MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness

Comparing linear discriminant analysis and supervised learning algorithms for binary classification-A method comparison study

In psychology, linear discriminant analysis (LDA) is the method of choice for two-group classification tasks based on questionnaire data. In this study, we present a comparison of LDA with several supervised learning algorithms. In particular, we examine to what extent the predictive performance of LDA relies on the multivariate normality assumption. As nonparametric alternatives, the linear support vector machine (SVM), classification and regression tree (CART), random forest (RF), probabilistic neural network (PNN), and the ensemble k conditional nearest neighbor (EkCNN) algorithms are applied. Predictive performance is determined using measures of overall performance, discrimination, and calibration, and is compared in two reference data sets as well as in a simulation study. The reference data are Likert-type data, and comprise 5 and 10 predictor variables, respectively. Simulations are based on the reference data and are done for a balanced and an unbalanced scenario in each case. In order to compare the algorithms' performance, data are simulated from multivariate distributions with differing degrees of nonnormality. Results differ depending on the specific performance measure. The main finding is that LDA is always outperformed by RF in the bimodal data with respect to overall performance. Discriminative ability of the RF algorithm is often higher compared to LDA, but its model calibration is usually worse. Still LDA mostly ranges second in cases it is outperformed by another algorithm, or the differences are only marginal. In consequence, we still recommend LDA for this type of application.

Kurtosis removal for data pre-processing

Mesokurtic projections are linear projections with null fourth cumulants. They might be useful data pre-processing tools when nonnormality, as measured by the fourth cumulants, is either an opportunity or a challenge. Nonnull fourth cumulants are opportunities when projections with extreme kurtosis are used to identify interesting nonnormal features, as for example clusters and outliers. Unfortunately, this approach suffers from the curse of dimensionality, which may be addressed by projecting the data onto the subspace orthogonal to mesokurtic projections. Nonnull fourth cumulants are challenges when using statistical methods whose sampling properties heavily depend on the fourth cumulant themselves. Mesokurtic projections ease the problem by allowing to use the inferential properties of the same methods under normality. The paper shows necessary and sufficient conditions for the existence of mesokurtic projections and compares them with other gaussianization methods. Theoretical and empirical results suggest that mesokurtic transformations are particularly useful when sampling from finite normal mixtures. The practical use of mesokurtic projections is illustrated with the AIS and the RANDU datasets.

Self-Concept in China: Validation of the Chinese Version of the Five-Factor Self-Concept (AF5) Questionnaire

The principle of invariance is a mandatory methodological requirement for the psychological measures, even when items such as self-concept measures frequently present asymmetric heavy-tailed distributions. Few validated self-concept instruments can be applied in Eastern–Western cross-cultural studies. The Five-Factor Self-Concept Questionnaire (AF5) is one of the few psychometrically sound instruments used to assess multidimensional self-concept in Spanish-speaking samples. The availability of the AF5 in Spanish and Chinese would facilitate cross-cultural research. To validate the Chinese version of the AF5, we used multisample confirmatory factor analysis with transformed dichotomous scales from the median to compare four alternative theoretical models. The sample consisted of 2507 participants (52.3% women) from China (n = 1298) and Spain (n = 1209), ranging in age from 19 to 35. Analyses confirmed the five-factor structure of the Chinese AF5 (i.e., academic, social, emotional, family, and physical) compared to the Spanish sample. Moreover, the Chinese version of the AF5 was found to be invariant in terms of item-factor weights, factor variance, and between-factor covariance, compared to the original Spanish version. The findings from this first validation study indicate that the Chinese version of the AF5 is an acceptable measure for use with Chinese-speaking adolescents and young adults.