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Title: Estimation of factor scores: Comparing parametric and non-parametric approaches. Authors:  Tim Fabian Schaffland - University of Tuebingen (Germany) [presenting]
Stefano Noventa - University of Tuebingen (Germany)
Augustin Kelava - Eberhard Karls Universitaet Tuebingen (Germany)
Abstract: Estimation of factor scores in latent variable models has repeatedly attracted the interest of researchers for decades. Already in 1935 Thurstone proposed the regression method, and in 1937 Bartlett suggested his well-known approach. Still today, factor score estimation and their properties, for example the bias of their moments, raise debate and interest. We will compare the Bartlett estimator, the regression method, the least square estimation, and one new approach which makes no distributional assumptions on the latent variables. Factor scores are estimated by combining the empirical CDF and the independence assumption between the measurement errors and the latent factors. This results in factor score estimates that in theory could consistently replicate the true joint distribution of the latent variables and the measurement error. In a simulation study we vary the (multivariate) distribution of the underlying factors and examine the performance of the different approaches in recovering the first four moments of the joint distribution of the latent variables. Additionally, the influence of the factor loadings on the estimation is investigated. Two different ways of estimating the factor loadings are used as well as the true values of the loadings. We conclude with the implications and recommendations for factor score estimation in an applied context.