Assessing an Alternative for “Negative Variance Components”: A Gentle Introduction to Bayesian Covariance Structure Modeling for Negative Associations Among Patients With Personalized Treatments

Jean Paul Fox*, Wouter A.C. Smink

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
7 Downloads (Pure)

Abstract

The multilevel model (MLM) is the popular approach to describe dependences of hierarchically clustered observations. A main feature is the capability to estimate (cluster-specific) random effect parameters, whiletheir distribution describes the variation across clusters. However, the MLMcan only model positive associationsamong clustered observations, and it is not suitable for small sample sizes. The limitation of the MLMbecomes apparent when estimation methods produce negative estimates for random effect variances, whichcan be seen as an indication that observations are negatively correlated.A gentle introduction to Bayesian covariancestructure modeling (BCSM) is given, which makes it possible to model also negatively correlatedobservations. The BCSMdoes notmodel dependences through random (cluster-specific) effects, but througha covariance matrix. We show that this makes the BCSM particularly useful for small data samples. Wedraw specific attention to detect effects of a personalized intervention. The effect of a personalized treatmentcan differ across individuals, and this can lead to negative associations among measurements of individualswho are treated by the same therapist. It is shown that the BCSM enables the modeling of negative associationsamong clustered measurements and aids in the interpretation of negative clustering effects. Through asimulation study and by analysis of a real data example, we discuss the suitability of the BCSM for smalldata sets and for exploring effects of individualized treatments, specifically when (standard)MLM softwareproduces negative or zero variance estimates

Original languageEnglish
JournalPsychological methods
DOIs
Publication statusE-pub ahead of print/First online - 20 Dec 2021

Keywords

  • Bayesian covariance structure modeling (bcsm)
  • Individualized treatment
  • Multilevel modeling
  • Negative clustering effects
  • Negative variance estimates
  • 22/1 OA procedure

Fingerprint

Dive into the research topics of 'Assessing an Alternative for “Negative Variance Components”: A Gentle Introduction to Bayesian Covariance Structure Modeling for Negative Associations Among Patients With Personalized Treatments'. Together they form a unique fingerprint.

Cite this