Journal of Data Science

Abstract: Objectives: Exploratory Factor Analysis (EFA) is a very popular statistical technique for identifying potential latent structure underlying a set of observed indicator variables. EFA is used widely in the social sciences, business and finance, machine learning, and the health sciences, among others. Research has found that standard methods of estimating EFA model parameters do not work well when the sample size is relatively small (e.g. less than 50) and/or when the number of observed variables approaches the sample size in value. The purpose of the current study was to investigate and compare some alternative approaches to fitting EFA in the case of small samples and high dimensional data. Results of both a small simulation study, and an application of the methods to an intelligence test revealed that several alternative approaches designed to reduce the dimensionality of the observed variable covariance matrix worked very well in terms of recovering population factor structure with EFA. Implications of these results for practice are discussed..

Factor analysis (FA) is the most commonly used pattern recognition methodology in social and health research. A technique that may help to better retrieve true information from FA is the rotation of the information axes. The purpose of this study was to evaluate whether the selection of rotation type affects the repeatability of the patterns derived from FA, under various scenarios of random error introduced, based on simulated data from the Standard Normal distribution. It was observed that when applying promax non - orthogonal rotation, the results were more repeatable as compared to the orthogonal rotation, irrespective of the level of random error introduced in the model.

Abstract: We apply model-based cluster analysis to data concerning types of democracies, creating an instrument for typologies. Noting several ad vantages of model-based clustering over traditional clustering methods, we fit a normal mixture model for types of democracy in the context of the majoritarian-consensus contrast using Lijphart’s (1999) data on ten variables for 36 democracies. The model for the full period (1945-1996) finds four types of democracies: two types representing a majoritarian-consensus contrast, and two mixed ones lying between the extremes. The four-cluster solution shows that most of the countries have high cluster membership probabilities, and the solution is found to be quite stable with respect to possible measurement error in the variables included in the model. For the recent-period (1971-1996) data, most countries remain in the same clusters as for the full-period data.

Abstract: Principal components analysis (PCA) is a widely used technique in nutritional epidemiology, to extract dietary patterns. To improve the interpretation of the derived patterns, it has been suggested to rotate the axes defined by PCA. This study aimed to evaluate whether rotation influences the repeatability of these patterns. For this reason PCA was applied in nutrient data of 500 participants (37 ± 15 years, 38% male) who were voluntarily enrolled in the study and asked to complete a semi-quantitative food frequency questionnaire (FFQ), twice within 15 days. The varimax and the quartimax orthogonal rotation methods, as well as the non-orthogonal promax and the oblimin methods were applied. The degree of agreement between the similar extracted patterns by each rotation method was assessed using the Bland and Altman method and Kendall’s tau-b coefficient. Good agreement was observed between the two administrations of the FFQ for the un-rotated components, while low-to-moderate agreement was observed for all rotation types (the quartimax and the oblimin method lead to more repeatable results). To conclude, when rotation is needed to improve food patterns’ interpretation, the quartimax and the oblimin methods seems to produce more robust results.