Logistic Multidimensional Data Analysis for Ordinal Response Variables using a Cumulative Link function
arxiv(2024)
摘要
We present a multidimensional data analysis framework for the analysis of
ordinal response variables. Underlying the ordinal variables, we assume a
continuous latent variable, leading to cumulative logit models. The framework
includes unsupervised methods, when no predictor variables are available, and
supervised methods, when predictor variables are available. We distinguish
between dominance variables and proximity variables, where dominance variables
are analyzed using inner product models, whereas the proximity variables are
analyzed using distance models. An expectation-majorization-minimization
algorithm is derived for estimation of the parameters of the models. We
illustrate our methodology with data from the International Social Survey
Programme.
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