Principal Component Analysis and Factor Analysis: differences and similarities in Nutritional Epidemiology application.

Introduction: Statistical methods such as Principal Component Analysis (PCA) and Factor Analysis (FA) are increasingly popular in Nutritional Epidemiology studies. However, misunderstandings regarding the choice and application of these methods have been observed.

Objectives: This study aims to compare and present the main differences and similarities between FA and PCA, focusing on their applicability to nutritional studies.

Methods: PCA and FA were applied on a matrix of 34 variables expressing the mean food intake of 1,102 individuals from a population-based study.

Results: Two factors were extracted and, together, they explained 57.66% of the common variance of food group variables, while five components were extracted, explaining 26.25% of the total variance of food group variables. Among the main differences of these two methods are: normality assumption, matrices of variance-covariance/correlation and its explained variance, factorial scores, and associated error. The similarities are: both analyses are used for data reduction, the sample size usually needs to be big, correlated data, and they are based on matrices of variance-covariance.

Conclusion: PCA and FA should not be treated as equal statistical methods, given that the theoretical rationale and assumptions for using these methods as well as the interpretation of results are different.