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Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, in some specific cases the interest involves the effects of latent factors not only in the mean, but in the entire response distribution, represented by a quantile. This paper introduces a new class of models, named quantile factor models, which combines factor model theory with distribution-free quantile regression producing a robust statistical method. Bayesian estimation for the proposed model is performed using an efficient Markov chain Monte Carlo algorithm. The proposed model is evaluated using synthetic datasets in different settings, in order to evaluate its robustness and performance under different quantiles compared to more usual methods. The model is also applied to a financial sector dataset and a heart disease experiment.