A clusterwise simultaneous component method for capturing within-cluster differences in component variances and correlations

Detecting which variables alter component interpretation across multiple groups: A resampling-based method

In psychology, many studies measure the same variables in different groups. In the case of a large number of variables when a strong a priori idea about the underlying latent construct is lacking, researchers often start by reducing the variables to a few principal components in an exploratory way. Herewith, one often wants to evaluate whether the components represent the same construct in the different groups. To this end, it makes sense to remove outlying variables that have significantly different loadings on the extracted components across the groups, hampering equivalent interpretations of the components. Moreover, identifying such outlying variables is important when testing theories about which variables behave similarly or differently across groups. In this article, we first scrutinize the lower bound congruence method (LBCM; De Roover, Timmerman, & Ceulemans in Behavior Research Methods, 49, 216-229, 2017), which was recently proposed for solving the outlying-variable detection problem. LBCM investigates how Tucker's congruence between the loadings of the obtained cluster-loading matrices improves when specific variables are discarded. We show that LBCM has the tendency to output outlying variables that either are false positives or concern very small, and thus practically insignificant, loading differences. To address this issue, we present a new heuristic: the lower and resampled upper bound congruence method (LRUBCM). This method uses a resampling technique to obtain a sampling distribution for the congruence coefficient, under the hypothesis that no outlying variable is present. In a simulation study, we show that LRUBCM outperforms LBCM. Finally, we illustrate the use of the method by means of empirical data.

Modeling Nonstationary Emotion Dynamics in Dyads using a Time-Varying Vector-Autoregressive Model

Emotion dynamics are likely to arise in an interpersonal context. Standard methods to study emotions in interpersonal interaction are limited because stationarity is assumed. This means that the dynamics, for example, time-lagged relations, are invariant across time periods. However, this is generally an unrealistic assumption. Whether caused by an external (e.g., divorce) or an internal (e.g., rumination) event, emotion dynamics are prone to change. The semi-parametric time-varying vector-autoregressive (TV-VAR) model is based on well-studied generalized additive models, implemented in the software R. The TV-VAR can explicitly model changes in temporal dependency without pre-existing knowledge about the nature of change. A simulation study is presented, showing that the TV-VAR model is superior to the standard time-invariant VAR model when the dynamics change over time. The TV-VAR model is applied to empirical data on daily feelings of positive affect (PA) from a single couple. Our analyses indicate reliable changes in the male's emotion dynamics over time, but not in the female's-which were not predicted by her own affect or that of her partner. This application illustrates the usefulness of using a TV-VAR model to detect changes in the dynamics in a system.

Simultaneous Component Analysis by Means of Tucker3

A new model for simultaneous component analysis (SCA) is introduced that contains the existing SCA models with common loading matrix as special cases. The new SCA-T3 model is a multi-set generalization of the Tucker3 model for component analysis of three-way data. For each mode (observational units, variables, sets) a different number of components can be chosen and the obtained solution can be rotated without loss of fit to facilitate interpretation. SCA-T3 can be fitted on centered multi-set data and also on the corresponding covariance matrices. For this purpose, alternating least squares algorithms are derived. SCA-T3 is evaluated in a simulation study, and its practical merits are demonstrated for several benchmark datasets.

What's hampering measurement invariance: detecting non-invariant items using clusterwise simultaneous component analysis

The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA framework, methods have been proposed to trace such non-invariant items, but these methods have some disadvantages in that they require researchers to run a multitude of analyses and in that they imply assumptions that are often questionable. In this paper, we propose an alternative strategy which builds on clusterwise simultaneous component analysis (SCA). Clusterwise SCA, being an exploratory technique, assigns the groups under study to a few clusters based on differences and similarities in the component structure of the items, and thus based on the covariance matrices. Non-invariant items can then be traced by comparing the cluster-specific component loadings via congruence coefficients, which is far more parsimonious than comparing the component structure of all separate groups. In this paper we present a heuristic for this procedure. Afterwards, one can return to the multigroup CFA framework and check whether removing the non-invariant items or removing some of the equality restrictions for these items, yields satisfactory invariance test results. An empirical application concerning cross-cultural emotion data is used to demonstrate that this novel approach is useful and can co-exist with the traditional CFA approaches.

Common and cluster-specific simultaneous component analysis

In many fields of research, so-called 'multiblock' data are collected, i.e., data containing multivariate observations that are nested within higher-level research units (e.g., inhabitants of different countries). Each higher-level unit (e.g., country) then corresponds to a 'data block'. For such data, it may be interesting to investigate the extent to which the correlation structure of the variables differs between the data blocks. More specifically, when capturing the correlation structure by means of component analysis, one may want to explore which components are common across all data blocks and which components differ across the data blocks. This paper presents a common and cluster-specific simultaneous component method which clusters the data blocks according to their correlation structure and allows for common and cluster-specific components. Model estimation and model selection procedures are described and simulation results validate their performance. Also, the method is applied to data from cross-cultural values research to illustrate its empirical value.