Principal Covariates Clusterwise Regression (PCCR): Accounting for Multicollinearity and Population Heterogeneity in Hierarchically Organized Data
Tom Frans Wilderjans (),
Eva Gaer,
Henk A. L. Kiers,
Iven Mechelen and
Eva Ceulemans
Additional contact information
Tom Frans Wilderjans: Leiden University
Eva Gaer: KU Leuven
Henk A. L. Kiers: University of Groningen
Iven Mechelen: KU Leuven
Eva Ceulemans: KU Leuven
Psychometrika, 2017, vol. 82, issue 1, No 5, 86-111
Abstract:
Abstract In the behavioral sciences, many research questions pertain to a regression problem in that one wants to predict a criterion on the basis of a number of predictors. Although in many cases, ordinary least squares regression will suffice, sometimes the prediction problem is more challenging, for three reasons: first, multiple highly collinear predictors can be available, making it difficult to grasp their mutual relations as well as their relations to the criterion. In that case, it may be very useful to reduce the predictors to a few summary variables, on which one regresses the criterion and which at the same time yields insight into the predictor structure. Second, the population under study may consist of a few unknown subgroups that are characterized by different regression models. Third, the obtained data are often hierarchically structured, with for instance, observations being nested into persons or participants within groups or countries. Although some methods have been developed that partially meet these challenges (i.e., principal covariates regression (PCovR), clusterwise regression (CR), and structural equation models), none of these methods adequately deals with all of them simultaneously. To fill this gap, we propose the principal covariates clusterwise regression (PCCR) method, which combines the key idea’s behind PCovR (de Jong & Kiers in Chemom Intell Lab Syst 14(1–3):155–164, 1992) and CR (Späth in Computing 22(4):367–373, 1979). The PCCR method is validated by means of a simulation study and by applying it to cross-cultural data regarding satisfaction with life.
Keywords: clusterwise regression; component analysis; multicollinearity; population heterogeneity; hierarchically organized data (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
http://link.springer.com/10.1007/s11336-016-9522-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9522-0
Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2
DOI: 10.1007/s11336-016-9522-0
Access Statistics for this article
Psychometrika is currently edited by Irini Moustaki
More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().