AU - Van Diest, Ilse

AU - Onghena, Patrick

AU - Ceulemans, Eva

PY - 2014/3

Y1 - 2014/3

N2 - Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.

AB - Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.

KW - principal component analysis

KW - multivariate time series data

KW - time contiguity

KW - segmentation

KW - dimensionality

KW - HIDDEN MARKOV-MODELS

KW - DYNAMIC FACTOR MODEL

KW - LONGITUDINAL DATA

KW - STATISTICAL-METHODS

KW - GROWTH-CURVES

KW - MULTIVARIATE

KW - EMOTION

KW - SERIES

KW - SYSTEMS

KW - SUBJECT

U2 - 10.1037/a0034525

DO - 10.1037/a0034525

M3 - Article

VL - 19

SP - 113

EP - 132

JO - Psychological Methods

JF - Psychological Methods

SN - 1082-989X

IS - 1

ER -