2016/05/13 by William Fithian, Fithian, William, Julie Josse +1
Agricultural and Biological Sciences · Mathematics · #FOS: Computer and information sciences #Genetics and Plant Breeding #Methodology (stat.ME) #Sensory Analysis and Statistical Methods #Statistical Methods and Applications
paper · pdf · doi:10.48550/arxiv.1605.04212
openalex publication_date 2016/05/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Multiple Correspondence Analysis (MCA) is a dimension reduction method which plays a large role in the analysis of tables with categorical nominal variables such as survey data. Though it is usually motivated and derived using geometric considerations, in fact we prove that it amounts to a single proximal Newtown step of a natural bilinear exponential family model for categorical data the multinomial logit bilinear model. We compare and contrast the behavior of MCA with that of the model on simulations and discuss new insights on the properties of both exploratory multivariate methods and their cognate models. One main conclusion is that we could recommend to approximate the multilogit model parameters using MCA. Indeed, estimating the parameters of the model is not a trivial task whereas MCA has the great advantage of being easily solved by singular value decomposition and scalable to large data.