Principal covariates clusterwise regression (PCCR): Accounting for multicollinearity and population heterogeneity in hierarchically organized data

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, 1992) and CR (Späth, 1979). The PCCR method is validated by means of a simulation study and by applying it to cross-cultural data regarding satisfaction with life.Multivariate analysis of psychological dat

Academic self-concept, gender and single-sex schooling

This paper assesses gender differences in academic self-concept for a cohort of children born in 1958 (the National Child Development Study). We address the question of whether attending single-sex or co-educational schools affected students’ perceptions of their own academic abilities (academic self-concept). Academic selfconcept was found to be highly gendered, even controlling for prior test scores. Boys had higher self-concepts in maths and science, and girls in English. Single-sex schooling reduced the gender gap in self-concept, while selective schooling was linked to lower academic self-concept overall

Equality of opportunity versus equality of opportunity sets

We characterize two different approaches to the idea of equality of opportunity. Roemer’s social ordering is motivated by a concern to compensate for the effects of certain (non-responsibility) factors on outcomes. Van de gaer’s social ordering is concerned with the equalization of the opportunity sets to which people have access. We show how different invariance axioms open the possibility to go beyond the simple additive specification implied by both rules. This offers scope for a broader interpretation of responsibility-sensitive egalitarianism.equality of opportunity, opportunity sets, responsibility-sensitive egalitarianism

Principal Covariates Clusterwise Regression (PCCR):Accounting for multicollinearity and population heterogeneity in hierarchically organized data.

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