Logistic Multidimensional Data Analysis for Ordinal Response Variables using a Cumulative Link function
M de Rooij, L Breemer, D Woestenburg… - arXiv preprint arXiv …, 2024 - arxiv.org
M de Rooij, L Breemer, D Woestenburg, F Busing
arXiv preprint arXiv:2402.07629, 2024•arxiv.orgWe 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. 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 …
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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