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Title: Unique representations of sparse factor models Authors:  Sylvia Kaufmann - Study Center Gerzensee (Switzerland) [presenting]
Markus Pape - Ruhr University Bochum (Germany)
Abstract: In factor analysis, not all latent factors necessarily need to be linked to all observed data series. Hence, the loadings matrix may contain many zeros. In confirmatory factor analysis (CFA), the pattern of zero and nonzero entries is assumed to be known, and the free parameters are estimated subject to this pattern, usually by maximum likelihood. Statistical tests are available to check how well the estimated parameters from CFA actually fit the data. Recently, Bayesian exploratory approaches were suggested to estimate the sparse loading structure. In this paper, we investigate under which circumstances such sparsity patterns are unique and in which cases it may be necessary to consider the existence of multiple patterns with similar degrees of sparsity for a given data set. Moreover, we propose two MCMC approaches that can be used to discover possibly multiple sparse representations for the loadings matrix. Both approaches are further investigated in a simulation study and in an application using a Swiss inflation data set.